CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available" lang="en" dir="ltr"> <head> <meta charset="UTF-8"> <title>Sediment transport - Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available";var cookie=document.cookie.match(/(?:^|; )enwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy", "wgMonthNames":["","January","February","March","April","May","June","July","August","September","October","November","December"],"wgRequestId":"10d7227e-ed6f-447f-88d0-0d1bd062e4e8","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Sediment_transport","wgTitle":"Sediment transport","wgCurRevisionId":1257556380,"wgRevisionId":1257556380,"wgArticleId":7999492,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Webarchive template wayback links","Articles with short description","Short description matches Wikidata","Articles with excerpts","Fluid mechanics","Sedimentology","Environmental engineering","Hydrology","Physical geography","Geological processes","Transport phenomena"],"wgPageViewLanguage":"en","wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgRelevantPageName":"Sediment_transport","wgRelevantArticleId":7999492,"wgIsProbablyEditable":true, "wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":false,"wgFlaggedRevsParams":{"tags":{"status":{"levels":1}}},"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"en","pageLanguageDir":"ltr","pageVariantFallbacks":"en"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":false,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":60000,"wgRelatedArticlesCompat":[],"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q7445303","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled": false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.cite.styles":"ready","ext.math.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","jquery.makeCollapsible.styles":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["ext.cite.ux-enhancements","mediawiki.page.media","ext.scribunto.logs","site","mediawiki.page.ready","jquery.makeCollapsible","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.ReferenceTooltips","ext.gadget.switcher","ext.urlShortener.toolbar","ext.centralauth.centralautologin", "mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints","ext.growthExperiments.SuggestedEditSession","wikibase.sidebar.tracking"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=en&modules=ext.cite.styles%7Cext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cjquery.makeCollapsible.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=en&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=en&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.5"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Wafrica_amo_2007209_lrg.jpg/1200px-Wafrica_amo_2007209_lrg.jpg"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="1575"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Wafrica_amo_2007209_lrg.jpg/800px-Wafrica_amo_2007209_lrg.jpg"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="1050"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Wafrica_amo_2007209_lrg.jpg/640px-Wafrica_amo_2007209_lrg.jpg"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="840"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Sediment transport - Wikipedia"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//en.m.wikipedia.org/wiki/Sediment_transport"> <link rel="alternate" type="application/x-wiki" title="Edit this page" href="/w/index.php?title=Sediment_transport&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedia (en)"> <link rel="EditURI" type="application/rsd+xml" href="//en.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://en.wikipedia.org/wiki/Sediment_transport"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atom feed" href="/w/index.php?title=Special:RecentChanges&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="//login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Sediment_transport rootpage-Sediment_transport skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Jump to content</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Main menu" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Main menu</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Main menu</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">hide</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigation </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Main_Page" title="Visit the main page [z]" accesskey="z"><span>Main page</span></a></li><li id="n-contents" class="mw-list-item"><a href="/wiki/Wikipedia:Contents" title="Guides to browsing Wikipedia"><span>Contents</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Portal:Current_events" title="Articles related to current events"><span>Current events</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Special:Random" title="Visit a randomly selected article [x]" accesskey="x"><span>Random article</span></a></li><li id="n-aboutsite" class="mw-list-item"><a href="/wiki/Wikipedia:About" title="Learn about Wikipedia and how it works"><span>About Wikipedia</span></a></li><li id="n-contactpage" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us" title="How to contact Wikipedia"><span>Contact us</span></a></li> </ul> </div> </div> <div id="p-interaction" class="vector-menu mw-portlet mw-portlet-interaction" > <div class="vector-menu-heading"> Contribute </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/Help:Contents" title="Guidance on how to use and edit Wikipedia"><span>Help</span></a></li><li id="n-introduction" class="mw-list-item"><a href="/wiki/Help:Introduction" title="Learn how to edit Wikipedia"><span>Learn to edit</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Community_portal" title="The hub for editors"><span>Community portal</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Special:RecentChanges" title="A list of recent changes to Wikipedia [r]" accesskey="r"><span>Recent changes</span></a></li><li id="n-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_upload_wizard" title="Add images or other media for use on Wikipedia"><span>Upload file</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Main_Page" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="The Free Encyclopedia" src="/static/images/mobile/copyright/wikipedia-tagline-en.svg" width="117" height="13" style="width: 7.3125em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Special:Search" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Search Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Search Wikipedia" aria-label="Search Wikipedia" autocapitalize="sentences" title="Search Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Personal tools"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Appearance" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Appearance</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_en.wikipedia.org&uselang=en" class=""><span>Donate</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:CreateAccount&returnto=Sediment+transport" title="You are encouraged to create an account and log in; however, it is not mandatory" class=""><span>Create account</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:UserLogin&returnto=Sediment+transport" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o" class=""><span>Log in</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Log in and more options" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Personal tools" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Personal tools</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_en.wikipedia.org&uselang=en"><span>Donate</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:CreateAccount&returnto=Sediment+transport" title="You are encouraged to create an account and log in; however, it is not mandatory"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Create account</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:UserLogin&returnto=Sediment+transport" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Log in</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pages for logged out editors <a href="/wiki/Help:Introduction" aria-label="Learn more about editing"><span>learn more</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:MyContributions" title="A list of edits made from this IP address [y]" accesskey="y"><span>Contributions</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:MyTalk" title="Discussion about edits from this IP address [n]" accesskey="n"><span>Talk</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Contents" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Contents</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-Environments" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Environments"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Environments</span> </div> </a> <button aria-controls="toc-Environments-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Environments subsection</span> </button> <ul id="toc-Environments-sublist" class="vector-toc-list"> <li id="toc-Aeolian" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Aeolian"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Aeolian</span> </div> </a> <ul id="toc-Aeolian-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Fluvial" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Fluvial"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Fluvial</span> </div> </a> <ul id="toc-Fluvial-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Coastal" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Coastal"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Coastal</span> </div> </a> <ul id="toc-Coastal-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Glacial" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Glacial"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Glacial</span> </div> </a> <ul id="toc-Glacial-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Hillslope" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Hillslope"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.5</span> <span>Hillslope</span> </div> </a> <ul id="toc-Hillslope-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Debris_flow" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Debris_flow"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.6</span> <span>Debris flow</span> </div> </a> <ul id="toc-Debris_flow-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Applications" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Applications</span> </div> </a> <ul id="toc-Applications-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Initiation_of_motion" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Initiation_of_motion"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Initiation of motion</span> </div> </a> <button aria-controls="toc-Initiation_of_motion-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Initiation of motion subsection</span> </button> <ul id="toc-Initiation_of_motion-sublist" class="vector-toc-list"> <li id="toc-Stress_balance" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Stress_balance"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Stress balance</span> </div> </a> <ul id="toc-Stress_balance-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Critical_shear_stress" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Critical_shear_stress"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Critical shear stress</span> </div> </a> <ul id="toc-Critical_shear_stress-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Particle_Reynolds_number" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Particle_Reynolds_number"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Particle Reynolds number</span> </div> </a> <ul id="toc-Particle_Reynolds_number-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bed_shear_stress" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bed_shear_stress"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Bed shear stress</span> </div> </a> <ul id="toc-Bed_shear_stress-sublist" class="vector-toc-list"> <li id="toc-Depth-slope_product" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Depth-slope_product"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4.1</span> <span>Depth-slope product</span> </div> </a> <ul id="toc-Depth-slope_product-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Shear_velocity,_velocity,_and_friction_factor" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Shear_velocity,_velocity,_and_friction_factor"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4.2</span> <span>Shear velocity, velocity, and friction factor</span> </div> </a> <ul id="toc-Shear_velocity,_velocity,_and_friction_factor-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Unsteady_flow" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Unsteady_flow"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4.3</span> <span>Unsteady flow</span> </div> </a> <ul id="toc-Unsteady_flow-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Example" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Example"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5</span> <span>Example</span> </div> </a> <ul id="toc-Example-sublist" class="vector-toc-list"> <li id="toc-Set-up" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Set-up"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5.1</span> <span>Set-up</span> </div> </a> <ul id="toc-Set-up-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Solution" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Solution"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5.2</span> <span>Solution</span> </div> </a> <ul id="toc-Solution-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Modes_of_entrainment" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Modes_of_entrainment"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Modes of entrainment</span> </div> </a> <button aria-controls="toc-Modes_of_entrainment-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Modes of entrainment subsection</span> </button> <ul id="toc-Modes_of_entrainment-sublist" class="vector-toc-list"> <li id="toc-Rouse_number" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Rouse_number"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Rouse number</span> </div> </a> <ul id="toc-Rouse_number-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Settling_velocity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Settling_velocity"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Settling velocity</span> </div> </a> <ul id="toc-Settling_velocity-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Hjulström–Sundborg_diagram" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Hjulström–Sundborg_diagram"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Hjulström–Sundborg diagram</span> </div> </a> <ul id="toc-Hjulström–Sundborg_diagram-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Transport_rate" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Transport_rate"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Transport rate</span> </div> </a> <button aria-controls="toc-Transport_rate-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Transport rate subsection</span> </button> <ul id="toc-Transport_rate-sublist" class="vector-toc-list"> <li id="toc-Bed_load" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bed_load"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Bed load</span> </div> </a> <ul id="toc-Bed_load-sublist" class="vector-toc-list"> <li id="toc-Notable_bed_load_transport_formulae" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Notable_bed_load_transport_formulae"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1.1</span> <span>Notable bed load transport formulae</span> </div> </a> <ul id="toc-Notable_bed_load_transport_formulae-sublist" class="vector-toc-list"> <li id="toc-Meyer-Peter_Müller_and_derivatives" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Meyer-Peter_Müller_and_derivatives"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1.1.1</span> <span>Meyer-Peter Müller and derivatives</span> </div> </a> <ul id="toc-Meyer-Peter_Müller_and_derivatives-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Wilcock_and_Crowe" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Wilcock_and_Crowe"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1.1.2</span> <span>Wilcock and Crowe</span> </div> </a> <ul id="toc-Wilcock_and_Crowe-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Wilcock_and_Kenworthy" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Wilcock_and_Kenworthy"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1.1.3</span> <span>Wilcock and Kenworthy</span> </div> </a> <ul id="toc-Wilcock_and_Kenworthy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kuhnle_et_al." class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Kuhnle_et_al."> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1.1.4</span> <span>Kuhnle <i>et al.</i></span> </div> </a> <ul id="toc-Kuhnle_et_al.-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Suspended_load" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Suspended_load"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Suspended load</span> </div> </a> <ul id="toc-Suspended_load-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bed_material_load" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bed_material_load"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>Bed material load</span> </div> </a> <ul id="toc-Bed_material_load-sublist" class="vector-toc-list"> <li id="toc-Engelund–Hansen" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Engelund–Hansen"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3.1</span> <span>Engelund–Hansen</span> </div> </a> <ul id="toc-Engelund–Hansen-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Wash_load" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Wash_load"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.4</span> <span>Wash load</span> </div> </a> <ul id="toc-Wash_load-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Total_load" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Total_load"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.5</span> <span>Total load</span> </div> </a> <ul id="toc-Total_load-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Bed_load_sediment_mitigation_at_intake_structures" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Bed_load_sediment_mitigation_at_intake_structures"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Bed load sediment mitigation at intake structures</span> </div> </a> <ul id="toc-Bed_load_sediment_mitigation_at_intake_structures-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Sediment transport</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 11 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-11" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">11 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Sedimentvervoer" title="Sedimentvervoer – Afrikaans" lang="af" hreflang="af" data-title="Sedimentvervoer" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Settetransport" title="Settetransport – Estonian" lang="et" hreflang="et" data-title="Settetransport" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D9%86%D8%AA%D9%82%D8%A7%D9%84_%D8%B1%D8%B3%D9%88%D8%A8" title="انتقال رسوب – Persian" lang="fa" hreflang="fa" data-title="انتقال رسوب" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9C%A0%EC%82%AC_(%EC%88%98%EB%A6%AC%ED%95%99)" title="유사 (수리학) – Korean" lang="ko" hreflang="ko" data-title="유사 (수리학)" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Transpor_sedimen" title="Transpor sedimen – Indonesian" lang="id" hreflang="id" data-title="Transpor sedimen" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A1%D7%97%D7%95%D7%A4%D7%AA" title="סחופת – Hebrew" lang="he" hreflang="he" data-title="סחופת" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%81%8B%E6%90%AC%E4%BD%9C%E7%94%A8" title="運搬作用 – Japanese" lang="ja" hreflang="ja" data-title="運搬作用" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Sedimenttransport" title="Sedimenttransport – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Sedimenttransport" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Sediment_ta%C5%9F%C4%B1nmas%C4%B1" title="Sediment taşınması – Turkish" lang="tr" hreflang="tr" data-title="Sediment taşınması" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%BD%D1%81%D0%BF%D0%BE%D1%80%D1%82%D1%83%D0%B2%D0%B0%D0%BD%D0%BD%D1%8F_%D0%B2%D1%96%D0%B4%D0%BA%D0%BB%D0%B0%D0%B4%D1%96%D0%B2" title="Транспортування відкладів – Ukrainian" lang="uk" hreflang="uk" data-title="Транспортування відкладів" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%90%AC%E9%81%8B%E4%BD%9C%E7%94%A8" title="搬運作用 – Chinese" lang="zh" hreflang="zh" data-title="搬運作用" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q7445303#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Sediment_transport" title="View the content page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:Sediment_transport" rel="discussion" title="Discuss improvements to the content page [t]" accesskey="t"><span>Talk</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Change language variant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">English</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Views"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Sediment_transport"><span>Read</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Sediment_transport&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Sediment_transport&action=history" title="Past revisions of this page [h]" accesskey="h"><span>View history</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Tools" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Tools</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Tools</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">hide</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="More options" > <div class="vector-menu-heading"> Actions </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Sediment_transport"><span>Read</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Sediment_transport&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Sediment_transport&action=history"><span>View history</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> General </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:WhatLinksHere/Sediment_transport" title="List of all English Wikipedia pages containing links to this page [j]" accesskey="j"><span>What links here</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:RecentChangesLinked/Sediment_transport" rel="nofollow" title="Recent changes in pages linked from this page [k]" accesskey="k"><span>Related changes</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_Upload_Wizard" title="Upload files [u]" accesskey="u"><span>Upload file</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:SpecialPages" title="A list of all special pages [q]" accesskey="q"><span>Special pages</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Sediment_transport&oldid=1257556380" title="Permanent link to this revision of this page"><span>Permanent link</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Sediment_transport&action=info" title="More information about this page"><span>Page information</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:CiteThisPage&page=Sediment_transport&id=1257556380&wpFormIdentifier=titleform" title="Information on how to cite this page"><span>Cite this page</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FSediment_transport"><span>Get shortened URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FSediment_transport"><span>Download QR code</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Print/export </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=Sediment_transport&action=show-download-screen" title="Download this page as a PDF file"><span>Download as PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Sediment_transport&printable=yes" title="Printable version of this page [p]" accesskey="p"><span>Printable version</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> In other projects </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Sediment_transport" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q7445303" title="Structured data on this page hosted by Wikidata [g]" accesskey="g"><span>Wikidata item</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Movement of solid particles, typically by gravity and fluid entrainment</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Wafrica_amo_2007209_lrg.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Wafrica_amo_2007209_lrg.jpg/260px-Wafrica_amo_2007209_lrg.jpg" decoding="async" width="260" height="341" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Wafrica_amo_2007209_lrg.jpg/390px-Wafrica_amo_2007209_lrg.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Wafrica_amo_2007209_lrg.jpg/520px-Wafrica_amo_2007209_lrg.jpg 2x" data-file-width="3200" data-file-height="4200" /></a><figcaption>Dust blowing from the Sahara Desert over the Atlantic Ocean towards the <a href="/wiki/Canary_Islands" title="Canary Islands">Canary Islands</a></figcaption></figure> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><style data-mw-deduplicate="TemplateStyles:r1246091330">.mw-parser-output .sidebar{width:22em;float:right;clear:right;margin:0.5em 0 1em 1em;background:var(--background-color-neutral-subtle,#f8f9fa);border:1px solid var(--border-color-base,#a2a9b1);padding:0.2em;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse;display:table}body.skin-minerva .mw-parser-output .sidebar{display:table!important;float:right!important;margin:0.5em 0 1em 1em!important}.mw-parser-output .sidebar-subgroup{width:100%;margin:0;border-spacing:0}.mw-parser-output .sidebar-left{float:left;clear:left;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-none{float:none;clear:both;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-outer-title{padding:0 0.4em 0.2em;font-size:125%;line-height:1.2em;font-weight:bold}.mw-parser-output .sidebar-top-image{padding:0.4em}.mw-parser-output .sidebar-top-caption,.mw-parser-output .sidebar-pretitle-with-top-image,.mw-parser-output .sidebar-caption{padding:0.2em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-pretitle{padding:0.4em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-title,.mw-parser-output .sidebar-title-with-pretitle{padding:0.2em 0.8em;font-size:145%;line-height:1.2em}.mw-parser-output .sidebar-title-with-pretitle{padding:0.1em 0.4em}.mw-parser-output .sidebar-image{padding:0.2em 0.4em 0.4em}.mw-parser-output .sidebar-heading{padding:0.1em 0.4em}.mw-parser-output .sidebar-content{padding:0 0.5em 0.4em}.mw-parser-output .sidebar-content-with-subgroup{padding:0.1em 0.4em 0.2em}.mw-parser-output .sidebar-above,.mw-parser-output .sidebar-below{padding:0.3em 0.8em;font-weight:bold}.mw-parser-output .sidebar-collapse .sidebar-above,.mw-parser-output .sidebar-collapse .sidebar-below{border-top:1px solid #aaa;border-bottom:1px solid #aaa}.mw-parser-output .sidebar-navbar{text-align:right;font-size:115%;padding:0 0.4em 0.4em}.mw-parser-output .sidebar-list-title{padding:0 0.4em;text-align:left;font-weight:bold;line-height:1.6em;font-size:105%}.mw-parser-output .sidebar-list-title-c{padding:0 0.4em;text-align:center;margin:0 3.3em}@media(max-width:640px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}body.skin--responsive .mw-parser-output .sidebar a>img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><td class="sidebar-pretitle">Part of a series on</td></tr><tr><th class="sidebar-title-with-pretitle" style="background:#82C3D8; padding:0.2em; font-size:160%; font-weight:bold;"><a href="/wiki/Sediment" title="Sediment">Sediments</a></th></tr><tr><td class="sidebar-image"><span typeof="mw:File"><a href="/wiki/File:Channel-StellartonFm-CoalburnPit.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Channel-StellartonFm-CoalburnPit.JPG/190px-Channel-StellartonFm-CoalburnPit.JPG" decoding="async" width="190" height="142" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Channel-StellartonFm-CoalburnPit.JPG/285px-Channel-StellartonFm-CoalburnPit.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/24/Channel-StellartonFm-CoalburnPit.JPG/380px-Channel-StellartonFm-CoalburnPit.JPG 2x" data-file-width="1809" data-file-height="1356" /></a></span></td></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;font-size:100%;font-weight:bold;;color: var(--color-base)">By origin</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Terrigenous_sediment" title="Terrigenous sediment">Terrigenous (lithogenous)</a></li> <li><a href="/wiki/Biogenous_sediment" class="mw-redirect" title="Biogenous sediment">Biogenous</a></li></ul> </div> <div class="hlist"> <ul><li>Cosmogenous</li> <li>Hydrogenous</li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;font-size:100%;font-weight:bold;;color: var(--color-base)">By texture</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Roundness_(geology)" title="Roundness (geology)">Roundness</a></li> <li><a href="/wiki/Sorting_(sediment)" title="Sorting (sediment)">Sorting</a></li></ul> </div> <div class="hlist"> <ul><li><a href="/wiki/Grain_size" title="Grain size">Grain size</a> <ul><li><a href="/wiki/Boulder" title="Boulder">boulder</a></li> <li><a href="/wiki/Cobble_(geology)" title="Cobble (geology)">cobble</a><br /></li> <li><a href="/wiki/Gravel" title="Gravel">gravel</a> <ul><li><a href="/wiki/Pebble" title="Pebble">pebble</a></li> <li><a href="/wiki/Granule_(geology)" title="Granule (geology)">granule</a></li></ul></li></ul></li></ul> </div> <div class="hlist"> <ul><li><ul><li><a href="/wiki/Sand" title="Sand">sand</a></li> <li><a href="/wiki/Silt" title="Silt">silt</a></li> <li><a href="/wiki/Clay" title="Clay">clay</a></li> <li><a href="/wiki/Colloid" title="Colloid">colloid</a></li></ul></li></ul> </div> <div class="hlist"> <ul><li>Other <ul><li><a href="/wiki/Oolite" title="Oolite">oolite</a></li> <li><a href="/wiki/Scree" title="Scree">scree</a></li> <li><a href="/wiki/Till" title="Till">till</a></li></ul></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;font-size:100%;font-weight:bold;;color: var(--color-base)">By composition</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Manganese_nodules" class="mw-redirect" title="Manganese nodules">Manganese nodules</a></li></ul> </div> <div class="hlist"> <ul><li><a href="/wiki/Oolitic_aragonite_sand" title="Oolitic aragonite sand">Oolitic aragonite sand</a></li> <li><a href="/wiki/Tektites" class="mw-redirect" title="Tektites">Tektites</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="text-align:center;font-size:100%;font-weight:bold;;color: var(--color-base)"><a href="/wiki/Sedimentation" title="Sedimentation">By process</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Sedimentation" title="Sedimentation">Sedimentation</a></li> <li><a href="/wiki/Sedimentary_budget" title="Sedimentary budget">Sedimentary budget</a></li></ul> </div> <div class="hlist"> <ul><li><a class="mw-selflink selflink">Sediment transport</a> <ul><li><a href="/wiki/Coastal_sediment_transport" title="Coastal sediment transport">coastal</a></li></ul></li></ul> </div> <div class="hlist"> <ul><li><a href="/wiki/Weathering" title="Weathering">Weathering</a></li> <li><a href="/wiki/Erosion" title="Erosion">Erosion</a></li> <li><a href="/wiki/Aeolian_transport" class="mw-redirect" title="Aeolian transport">Aeolian (windborne) transport</a></li> <li><a href="/wiki/Biomineralization" title="Biomineralization">Biomineralization</a></li> <li><a href="/wiki/Bioturbation" title="Bioturbation">Bioturbation</a></li></ul> </div> <div class="hlist"> <ul><li><a href="/wiki/Compaction_(geology)" title="Compaction (geology)">Compaction</a></li> <li><a href="/wiki/Concretion" title="Concretion">Concretion</a></li> <li><a href="/wiki/Exner_equation" title="Exner equation">Exner equation</a></li> <li><a href="/wiki/Fluvial_processes" class="mw-redirect" title="Fluvial processes">Fluvial processes</a></li> <li><a href="/wiki/Glacier_flow" class="mw-redirect" title="Glacier flow">Glacier flow</a> <ul><li><a href="/wiki/Ice-sheet_dynamics" class="mw-redirect" title="Ice-sheet dynamics">ice-sheet dynamics</a></li> <li><a href="/wiki/Ice_rafting" title="Ice rafting">ice rafting</a></li></ul></li></ul> </div> <div class="hlist"> <ul><li><a href="/wiki/Lithification" title="Lithification">Lithification</a></li> <li><a href="/wiki/Siltation" title="Siltation">Siltation</a></li> <li><a href="/wiki/Turbidity_currents" class="mw-redirect" title="Turbidity currents">Turbidity currents</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;font-size:100%;font-weight:bold;;color: var(--color-base)"><a href="/wiki/Sedimentary_structures" title="Sedimentary structures">By structure</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Sedimentary_structures" title="Sedimentary structures">Sedimentary structures</a></li> <li><a href="/wiki/Bedforms" class="mw-redirect" title="Bedforms">Bedforms</a> <ul><li><a href="/wiki/Cross-bedding" title="Cross-bedding">cross-bedding</a></li> <li><a href="/wiki/Dunes" class="mw-redirect" title="Dunes">duness</a></li> <li><a href="/wiki/Graded_bedding" title="Graded bedding">graded bedding</a></li> <li><a href="/wiki/Ripple_marks" title="Ripple marks">ripple marks</a></li></ul></li> <li><a href="/wiki/Alluvial_fan" title="Alluvial fan">Alluvial fan</a></li> <li><a href="/wiki/Alluvial_river" title="Alluvial river">Alluvial river</a></li> <li><a href="/wiki/Fault_(geology)" title="Fault (geology)">Fault</a></li> <li><a href="/wiki/Fold_(geology)" title="Fold (geology)">Fold</a></li> <li><a href="/wiki/Paleocurrent" title="Paleocurrent">Paleocurrent indicators</a> <ul><li><a href="/wiki/Sole_markings" title="Sole markings">sole markings</a></li> <li><a href="/wiki/Imbrication_(sedimentology)" title="Imbrication (sedimentology)">imbrication</a></li></ul></li> <li><a href="/wiki/River_delta" title="River delta">River delta</a></li> <li><a href="/wiki/Sediment%E2%80%93water_interface" title="Sediment–water interface">Sediment–water interface</a></li> <li><a href="/wiki/Sedimentary_basin" title="Sedimentary basin">Sedimentary basin</a></li> <li><a href="/wiki/Soft-sediment_deformation_structures" title="Soft-sediment deformation structures">Soft-sediment deformation</a></li> <li><a href="/wiki/Unconformity" title="Unconformity">Unconformity</a></li> <li><a href="/wiki/Vegetation-induced_sedimentary_structures" title="Vegetation-induced sedimentary structures">Vegetation-induced</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;font-size:100%;font-weight:bold;;color: var(--color-base)">Soil sediment</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Soil" title="Soil">Soil</a> <ul><li><a href="/wiki/Soil_matrix" title="Soil matrix">matrix</a></li> <li><a href="/wiki/Pore_space_in_soil" title="Pore space in soil">pore space</a></li> <li><a href="/wiki/Permeability_of_soils" title="Permeability of soils">permeability</a></li></ul></li> <li><a href="/wiki/Soil_morphology" title="Soil morphology">morphology</a> <ul><li><a href="/wiki/Soil_texture" title="Soil texture">texture</a></li> <li><a href="/wiki/Soil_value" title="Soil value">value</a></li> <li><a href="/wiki/Soil_color" title="Soil color">color</a></li></ul></li> <li><a href="/wiki/Catena_(soil)" title="Catena (soil)">Catena</a></li> <li><a href="/wiki/Soil_horizon" title="Soil horizon">Soil horizon</a></li> <li><a href="/wiki/Humus" title="Humus">Humus</a></li> <li><a href="/wiki/Humin" title="Humin">Humin</a></li> <li><a href="/wiki/Soil_salinity" title="Soil salinity">Soil salinity</a></li> <li><a href="/wiki/Hydropedology" title="Hydropedology">Hydropedology</a></li> <li><a href="/wiki/Mineralization_(soil_science)" title="Mineralization (soil science)">Mineralization</a></li> <li><a href="/wiki/Microbiologically_induced_calcite_precipitation" title="Microbiologically induced calcite precipitation">Microbial calcite precipitation</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;font-size:100%;font-weight:bold;;color: var(--color-base)"><a href="/wiki/Marine_sediment" title="Marine sediment">Marine sediment</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Abyssal_fan" title="Abyssal fan">Abyssal fan</a></li> <li><a href="/wiki/Aragonite" title="Aragonite">Aragonite</a> <ul><li><a href="/wiki/Aragonite_sea" title="Aragonite sea">aragonite sea</a></li> <li><a href="/wiki/Oolitic_aragonite_sand" title="Oolitic aragonite sand">oolitic aragonite sand</a></li></ul></li> <li><a href="/wiki/Calcite" title="Calcite">Calcite</a> <ul><li><a href="/wiki/Calcite_sea" title="Calcite sea">calcite sea</a></li></ul></li> <li><a href="/wiki/Amorphous_calcium_carbonate" title="Amorphous calcium carbonate">Amorphous calcium carbonate</a></li> <li><a href="/wiki/Calcification" title="Calcification">Calcification</a></li> <li><a href="/wiki/Continental_rise" title="Continental rise">Continental rise</a></li> <li><a href="/wiki/Bay_mud" title="Bay mud">Bay mud</a></li> <li><a href="/wiki/Bioirrigation" title="Bioirrigation">Bioirrigation</a></li> <li><a href="/wiki/Coastal_sediment_transport" title="Coastal sediment transport">Coastal sediment transport</a></li> <li><a href="/wiki/Coastal_sediment_supply" title="Coastal sediment supply">Coastal sediment supply</a></li> <li><a href="/wiki/Evaporite" title="Evaporite">Evaporites</a></li> <li><a href="/wiki/Marine_clay" title="Marine clay">Marine clay</a> <ul><li><a href="/wiki/Pelagic_red_clay" title="Pelagic red clay">pelagic red clay</a></li></ul></li> <li><a href="/wiki/Marine_regression" title="Marine regression">Marine regression</a> <ul><li><a href="/wiki/Marine_transgression" title="Marine transgression">transgression</a></li></ul></li></ul> </div> <div class="hlist"> <ul><li><a href="/wiki/Pelagic_sediment" title="Pelagic sediment">Pelagic</a> <ul><li><a href="/wiki/Turbidite" title="Turbidite">turbidite</a></li> <li><a href="/wiki/Contourite" title="Contourite">contourite</a></li> <li><a href="/wiki/Hemipelagic_sediment" title="Hemipelagic sediment">hemipelagite</a></li></ul></li></ul> </div> <div class="hlist"> <ul><li><a href="/wiki/Salt_tectonics" title="Salt tectonics">Salt tectonics</a></li> <li><a href="/wiki/Sedimentary_basin" title="Sedimentary basin">Sedimentary basin</a></li> <li><a href="/wiki/Tidal_bundle" title="Tidal bundle">Tidal bundle</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;font-size:100%;font-weight:bold;;color: var(--color-base)"><a href="/wiki/Biogenous_sediment" class="mw-redirect" title="Biogenous sediment">Biogenous sediments</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Calcareous_ooze" class="mw-redirect" title="Calcareous ooze">Calcareous ooze</a> <ul><li><a href="/wiki/Marine_biogenic_calcification" title="Marine biogenic calcification">biogenic calcification</a></li> <li><a href="/wiki/Calcareous_nannoplankton" class="mw-redirect" title="Calcareous nannoplankton">calcareous nannoplankton</a></li></ul></li></ul> </div> <div class="hlist"> <ul><li><a href="/wiki/Siliceous_ooze" title="Siliceous ooze">Siliceous ooze</a> <ul><li><a href="/wiki/Biogenic_silica" title="Biogenic silica">biogenic silica</a></li> <li><a href="/wiki/Silicification" title="Silicification">silicification</a></li> <li><a href="/wiki/Diatomaceous_earth" title="Diatomaceous earth">diatomaceous earth</a></li> <li><a href="/wiki/Radiolarite" title="Radiolarite">radiolarite</a></li></ul></li></ul> </div> <div class="hlist"> <ul><li><a href="/wiki/Microfossil" title="Microfossil">Microfossil</a></li> <li><a href="/wiki/Reverse_weathering" title="Reverse weathering">Reverse weathering</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;font-size:100%;font-weight:bold;;color: var(--color-base)">Sedimentary ecology</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Soil_biomantle" title="Soil biomantle">Soil biomantle</a></li> <li><a href="/wiki/Soil_zoology" title="Soil zoology">Soil zoology</a></li> <li><a href="/wiki/Soil_borne_pathogen" title="Soil borne pathogen">soil pathogens</a></li> <li><a href="/wiki/Pedodiversity" title="Pedodiversity">Pedodiversity</a></li> <li><a href="/wiki/Soil_biodiversity" title="Soil biodiversity">Soil biodiversity</a></li></ul> </div> <div class="hlist"> <ul><li><a href="/wiki/Rhizosphere" title="Rhizosphere">Rhizosphere</a> <ul><li><a href="/wiki/Root_microbiome" title="Root microbiome">root microbiome</a></li></ul></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;font-size:100%;font-weight:bold;;color: var(--color-base)"><a href="/wiki/Soil_carbon" title="Soil carbon">Sedimentary carbon</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Mycorrhizal_fungi_and_soil_carbon_storage" title="Mycorrhizal fungi and soil carbon storage">Soil carbon storage</a></li> <li><a href="/wiki/Soil_carbon" title="Soil carbon">Soil carbon</a></li> <li><a href="/wiki/Coal" title="Coal">Coal</a></li> <li><a href="/wiki/Peat" title="Peat">Peat</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;font-size:100%;font-weight:bold;;color: var(--color-base)"><a href="/wiki/Sedimentary_rock" title="Sedimentary rock">Sedimentary rock</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Badlands" title="Badlands">Badlands</a></li> <li><a href="/wiki/Carbonate_rock" title="Carbonate rock">Carbonates</a> <ul><li><a href="/wiki/Limestone" title="Limestone">limestone</a></li> <li><a href="/wiki/Dolomite_(rock)" title="Dolomite (rock)">dolomite</a></li></ul></li></ul> </div> <div class="hlist"> <ul><li><a href="/wiki/Clastic_rock" title="Clastic rock">Clastic</a> <ul><li><a href="/wiki/Conglomerate_(geology)" title="Conglomerate (geology)">conglomerate</a></li></ul></li></ul> </div> <div class="hlist"> <ul><li><ul><li><a href="/wiki/Breccia" title="Breccia">breccia</a></li> <li><a href="/wiki/Sandstone" title="Sandstone">sandstone</a></li> <li><a href="/wiki/Mudrock" title="Mudrock">mudrock</a></li></ul></li></ul> </div> <div class="hlist"> <ul><li><a href="/wiki/Evaporite" title="Evaporite">Evaporite</a></li> <li><a href="/wiki/Chalk" title="Chalk">Chalk</a></li> <li><a href="/wiki/Chert" title="Chert">Chert</a></li> <li><a href="/wiki/Greywacke" title="Greywacke">Greywacke</a></li> <li><a href="/wiki/Iron-rich_sedimentary_rocks" title="Iron-rich sedimentary rocks">Iron-rich</a></li> <li><a href="/wiki/Organic-rich_sedimentary_rocks" title="Organic-rich sedimentary rocks">Organic-rich</a></li> <li><a href="/wiki/Phosphorite" title="Phosphorite">Phosphorite</a></li> <li><a href="/wiki/Siliceous_rock" title="Siliceous rock">Siliceous</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;font-size:100%;font-weight:bold;;color: var(--color-base)">Related</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li>History <ul><li><a href="/wiki/History_of_geology" title="History of geology">geology</a></li> <li><a href="/wiki/Geological_history_of_Earth" title="Geological history of Earth">geological</a></li> <li><a href="/wiki/History_of_paleontology" title="History of paleontology">paleontology</a></li> <li><a href="/wiki/History_of_soil_science" title="History of soil science">soil science</a></li></ul></li> <li><a href="/wiki/Legacy_sediment" title="Legacy sediment">Legacy sediment</a></li> <li>Principles <ul><li><a href="/wiki/Cross-cutting_relationships" title="Cross-cutting relationships">cross-cutting relationships</a></li> <li><a href="/wiki/Principle_of_lateral_continuity" title="Principle of lateral continuity">lateral continuity</a></li> <li><a href="/wiki/Principle_of_original_horizontality" title="Principle of original horizontality">original horizontality</a></li></ul></li> <li><a href="/wiki/Provenance_(geology)" title="Provenance (geology)">Provenance</a></li> <li><a href="/wiki/Geologic_record" title="Geologic record">Sedimentary record</a></li> <li><a href="/wiki/Sedimentology" title="Sedimentology">Sedimentology</a></li> <li><a href="/wiki/Stratigraphy" title="Stratigraphy">Stratigraphy</a></li> <li><a href="/wiki/Rock_cycle" title="Rock cycle">Rock cycle</a> <ul><li><a href="/wiki/Calcium_cycle" title="Calcium cycle">calcium</a></li> <li><a href="/wiki/Silica_cycle" title="Silica cycle">silica</a></li> <li><a href="/wiki/Carbonate-silicate_cycle" class="mw-redirect" title="Carbonate-silicate cycle">carbonate-silicate</a></li></ul></li> <li><a href="/wiki/Paleolimnology" title="Paleolimnology">Paleolimnology</a></li> <li><a href="/wiki/Biosignature" title="Biosignature">Biosignature</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-below hlist" style="background-color: #82C3D8; border-color: #A2B8BF"> <ul><li><span class="nowrap"><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Sediments" title="Category:Sediments">Category</a></span></li></ul></td></tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Sediment_sidebar" title="Template:Sediment sidebar"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/w/index.php?title=Template_talk:Sediment_sidebar&action=edit&redlink=1" class="new" title="Template talk:Sediment sidebar (page does not exist)"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Sediment_sidebar" title="Special:EditPage/Template:Sediment sidebar"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>Sediment transport</b> is the movement of solid particles (<a href="/wiki/Sediment" title="Sediment">sediment</a>), typically due to a combination of gravity acting on the sediment, and the movement of the <a href="/wiki/Fluid" title="Fluid">fluid</a> in which the sediment is entrained. Sediment transport occurs in natural systems where the particles are <a href="/wiki/Clastic" class="mw-redirect" title="Clastic">clastic</a> rocks (<a href="/wiki/Sand" title="Sand">sand</a>, <a href="/wiki/Gravel" title="Gravel">gravel</a>, <a href="/wiki/Boulders" class="mw-redirect" title="Boulders">boulders</a>, etc.), <a href="/wiki/Mud" title="Mud">mud</a>, or <a href="/wiki/Clay" title="Clay">clay</a>; the fluid is air, water, or ice; and the force of gravity acts to move the particles along the sloping surface on which they are resting. Sediment transport due to fluid motion occurs in <a href="/wiki/River" title="River">rivers</a>, <a href="/wiki/Ocean" title="Ocean">oceans</a>, <a href="/wiki/Lake" title="Lake">lakes</a>, <a href="/wiki/Sea" title="Sea">seas</a>, and other bodies of water due to <a href="/wiki/Current_(fluid)" title="Current (fluid)">currents</a> and <a href="/wiki/Tide" title="Tide">tides</a>. Transport is also caused by <a href="/wiki/Glacier" title="Glacier">glaciers</a> as they flow, and on terrestrial surfaces under the influence of <a href="/wiki/Wind" title="Wind">wind</a>. Sediment transport due only to gravity can occur on sloping surfaces in general, including <a href="/wiki/Hill" title="Hill">hillslopes</a>, <a href="/wiki/Escarpment" title="Escarpment">scarps</a>, <a href="/wiki/Cliff" title="Cliff">cliffs</a>, and the <a href="/wiki/Continental_shelf" title="Continental shelf">continental shelf</a>—continental slope boundary. </p><p>Sediment transport is important in the fields of <a href="/wiki/Sedimentary_geology" class="mw-redirect" title="Sedimentary geology">sedimentary geology</a>, <a href="/wiki/Geomorphology" title="Geomorphology">geomorphology</a>, <a href="/wiki/Civil_engineering" title="Civil engineering">civil engineering</a>, <a href="/wiki/Hydraulic_engineering" title="Hydraulic engineering">hydraulic engineering</a> and <a href="/wiki/Environmental_engineering" title="Environmental engineering">environmental engineering</a> (see <a href="#Applications">applications</a>, below). Knowledge of sediment transport is most often used to determine whether <a href="/wiki/Erosion" title="Erosion">erosion</a> or <a href="/wiki/Deposition_(sediment)" class="mw-redirect" title="Deposition (sediment)">deposition</a> will occur, the magnitude of this erosion or deposition, and the time and distance over which it will occur. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Environments">Environments</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=1" title="Edit section: Environments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Aeolian">Aeolian</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=2" title="Edit section: Aeolian"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Aeolian_processes" title="Aeolian processes">Aeolian processes</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:KelsoSand.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/KelsoSand.JPG/220px-KelsoSand.JPG" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/KelsoSand.JPG/330px-KelsoSand.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d9/KelsoSand.JPG/440px-KelsoSand.JPG 2x" data-file-width="2592" data-file-height="1944" /></a><figcaption>Sand blowing off a crest in the <a href="/wiki/Kelso_Dunes" title="Kelso Dunes">Kelso Dunes</a> of the <a href="/wiki/Mojave_Desert" title="Mojave Desert">Mojave Desert</a>, California</figcaption></figure> <p><i>Aeolian</i> or <i>eolian</i> (depending on the parsing of <a href="/wiki/%C3%86" title="Æ">æ</a>) is the term for sediment transport by <a href="/wiki/Wind" title="Wind">wind</a>. This process results in the formation of <a href="/wiki/Ripple_marks" title="Ripple marks">ripples</a> and sand <a href="/wiki/Dune" title="Dune">dunes</a>. Typically, the size of the transported sediment is fine <a href="/wiki/Sand" title="Sand">sand</a> (<1 mm) and smaller, because <a href="/wiki/Air" class="mw-redirect" title="Air">air</a> is a fluid with low <a href="/wiki/Density" title="Density">density</a> and <a href="/wiki/Viscosity" title="Viscosity">viscosity</a>, and can therefore not exert very much <a href="/wiki/Shear_strength" title="Shear strength">shear</a> on its bed. </p><p><a href="/wiki/Bedform" title="Bedform">Bedforms</a> are generated by aeolian sediment transport in the terrestrial near-surface environment. Ripples<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> and dunes<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> form as a natural self-organizing response to sediment transport. </p><p>Aeolian sediment transport is common on beaches and in the arid regions of the world, because it is in these environments that vegetation does not prevent the presence and motion of fields of sand. </p><p>Wind-blown very fine-grained <a href="/wiki/Dust" title="Dust">dust</a> is capable of entering the upper atmosphere and moving across the globe. Dust from the <a href="/wiki/Sahara" title="Sahara">Sahara</a> deposits on the <a href="/wiki/Canary_Islands" title="Canary Islands">Canary Islands</a> and islands in the <a href="/wiki/Caribbean" title="Caribbean">Caribbean</a>,<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> and dust from the <a href="/wiki/Gobi_Desert" title="Gobi Desert">Gobi Desert</a> has deposited on the <a href="/wiki/Western_United_States" title="Western United States">western United States</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> This sediment is important to the soil budget and ecology of several islands. </p><p>Deposits of fine-grained wind-blown <a href="/wiki/Glacier" title="Glacier">glacial</a> sediment are called <a href="/wiki/Loess" title="Loess">loess</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Fluvial">Fluvial</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=3" title="Edit section: Fluvial"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="excerpt-block"><style data-mw-deduplicate="TemplateStyles:r1066933788">.mw-parser-output .excerpt-hat .mw-editsection-like{font-style:normal}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable dablink excerpt-hat selfref">This section is an excerpt from <a href="/wiki/Fluvial_sediment_processes" title="Fluvial sediment processes">Fluvial sediment processes</a>.<span class="mw-editsection-like plainlinks"><span class="mw-editsection-bracket">[</span><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Fluvial_sediment_processes&action=edit">edit</a><span class="mw-editsection-bracket">]</span></span></div><div class="excerpt"> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Matanuska_River_8727.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Matanuska_River_8727.JPG/220px-Matanuska_River_8727.JPG" decoding="async" width="220" height="147" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Matanuska_River_8727.JPG/330px-Matanuska_River_8727.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Matanuska_River_8727.JPG/440px-Matanuska_River_8727.JPG 2x" data-file-width="4272" data-file-height="2848" /></a><figcaption>Deep, eroding <a href="/wiki/Glaciofluvial_deposit" class="mw-redirect" title="Glaciofluvial deposit">glaciofluvial deposits</a> alongside the <a href="/wiki/Matanuska_River" title="Matanuska River">Matanuska River</a>, <a href="/wiki/Alaska" title="Alaska">Alaska</a></figcaption></figure> <p>In <a href="/wiki/Geography" title="Geography">geography</a> and <a href="/wiki/Geology" title="Geology">geology</a>, <a href="/wiki/Fluvial_sediment_processes" title="Fluvial sediment processes">fluvial sediment processes</a> or fluvial sediment transport are associated with <a href="/wiki/River" title="River">rivers</a> and <a href="/wiki/Stream" title="Stream">streams</a> and the <a href="/wiki/Deposition_(geology)" title="Deposition (geology)">deposits</a> and <a href="/wiki/Landform" title="Landform">landforms</a> created by <a href="/wiki/Sediment" title="Sediment">sediments</a>. It can result in the formation of <a href="/wiki/Ripple_marks" title="Ripple marks">ripples</a> and <a href="/wiki/Dune" title="Dune">dunes</a>, in <a href="/wiki/Fractal" title="Fractal">fractal</a>-shaped patterns of erosion, in complex patterns of natural river systems, and in the development of <a href="/wiki/Floodplain" title="Floodplain">floodplains</a> and the occurrence of <a href="/wiki/Flash_floods" class="mw-redirect" title="Flash floods">flash floods</a>. Sediment moved by water can be larger than sediment moved by air because water has both a higher <a href="/wiki/Density" title="Density">density</a> and <a href="/wiki/Viscosity" title="Viscosity">viscosity</a>. In typical rivers the largest carried sediment is of <a href="/wiki/Sand" title="Sand">sand</a> and <a href="/wiki/Gravel" title="Gravel">gravel</a> size, but larger floods can carry <a href="/wiki/Cobble_(geology)" title="Cobble (geology)">cobbles</a> and even <a href="/wiki/Boulders" class="mw-redirect" title="Boulders">boulders</a>. </p> When the stream or rivers are associated with <a href="/wiki/Glacier" title="Glacier">glaciers</a>, <a href="/wiki/Ice_sheet" title="Ice sheet">ice sheets</a>, or <a href="/wiki/Ice_cap" title="Ice cap">ice caps</a>, the term <i><a href="/wiki/Glaciofluvial" class="mw-redirect" title="Glaciofluvial">glaciofluvial</a></i> or <a href="/wiki/Fluvioglacial_landform" title="Fluvioglacial landform"><i>fluvioglacial</i></a> is used, as in <a href="/wiki/Periglacial" class="mw-redirect" title="Periglacial">periglacial</a> flows and <a href="/wiki/Glacial_lake_outburst_flood" title="Glacial lake outburst flood">glacial lake outburst floods</a>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Fluvial sediment processes include the motion of sediment and <a href="/wiki/Erosion" title="Erosion">erosion</a> or <a href="/wiki/Deposition_(geology)" title="Deposition (geology)">deposition</a> on the <a href="/wiki/River_bed" class="mw-redirect" title="River bed">river bed</a>.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup></div></div> <div class="mw-heading mw-heading3"><h3 id="Coastal">Coastal</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=4" title="Edit section: Coastal"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Coastal_sediment_transport" title="Coastal sediment transport">Coastal sediment transport</a></div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Laysan_beach.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Laysan_beach.jpg/220px-Laysan_beach.jpg" decoding="async" width="220" height="251" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Laysan_beach.jpg/330px-Laysan_beach.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/30/Laysan_beach.jpg/440px-Laysan_beach.jpg 2x" data-file-width="944" data-file-height="1076" /></a><figcaption>Sand <a href="/wiki/Ripple_marks" title="Ripple marks">ripples</a>, <a href="/w/index.php?title=Laysan_Beach&action=edit&redlink=1" class="new" title="Laysan Beach (page does not exist)">Laysan Beach</a>, <a href="/wiki/Hawaii" title="Hawaii">Hawaii</a>. Coastal sediment transport results in these evenly spaced ripples along the shore. <a href="/wiki/Monk_seal" title="Monk seal">Monk seal</a> for scale.</figcaption></figure> <p>Coastal sediment transport takes place in near-shore environments due to the motions of waves and currents. At the mouths of rivers, coastal sediment and fluvial sediment transport processes mesh to create <a href="/wiki/River_delta" title="River delta">river deltas</a>. </p><p>Coastal sediment transport results in the formation of characteristic coastal landforms such as <a href="/wiki/Beach" title="Beach">beaches</a>, <a href="/wiki/Barrier_islands" class="mw-redirect" title="Barrier islands">barrier islands</a>, and capes.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Glacier.zermatt.arp.750pix.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Glacier.zermatt.arp.750pix.jpg/220px-Glacier.zermatt.arp.750pix.jpg" decoding="async" width="220" height="158" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Glacier.zermatt.arp.750pix.jpg/330px-Glacier.zermatt.arp.750pix.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Glacier.zermatt.arp.750pix.jpg/440px-Glacier.zermatt.arp.750pix.jpg 2x" data-file-width="748" data-file-height="536" /></a><figcaption>A <a href="/wiki/Glacier" title="Glacier">glacier</a> joining the <a href="/wiki/Gorner_Glacier" title="Gorner Glacier">Gorner Glacier</a>, <a href="/wiki/Zermatt,_Switzerland" class="mw-redirect" title="Zermatt, Switzerland">Zermatt, Switzerland</a>. These glaciers transport <a href="/wiki/Sediment" title="Sediment">sediment</a> and leave behind <a href="/wiki/Lateral_moraines" class="mw-redirect" title="Lateral moraines">lateral moraines</a>.</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Glacial">Glacial</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=5" title="Edit section: Glacial"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>As glaciers move over their beds, they entrain and move material of all sizes. Glaciers can carry the largest sediment, and areas of glacial deposition often contain a large number of <a href="/wiki/Glacial_erratics" class="mw-redirect" title="Glacial erratics">glacial erratics</a>, many of which are several metres in diameter. Glaciers also pulverize rock into "<a href="/wiki/Glacial_flour" class="mw-redirect" title="Glacial flour">glacial flour</a>", which is so fine that it is often carried away by winds to create <a href="/wiki/Loess" title="Loess">loess</a> deposits thousands of kilometres afield. Sediment entrained in glaciers often moves approximately along the glacial <a href="/wiki/Flowline" class="mw-redirect" title="Flowline">flowlines</a>, causing it to appear at the surface in the <a href="/wiki/Ablation_zone" title="Ablation zone">ablation zone</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Hillslope">Hillslope</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=6" title="Edit section: Hillslope"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In hillslope sediment transport, a variety of processes move <a href="/wiki/Regolith" title="Regolith">regolith</a> downslope. These include: </p> <ul><li><a href="/wiki/Soil_creep" class="mw-redirect" title="Soil creep">Soil creep</a></li> <li><a href="/wiki/Tree_throw" title="Tree throw">Tree throw</a></li> <li>Movement of soil by <a href="/wiki/Burrow" title="Burrow">burrowing</a> animals</li> <li><a href="/wiki/Slump_(geology)" title="Slump (geology)">Slumping</a> and <a href="/wiki/Landslide" title="Landslide">landsliding</a> of the hillslope</li></ul> <p>These processes generally combine to give the hillslope a profile that looks like a solution to the <a href="/wiki/Diffusion_equation" title="Diffusion equation">diffusion equation</a>, where the diffusivity is a parameter that relates to the ease of sediment transport on the particular hillslope. For this reason, the tops of hills generally have a parabolic concave-up profile, which grades into a convex-up profile around valleys. </p><p>As hillslopes steepen, however, they become more prone to episodic <a href="/wiki/Landslide" title="Landslide">landslides</a> and other <a href="/wiki/Mass_wasting" title="Mass wasting">mass wasting</a> events. Therefore, hillslope processes are better described by a nonlinear diffusion equation in which classic diffusion dominates for shallow slopes and erosion rates go to infinity as the hillslope reaches a critical <a href="/wiki/Angle_of_repose" title="Angle of repose">angle of repose</a>.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Debris_flow">Debris flow</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=7" title="Edit section: Debris flow"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Large masses of material are moved in <a href="/wiki/Debris_flow" title="Debris flow">debris flows</a>, <a href="/wiki/Hyperconcentrated_flow" title="Hyperconcentrated flow">hyperconcentrated</a> mixtures of mud, clasts that range up to boulder-size, and water. Debris flows move as <a href="/wiki/Granular_flow" class="mw-redirect" title="Granular flow">granular flows</a> down steep mountain valleys and washes. Because they transport sediment as a granular mixture, their transport mechanisms and capacities scale differently from those of fluvial systems. </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=8" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:IsfjordenSediment.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2d/IsfjordenSediment.JPG/220px-IsfjordenSediment.JPG" decoding="async" width="220" height="155" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2d/IsfjordenSediment.JPG/330px-IsfjordenSediment.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2d/IsfjordenSediment.JPG/440px-IsfjordenSediment.JPG 2x" data-file-width="3212" data-file-height="2259" /></a><figcaption>Suspended sediment from a stream emptying into a fjord (<a href="/wiki/Isfjord,_Svalbard" class="mw-redirect" title="Isfjord, Svalbard">Isfjorden</a>, Svalbard, Norway)</figcaption></figure> <p>Sediment transport is applied to solve many environmental, geotechnical, and geological problems. Measuring or quantifying sediment transport or erosion is therefore important for <a href="/wiki/Coastal_engineering" title="Coastal engineering">coastal engineering</a>. Several sediment erosion devices have been designed in order to quantify sediment erosion (e.g., Particle Erosion Simulator (PES)). One such device, also referred to as the BEAST (Benthic Environmental Assessment Sediment Tool) has been calibrated in order to quantify rates of sediment erosion.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>Movement of sediment is important in providing habitat for fish and other organisms in rivers. Therefore, managers of highly regulated rivers, which are often sediment-starved due to dams, are often advised to stage short <a href="/wiki/Flood" title="Flood">floods</a> to refresh the bed material and rebuild bars. This is also important, for example, in the <a href="/wiki/Grand_Canyon" title="Grand Canyon">Grand Canyon</a> of the <a href="/wiki/Colorado_River" title="Colorado River">Colorado River</a>, to rebuild shoreline habitats also used as campsites. </p><p>Sediment discharge into a reservoir formed by a dam forms a reservoir <a href="/wiki/River_delta" title="River delta">delta</a>. This delta will fill the basin, and eventually, either the reservoir will need to be dredged or the dam will need to be removed. Knowledge of sediment transport can be used to properly plan to extend the life of a dam. </p><p>Geologists can use inverse solutions of transport relationships to understand flow depth, velocity, and direction, from sedimentary rocks and young deposits of alluvial materials. </p><p>Flow in culverts, over dams, and around bridge piers can cause erosion of the bed. This erosion can damage the environment and expose or unsettle the foundations of the structure. Therefore, good knowledge of the mechanics of sediment transport in a built environment are important for civil and hydraulic engineers. </p><p>When suspended sediment transport is increased due to human activities, causing environmental problems including the filling of channels, it is called <a href="/wiki/Siltation" title="Siltation">siltation</a> after the grain-size fraction dominating the process. </p> <div class="mw-heading mw-heading2"><h2 id="Initiation_of_motion">Initiation of motion</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=9" title="Edit section: Initiation of motion"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Sediment1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Sediment1.png/220px-Sediment1.png" decoding="async" width="220" height="102" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Sediment1.png/330px-Sediment1.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Sediment1.png/440px-Sediment1.png 2x" data-file-width="1744" data-file-height="806" /></a><figcaption>Mechanisms of movement in sediment transport. (a) Roll: sediment particle is rotated by shear stress along the ground (b) Lift: Sediment particle is lifted by the shear stress into the bulk (c) Pluck: Sediment particle is extracted from crevices in the ground by shear stress</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Stress_balance">Stress balance</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=10" title="Edit section: Stress balance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For a fluid to begin transporting sediment that is currently at rest on a surface, the boundary (or bed) <a href="/wiki/Shear_stress" title="Shear stress">shear stress</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{b}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{b}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/721b220270c8a21caf5bc857eb43133412b20f97" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.954ex; height:2.009ex;" alt="{\displaystyle \tau _{b}}"></span> exerted by the fluid must exceed the critical shear stress <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{c}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{c}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ea61c9e95de7b5b55eb1ef4b3e03290002e91089" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.96ex; height:2.009ex;" alt="{\displaystyle \tau _{c}}"></span> for the initiation of motion of grains at the bed. This basic criterion for the initiation of motion can be written as: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{b}=\tau _{c}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{b}=\tau _{c}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/91194a8d051d17ce806426088b7d0543d814a3a3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.013ex; height:2.009ex;" alt="{\displaystyle \tau _{b}=\tau _{c}}"></span>.</dd></dl> <p>This is typically represented by a comparison between a <a href="/wiki/Dimensionless" class="mw-redirect" title="Dimensionless">dimensionless</a> shear stress <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{b}*}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{b}*}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09e8a7d9cadc0086015f93d2f6e29334503bf774" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.116ex; height:2.009ex;" alt="{\displaystyle \tau _{b}*}"></span> and a dimensionless critical shear stress <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{c}*}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{c}*}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d3a109fadec6170cc85d26d7da6286c21073d62" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.123ex; height:2.009ex;" alt="{\displaystyle \tau _{c}*}"></span>. The nondimensionalization is in order to compare the driving forces of particle motion (shear stress) to the resisting forces that would make it stationary (particle density and size). This dimensionless shear stress, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau *}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau *}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df6ef55b609bc41060a8ff820c86e3f2458196e9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.364ex; height:1.676ex;" alt="{\displaystyle \tau *}"></span>, is called the <a href="/wiki/Shields_parameter" title="Shields parameter">Shields parameter</a> and is defined as:<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau *={\frac {\tau }{(\rho _{s}-\rho _{f})(g)(D)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> <mo>∗</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>τ</mi> <mrow> <mo stretchy="false">(</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>g</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>D</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau *={\frac {\tau }{(\rho _{s}-\rho _{f})(g)(D)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/17ec7ec22981a7455ca62ba2bc22e7a142897038" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:22.151ex; height:5.509ex;" alt="{\displaystyle \tau *={\frac {\tau }{(\rho _{s}-\rho _{f})(g)(D)}}}"></span>.</dd></dl> <p>And the new equation to solve becomes: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{b}*=\tau _{c}*}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>∗</mo> <mo>=</mo> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{b}*=\tau _{c}*}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7cfbea8c5aae65fa0a2cfe96a88052e098d33e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.337ex; height:2.009ex;" alt="{\displaystyle \tau _{b}*=\tau _{c}*}"></span>.</dd></dl> <p>The equations included here describe sediment transport for <a href="/wiki/Clastic" class="mw-redirect" title="Clastic">clastic</a>, or <a href="/wiki/Granular" class="mw-redirect" title="Granular">granular</a> sediment. They do not work for <a href="/wiki/Clays" class="mw-redirect" title="Clays">clays</a> and <a href="/wiki/Muds" class="mw-redirect" title="Muds">muds</a> because these types of <a href="/wiki/Flocculation" title="Flocculation">floccular</a> sediments do not fit the geometric simplifications in these equations, and also interact thorough <a href="/wiki/Electrostatic" class="mw-redirect" title="Electrostatic">electrostatic</a> forces. The equations were also designed for <a href="/wiki/Fluvial" class="mw-redirect" title="Fluvial">fluvial</a> sediment transport of particles carried along in a liquid flow, such as that in a river, canal, or other open channel. </p><p>Only one size of particle is considered in this equation. However, river beds are often formed by a mixture of sediment of various sizes. In case of partial motion where only a part of the sediment mixture moves, the river bed becomes enriched in large gravel as the smaller sediments are washed away. The smaller sediments present under this layer of large gravel have a lower possibility of movement and total sediment transport decreases. This is called armouring effect.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Other forms of armouring of sediment or decreasing rates of sediment erosion can be caused by carpets of microbial mats, under conditions of high organic loading.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Critical_shear_stress">Critical shear stress</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=11" title="Edit section: Critical shear stress"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Shields_diagram.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Shields_diagram.jpg/300px-Shields_diagram.jpg" decoding="async" width="300" height="178" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Shields_diagram.jpg/450px-Shields_diagram.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Shields_diagram.jpg/600px-Shields_diagram.jpg 2x" data-file-width="1185" data-file-height="703" /></a><figcaption>Original Shields diagram, 1936</figcaption></figure> <p>The <a href="/wiki/Shields_formula" title="Shields formula">Shields</a> diagram empirically shows how the dimensionless critical shear stress (i.e. the dimensionless shear stress required for the initiation of motion) is a function of a particular form of the particle <a href="/wiki/Reynolds_number" title="Reynolds number">Reynolds number</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {Re} _{p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {Re} _{p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c42a182c054da3110a6ebe65621d97e0b9fea5c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.802ex; height:2.843ex;" alt="{\displaystyle \mathrm {Re} _{p}}"></span> or Reynolds number related to the particle. This allows the criterion for the initiation of motion to be rewritten in terms of a solution for a specific version of the particle Reynolds number, called <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {Re} _{p}*}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {Re} _{p}*}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/10079071d160bdca3512708d74f0e8f11a5a8323" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.965ex; height:2.843ex;" alt="{\displaystyle \mathrm {Re} _{p}*}"></span>. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{b}*=f\left(\mathrm {Re} _{p}*\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>∗</mo> <mo>=</mo> <mi>f</mi> <mrow> <mo>(</mo> <mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>∗</mo> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{b}*=f\left(\mathrm {Re} _{p}*\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1dc130efe957ac48e0e503d6386d4109b64bddfd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:14.654ex; height:3.009ex;" alt="{\displaystyle \tau _{b}*=f\left(\mathrm {Re} _{p}*\right)}"></span></dd></dl> <p>This can then be solved by using the empirically derived Shields curve to find <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{c}*}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{c}*}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d3a109fadec6170cc85d26d7da6286c21073d62" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.123ex; height:2.009ex;" alt="{\displaystyle \tau _{c}*}"></span> as a function of a specific form of the particle Reynolds number called the boundary Reynolds number. The mathematical solution of the equation was given by <a href="/wiki/Subhasish_Dey" title="Subhasish Dey">Dey</a>.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Particle_Reynolds_number">Particle Reynolds number</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=12" title="Edit section: Particle Reynolds number"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In general, a particle Reynolds number has the form: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {Re} _{p}={\frac {U_{p}D}{\nu }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mi>D</mi> </mrow> <mi>ν</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {Re} _{p}={\frac {U_{p}D}{\nu }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0143a645248778cd969eece924ed3e31d3413c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.308ex; height:5.509ex;" alt="{\displaystyle \mathrm {Re} _{p}={\frac {U_{p}D}{\nu }}}"></span></dd></dl> <p>Where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U_{p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5fdf01ea5c43d1e338d8b847556322c42a8c65a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.647ex; height:2.843ex;" alt="{\displaystyle U_{p}}"></span> is a characteristic particle velocity, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f34a0c600395e5d4345287e21fb26efd386990e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}"></span> is the grain diameter (a characteristic particle size), and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }"></span> is the kinematic viscosity, which is given by the dynamic viscosity, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd47b2a39f7a7856952afec1f1db72c67af6161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }"></span>, divided by the fluid density, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rho _{f}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rho _{f}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ddce369cfafedb10857e0bd81ec0971b6ee7bf7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.338ex; height:2.343ex;" alt="{\displaystyle {\rho _{f}}}"></span>. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu ={\frac {\mu }{\rho _{f}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>μ</mi> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu ={\frac {\mu }{\rho _{f}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bc54044b5444fbba202f05f2e27acbc6f2a98120" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:7.505ex; height:5.509ex;" alt="{\displaystyle \nu ={\frac {\mu }{\rho _{f}}}}"></span></dd></dl> <p>The specific particle Reynolds number of interest is called the boundary Reynolds number, and it is formed by replacing the velocity term in the particle Reynolds number by the <a href="/wiki/Shear_velocity" title="Shear velocity">shear velocity</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u_{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53f06376827f0e844992e08986763b37f6f771d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.293ex; margin-bottom: -0.379ex; width:2.384ex; height:2.009ex;" alt="{\displaystyle u_{*}}"></span>, which is a way of rewriting shear stress in terms of velocity. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u_{*}={\sqrt {\frac {\tau _{b}}{\rho _{f}}}}=\kappa z{\frac {\partial u}{\partial z}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mfrac> </msqrt> </mrow> <mo>=</mo> <mi>κ</mi> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>u</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>z</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{*}={\sqrt {\frac {\tau _{b}}{\rho _{f}}}}=\kappa z{\frac {\partial u}{\partial z}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e671ed3f64b8fcbf8b7ef95406527f7322d1db23" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:19.99ex; height:6.509ex;" alt="{\displaystyle u_{*}={\sqrt {\frac {\tau _{b}}{\rho _{f}}}}=\kappa z{\frac {\partial u}{\partial z}}}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{b}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{b}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/721b220270c8a21caf5bc857eb43133412b20f97" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.954ex; height:2.009ex;" alt="{\displaystyle \tau _{b}}"></span> is the bed shear stress (described below), and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \kappa }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>κ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \kappa }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54ddec2e922c5caea4e47d04feef86e782dc8e6d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.339ex; height:1.676ex;" alt="{\displaystyle \kappa }"></span> is the <a href="/wiki/Von_K%C3%A1rm%C3%A1n_constant" title="Von Kármán constant">von Kármán constant</a>, where </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \kappa ={0.407}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>κ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0.407</mn> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \kappa ={0.407}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5731332c9a07ea16a81422f67510be49dba86e04" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.734ex; height:2.176ex;" alt="{\displaystyle \kappa ={0.407}}"></span>.</dd></dl> <p>The particle Reynolds number is therefore given by: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {Re} _{p}*={\frac {u_{*}D}{\nu }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>∗</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msub> <mi>D</mi> </mrow> <mi>ν</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {Re} _{p}*={\frac {u_{*}D}{\nu }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/368136e4aa312bdb2e0fa6cdcf887492b9d2cd6d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:13.207ex; height:5.176ex;" alt="{\displaystyle \mathrm {Re} _{p}*={\frac {u_{*}D}{\nu }}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Bed_shear_stress">Bed shear stress</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=13" title="Edit section: Bed shear stress"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The boundary Reynolds number can be used with the Shields diagram to empirically solve the equation </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{c}*=f\left(\mathrm {Re} _{p}*\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>∗</mo> <mo>=</mo> <mi>f</mi> <mrow> <mo>(</mo> <mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>∗</mo> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{c}*=f\left(\mathrm {Re} _{p}*\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/024ed5cae1c8a736f2e62a3ad5b2c27aa297eb34" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:14.661ex; height:3.009ex;" alt="{\displaystyle \tau _{c}*=f\left(\mathrm {Re} _{p}*\right)}"></span>,</dd></dl> <p>which solves the right-hand side of the equation </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{b}*=\tau _{c}*}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>∗</mo> <mo>=</mo> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{b}*=\tau _{c}*}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7cfbea8c5aae65fa0a2cfe96a88052e098d33e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.337ex; height:2.009ex;" alt="{\displaystyle \tau _{b}*=\tau _{c}*}"></span>.</dd></dl> <p>In order to solve the left-hand side, expanded as </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{b}*={\frac {\tau _{b}}{(\rho _{s}-\rho _{f})(g)(D)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>∗</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mrow> <mo stretchy="false">(</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>g</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>D</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{b}*={\frac {\tau _{b}}{(\rho _{s}-\rho _{f})(g)(D)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/862021611cb7642aa0ba412a0ee9cef2c82acde6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:22.903ex; height:5.509ex;" alt="{\displaystyle \tau _{b}*={\frac {\tau _{b}}{(\rho _{s}-\rho _{f})(g)(D)}}}"></span>,</dd></dl> <p>the bed shear stress needs to be found, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tau _{b}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tau _{b}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d930e69d89018b22e20fbc3732f5f54145c986af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.954ex; height:2.009ex;" alt="{\displaystyle {\tau _{b}}}"></span>. There are several ways to solve for the bed shear stress. The simplest approach is to assume the flow is steady and uniform, using the reach-averaged depth and slope. because it is difficult to measure shear stress <i>in situ</i>, this method is also one of the most-commonly used. The method is known as the <a href="/wiki/Depth-slope_product" class="mw-redirect" title="Depth-slope product">depth-slope product</a>. </p> <div class="mw-heading mw-heading4"><h4 id="Depth-slope_product">Depth-slope product</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=14" title="Edit section: Depth-slope product"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Depth-slope_product" class="mw-redirect" title="Depth-slope product">Depth-slope product</a></div> <p>For a river undergoing approximately steady, uniform equilibrium flow, of approximately constant depth <i>h</i> and slope angle θ over the reach of interest, and whose width is much greater than its depth, the bed shear stress is given by some momentum considerations stating that the gravity force component in the flow direction equals exactly the friction force.<sup id="cite_ref-Chanson_16-0" class="reference"><a href="#cite_note-Chanson-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> For a wide channel, it yields: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{b}=\rho gh\sin(\theta )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>=</mo> <mi>ρ</mi> <mi>g</mi> <mi>h</mi> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>θ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{b}=\rho gh\sin(\theta )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0798edc0f7f69666539fb9ef145b7a6a83011795" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.852ex; height:2.843ex;" alt="{\displaystyle \tau _{b}=\rho gh\sin(\theta )}"></span></dd></dl> <p>For shallow slope angles, which are found in almost all natural lowland streams, the <a href="/wiki/Small-angle_formula" class="mw-redirect" title="Small-angle formula">small-angle formula</a> shows that <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin(\theta )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>θ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin(\theta )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/acafc444aea85d63a40dabf84f035a6b4955a948" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.755ex; height:2.843ex;" alt="{\displaystyle \sin(\theta )}"></span> is approximately equal to <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tan(\theta )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>θ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan(\theta )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2dbdbf63a30c035f2e8232b47930e745680b6e31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.259ex; height:2.843ex;" alt="{\displaystyle \tan(\theta )}"></span>, which is given by <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span>, the slope. Rewritten with this: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{b}=\rho ghS}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>=</mo> <mi>ρ</mi> <mi>g</mi> <mi>h</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{b}=\rho ghS}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3991d39209f83c193aedc6fae1d1619af8880fe7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.208ex; height:2.676ex;" alt="{\displaystyle \tau _{b}=\rho ghS}"></span></dd></dl> <div class="mw-heading mw-heading4"><h4 id="Shear_velocity,_velocity,_and_friction_factor"><span id="Shear_velocity.2C_velocity.2C_and_friction_factor"></span>Shear velocity, velocity, and friction factor</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=15" title="Edit section: Shear velocity, velocity, and friction factor"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For the steady case, by extrapolating the depth-slope product and the equation for shear velocity: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{b}=\rho ghS}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>=</mo> <mi>ρ</mi> <mi>g</mi> <mi>h</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{b}=\rho ghS}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3991d39209f83c193aedc6fae1d1619af8880fe7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.208ex; height:2.676ex;" alt="{\displaystyle \tau _{b}=\rho ghS}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u_{*}={\sqrt {\left({\frac {\tau _{b}}{\rho }}\right)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mi>ρ</mi> </mfrac> </mrow> <mo>)</mo> </mrow> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{*}={\sqrt {\left({\frac {\tau _{b}}{\rho }}\right)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/44ed31a64d0320706dc6ecf7b8b800ec45275612" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:14.017ex; height:7.509ex;" alt="{\displaystyle u_{*}={\sqrt {\left({\frac {\tau _{b}}{\rho }}\right)}}}"></span>,</dd></dl> <p>The depth-slope product can be rewritten as: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{b}=\rho u_{*}^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>=</mo> <mi>ρ</mi> <msubsup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{b}=\rho u_{*}^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b3364af9eefaf5a780471b5d03af534c9be8a61a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.638ex; height:3.009ex;" alt="{\displaystyle \tau _{b}=\rho u_{*}^{2}}"></span>.</dd></dl> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u*}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u*}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/37e6d3f6a1aad2880330a49cc71e6b4740dce288" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.492ex; height:1.676ex;" alt="{\displaystyle u*}"></span> is related to the mean flow velocity, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {u}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {u}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d707dfa8c7f2c1d6635efa659a22efb3c71e8f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:2.009ex;" alt="{\displaystyle {\bar {u}}}"></span>, through the generalized <a href="/wiki/Darcy%E2%80%93Weisbach_equation" title="Darcy–Weisbach equation">Darcy–Weisbach friction factor</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{f}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{f}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7765fc9102a19771111a01cd0b18c79e231029cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.798ex; height:2.843ex;" alt="{\displaystyle C_{f}}"></span>, which is equal to the Darcy-Weisbach friction factor divided by 8 (for mathematical convenience).<sup id="cite_ref-whipple_roughness_17-0" class="reference"><a href="#cite_note-whipple_roughness-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> Inserting this friction factor, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{b}=\rho C_{f}\left({\bar {u}}\right)^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>=</mo> <mi>ρ</mi> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{b}=\rho C_{f}\left({\bar {u}}\right)^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/89fcf3389dd2fb3545c4d37791076db03ebf49e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.246ex; height:3.509ex;" alt="{\displaystyle \tau _{b}=\rho C_{f}\left({\bar {u}}\right)^{2}}"></span>.</dd></dl> <div class="mw-heading mw-heading4"><h4 id="Unsteady_flow">Unsteady flow</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=16" title="Edit section: Unsteady flow"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For all flows that cannot be simplified as a single-slope infinite channel (as in the <a href="/wiki/Depth-slope_product" class="mw-redirect" title="Depth-slope product">depth-slope product</a>, above), the bed shear stress can be locally found by applying the <a href="/wiki/Shallow_water_equations" title="Shallow water equations">Saint-Venant equations</a> for <a href="/wiki/Continuity_equation" title="Continuity equation">continuity</a>, which consider accelerations within the flow. </p> <div class="mw-heading mw-heading3"><h3 id="Example">Example</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=17" title="Edit section: Example"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Set-up">Set-up</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=18" title="Edit section: Set-up"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The criterion for the initiation of motion, established earlier, states that </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{b}*=\tau _{c}*}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>∗</mo> <mo>=</mo> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{b}*=\tau _{c}*}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7cfbea8c5aae65fa0a2cfe96a88052e098d33e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.337ex; height:2.009ex;" alt="{\displaystyle \tau _{b}*=\tau _{c}*}"></span>.</dd></dl> <p>In this equation, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau *={\frac {\tau }{(\rho _{s}-\rho )(g)(D)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> <mo>∗</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>τ</mi> <mrow> <mo stretchy="false">(</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>−</mo> <mi>ρ</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>g</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>D</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau *={\frac {\tau }{(\rho _{s}-\rho )(g)(D)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ccc59604ae3aec4fa3be925f34f72e7a8d1392c6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:21.015ex; height:5.509ex;" alt="{\displaystyle \tau *={\frac {\tau }{(\rho _{s}-\rho )(g)(D)}}}"></span>, and therefore</dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\tau _{b}}{(\rho _{s}-\rho )(g)(D)}}={\frac {\tau _{c}}{(\rho _{s}-\rho )(g)(D)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mrow> <mo stretchy="false">(</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>−</mo> <mi>ρ</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>g</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>D</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mrow> <mo stretchy="false">(</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>−</mo> <mi>ρ</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>g</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>D</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\tau _{b}}{(\rho _{s}-\rho )(g)(D)}}={\frac {\tau _{c}}{(\rho _{s}-\rho )(g)(D)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c2062fc27459844e91b73497a6e63a19bf29ab0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:34.202ex; height:5.509ex;" alt="{\displaystyle {\frac {\tau _{b}}{(\rho _{s}-\rho )(g)(D)}}={\frac {\tau _{c}}{(\rho _{s}-\rho )(g)(D)}}}"></span>.</dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{c}*}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{c}*}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d3a109fadec6170cc85d26d7da6286c21073d62" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.123ex; height:2.009ex;" alt="{\displaystyle \tau _{c}*}"></span> is a function of boundary Reynolds number, a specific type of particle Reynolds number.</dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{c}*=f\left(\mathrm {Re} _{p}*\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>∗</mo> <mo>=</mo> <mi>f</mi> <mrow> <mo>(</mo> <mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>∗</mo> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{c}*=f\left(\mathrm {Re} _{p}*\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/024ed5cae1c8a736f2e62a3ad5b2c27aa297eb34" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:14.661ex; height:3.009ex;" alt="{\displaystyle \tau _{c}*=f\left(\mathrm {Re} _{p}*\right)}"></span>.</dd></dl> <p>For a particular particle Reynolds number, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{c}*}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{c}*}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d3a109fadec6170cc85d26d7da6286c21073d62" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.123ex; height:2.009ex;" alt="{\displaystyle \tau _{c}*}"></span> will be an empirical constant given by the Shields Curve or by another set of empirical data (depending on whether or not the grain size is uniform). </p><p>Therefore, the final equation to solve is: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\tau _{b}}{(\rho _{s}-\rho )(g)(D)}}=f\left(\mathrm {Re} _{p}*\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mrow> <mo stretchy="false">(</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>−</mo> <mi>ρ</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>g</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>D</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>f</mi> <mrow> <mo>(</mo> <mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>∗</mo> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\tau _{b}}{(\rho _{s}-\rho )(g)(D)}}=f\left(\mathrm {Re} _{p}*\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e7ec6a47cdb346d4a15c71f99ef3156e13651df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:27.09ex; height:5.509ex;" alt="{\displaystyle {\frac {\tau _{b}}{(\rho _{s}-\rho )(g)(D)}}=f\left(\mathrm {Re} _{p}*\right)}"></span>.</dd></dl> <div class="mw-heading mw-heading4"><h4 id="Solution">Solution</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=19" title="Edit section: Solution"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Some assumptions allow the solution of the above equation. </p><p>The first assumption is that a good approximation of reach-averaged shear stress is given by the depth-slope product. The equation then can be rewritten as: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rho ghS}=f\left(\mathrm {Re} _{p}*\right){(\rho _{s}-\rho )(g)(D)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>ρ</mi> <mi>g</mi> <mi>h</mi> <mi>S</mi> </mrow> <mo>=</mo> <mi>f</mi> <mrow> <mo>(</mo> <mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>∗</mo> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>−</mo> <mi>ρ</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>g</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>D</mi> <mo stretchy="false">)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rho ghS}=f\left(\mathrm {Re} _{p}*\right){(\rho _{s}-\rho )(g)(D)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/842fad61e0c3762d68ecf4692fab3b950b489b4c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:31.797ex; height:3.009ex;" alt="{\displaystyle {\rho ghS}=f\left(\mathrm {Re} _{p}*\right){(\rho _{s}-\rho )(g)(D)}}"></span>.</dd></dl> <p>Moving and re-combining the terms produces: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {hS}={{\frac {(\rho _{s}-\rho )}{\rho }}(D)}\left(f\left(\mathrm {Re} _{p}*\right)\right)=RD\left(f\left(\mathrm {Re} _{p}*\right)\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>S</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>−</mo> <mi>ρ</mi> <mo stretchy="false">)</mo> </mrow> <mi>ρ</mi> </mfrac> </mrow> <mo stretchy="false">(</mo> <mi>D</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mo>(</mo> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>∗</mo> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mi>R</mi> <mi>D</mi> <mrow> <mo>(</mo> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>∗</mo> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {hS}={{\frac {(\rho _{s}-\rho )}{\rho }}(D)}\left(f\left(\mathrm {Re} _{p}*\right)\right)=RD\left(f\left(\mathrm {Re} _{p}*\right)\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/205e21b48660af7fe1af570fb55fd7f9178ed943" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:46.622ex; height:6.176ex;" alt="{\displaystyle {hS}={{\frac {(\rho _{s}-\rho )}{\rho }}(D)}\left(f\left(\mathrm {Re} _{p}*\right)\right)=RD\left(f\left(\mathrm {Re} _{p}*\right)\right)}"></span></dd></dl> <p>where R is the <a href="/wiki/Submerged_specific_gravity" title="Submerged specific gravity">submerged specific gravity</a> of the sediment. </p><p>The second assumption is that the particle Reynolds number is high. This typically applies to particles of gravel-size or larger in a stream, and means the critical shear stress is constant. The Shields curve shows that for a bed with a uniform grain size, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{c}*=0.06}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>∗</mo> <mo>=</mo> <mn>0.06</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{c}*=0.06}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb960db8e82c29e6aa3d5da7f69ef0523353ea6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.355ex; height:2.509ex;" alt="{\displaystyle \tau _{c}*=0.06}"></span>.</dd></dl> <p>Later researchers<sup id="cite_ref-Parker1990_18-0" class="reference"><a href="#cite_note-Parker1990-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> have shown this value is closer to </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{c}*=0.03}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>∗</mo> <mo>=</mo> <mn>0.03</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{c}*=0.03}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/515fe7f233622c3ad7b07a2523d0891cbdbe38d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.355ex; height:2.509ex;" alt="{\displaystyle \tau _{c}*=0.03}"></span></dd></dl> <p>for more uniformly sorted beds. Therefore the replacement </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{c}*=f\left(\mathrm {Re} _{p}*\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>∗</mo> <mo>=</mo> <mi>f</mi> <mrow> <mo>(</mo> <mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>∗</mo> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{c}*=f\left(\mathrm {Re} _{p}*\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/024ed5cae1c8a736f2e62a3ad5b2c27aa297eb34" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:14.661ex; height:3.009ex;" alt="{\displaystyle \tau _{c}*=f\left(\mathrm {Re} _{p}*\right)}"></span></dd></dl> <p>is used to insert both values at the end. </p><p>The equation now reads: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {hS}=RD\tau _{c}*}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>S</mi> </mrow> <mo>=</mo> <mi>R</mi> <mi>D</mi> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {hS}=RD\tau _{c}*}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6dd8ee834e43f1b71fc6d03fd1d4bcbf1358ce1a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.748ex; height:2.509ex;" alt="{\displaystyle {hS}=RD\tau _{c}*}"></span></dd></dl> <p>This final expression shows the product of the channel depth and slope is equal to the Shield's criterion times the submerged specific gravity of the particles times the particle diameter. </p><p>For a typical situation, such as quartz-rich sediment <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(\rho _{s}=2650{\frac {kg}{m^{3}}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mn>2650</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>k</mi> <mi>g</mi> </mrow> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(\rho _{s}=2650{\frac {kg}{m^{3}}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4154317091075ebf6ad5acaa8c1851c909af38c6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:17.305ex; height:6.176ex;" alt="{\displaystyle \left(\rho _{s}=2650{\frac {kg}{m^{3}}}\right)}"></span> in water <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(\rho =1000{\frac {kg}{m^{3}}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow> <mi>ρ</mi> <mo>=</mo> <mn>1000</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>k</mi> <mi>g</mi> </mrow> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(\rho =1000{\frac {kg}{m^{3}}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9bade354bced0cf052c878bcdbe2a157b2534ae6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:16.302ex; height:6.176ex;" alt="{\displaystyle \left(\rho =1000{\frac {kg}{m^{3}}}\right)}"></span>, the submerged specific gravity is equal to 1.65. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R={\frac {(\rho _{s}-\rho )}{\rho }}=1.65}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>−</mo> <mi>ρ</mi> <mo stretchy="false">)</mo> </mrow> <mi>ρ</mi> </mfrac> </mrow> <mo>=</mo> <mn>1.65</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R={\frac {(\rho _{s}-\rho )}{\rho }}=1.65}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/912deb7fbba96a14c353055b0872254d6bd7e98d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:20.988ex; height:6.176ex;" alt="{\displaystyle R={\frac {(\rho _{s}-\rho )}{\rho }}=1.65}"></span></dd></dl> <p>Plugging this into the equation above, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {hS}=1.65(D)\tau _{c}*}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>S</mi> </mrow> <mo>=</mo> <mn>1.65</mn> <mo stretchy="false">(</mo> <mi>D</mi> <mo stretchy="false">)</mo> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {hS}=1.65(D)\tau _{c}*}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/debe3bb6d0f54cd30a45a1cf94e9d930b2672d68" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.927ex; height:2.843ex;" alt="{\displaystyle {hS}=1.65(D)\tau _{c}*}"></span>.</dd></dl> <p>For the Shield's criterion of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{c}*=0.06}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>∗</mo> <mo>=</mo> <mn>0.06</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{c}*=0.06}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb960db8e82c29e6aa3d5da7f69ef0523353ea6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.355ex; height:2.509ex;" alt="{\displaystyle \tau _{c}*=0.06}"></span>. 0.06 * 1.65 = 0.099, which is well within standard margins of error of 0.1. Therefore, for a uniform bed, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {hS}={0.1(D)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>S</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0.1</mn> <mo stretchy="false">(</mo> <mi>D</mi> <mo stretchy="false">)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {hS}={0.1(D)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cdb0204a68d70c7db0d9f1b09b3f37dae95aa097" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.642ex; height:2.843ex;" alt="{\displaystyle {hS}={0.1(D)}}"></span>.</dd></dl> <p>For these situations, the product of the depth and slope of the flow should be 10% of the diameter of the median grain diameter. </p><p>The mixed-grain-size bed value is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{c}*=0.03}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>∗</mo> <mo>=</mo> <mn>0.03</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{c}*=0.03}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/515fe7f233622c3ad7b07a2523d0891cbdbe38d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.355ex; height:2.509ex;" alt="{\displaystyle \tau _{c}*=0.03}"></span>, which is supported by more recent research as being more broadly applicable because most natural streams have mixed grain sizes.<sup id="cite_ref-Parker1990_18-1" class="reference"><a href="#cite_note-Parker1990-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> If this value is used, and D is changed to D_50 ("50" for the 50th percentile, or the median grain size, as an appropriate value for a mixed-grain-size bed), the equation becomes: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {hS}={0.05(D_{50})}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>S</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0.05</mn> <mo stretchy="false">(</mo> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>50</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {hS}={0.05(D_{50})}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/17e5f8bdb6e11ffb3c267a7ee9a703ce5db4c01a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.681ex; height:2.843ex;" alt="{\displaystyle {hS}={0.05(D_{50})}}"></span></dd></dl> <p>Which means that the depth times the slope should be about 5% of the median grain diameter in the case of a mixed-grain-size bed. </p> <div class="mw-heading mw-heading2"><h2 id="Modes_of_entrainment">Modes of entrainment</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=20" title="Edit section: Modes of entrainment"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The sediments entrained in a flow can be transported along the bed as <a href="/wiki/Bed_load" title="Bed load">bed load</a> in the form of sliding and rolling grains, or in suspension as <a href="/wiki/Suspended_load" title="Suspended load">suspended load</a> advected by the main flow.<sup id="cite_ref-Chanson_16-1" class="reference"><a href="#cite_note-Chanson-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> Some sediment materials may also come from the upstream reaches and be carried downstream in the form of <a href="/wiki/Wash_load" title="Wash load">wash load</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Rouse_number">Rouse number</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=21" title="Edit section: Rouse number"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The location in the flow in which a particle is entrained is determined by the <a href="/wiki/Rouse_number" title="Rouse number">Rouse number</a>, which is determined by the density <i>ρ</i><sub>s</sub> and diameter <i>d</i> of the sediment particle, and the density <i>ρ</i> and kinematic viscosity <i>ν</i> of the fluid, determine in which part of the flow the sediment particle will be carried.<sup id="cite_ref-whipple_sed_trans_19-0" class="reference"><a href="#cite_note-whipple_sed_trans-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P={\frac {w_{s}}{\kappa u_{\ast }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mrow> <mi>κ</mi> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P={\frac {w_{s}}{\kappa u_{\ast }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/14739bbc9b5c016b3b1b0069baed7b07f1df1832" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.886ex; margin-bottom: -0.286ex; width:9.403ex; height:5.009ex;" alt="{\displaystyle P={\frac {w_{s}}{\kappa u_{\ast }}}}"></span></dd></dl> <p>Here, the Rouse number is given by <i>P</i>. The term in the numerator is the (downwards) sediment the sediment <a href="/wiki/Terminal_velocity" title="Terminal velocity">settling velocity</a> <i>w</i><sub>s</sub>, which is discussed below. The upwards velocity on the grain is given as a product of the <a href="/wiki/Von_K%C3%A1rm%C3%A1n_constant" title="Von Kármán constant">von Kármán constant</a>, <i>κ</i> = 0.4, and the <a href="/wiki/Shear_velocity" title="Shear velocity">shear velocity</a>, <i>u</i><sub>∗</sub>. </p><p>The following table gives the approximate required Rouse numbers for transport as <a href="/wiki/Bed_load" title="Bed load">bed load</a>, <a href="/wiki/Suspended_load" title="Suspended load">suspended load</a>, and <a href="/wiki/Wash_load" title="Wash load">wash load</a>.<sup id="cite_ref-whipple_sed_trans_19-1" class="reference"><a href="#cite_note-whipple_sed_trans-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-moore_loose_ends_20-0" class="reference"><a href="#cite_note-moore_loose_ends-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p> <table class="wikitable"> <tbody><tr> <th>Mode of Transport </th> <th>Rouse Number </th></tr> <tr> <td>Initiation of motion </td> <td>>7.5 </td></tr> <tr> <td><a href="/wiki/Bed_load" title="Bed load">Bed load</a> </td> <td>>2.5, <7.5 </td></tr> <tr> <td><a href="/wiki/Suspended_load" title="Suspended load">Suspended load</a>: 50% Suspended </td> <td>>1.2, <2.5 </td></tr> <tr> <td><a href="/wiki/Suspended_load" title="Suspended load">Suspended load</a>: 100% Suspended </td> <td>>0.8, <1.2 </td></tr> <tr> <td><a href="/wiki/Wash_load" title="Wash load">Wash load</a> </td> <td><0.8 </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Settling_velocity">Settling velocity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=22" title="Edit section: Settling velocity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Settling_velocity" class="mw-redirect" title="Settling velocity">Settling velocity</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Stokes_sphere.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Stokes_sphere.svg/220px-Stokes_sphere.svg.png" decoding="async" width="220" height="317" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Stokes_sphere.svg/330px-Stokes_sphere.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Stokes_sphere.svg/440px-Stokes_sphere.svg.png 2x" data-file-width="403" data-file-height="580" /></a><figcaption>Streamlines around a sphere falling through a fluid. This illustration is accurate for <a href="/wiki/Laminar_flow" title="Laminar flow">laminar flow</a>, in which the particle <a href="/wiki/Reynolds_number" title="Reynolds number">Reynolds number</a> is small. This is typical for small particles falling through a viscous fluid; larger particles would result in the creation of a <a href="/wiki/Turbulence" title="Turbulence">turbulent</a> wake.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Modeled_Sediment_Trajectories_(1).png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Modeled_Sediment_Trajectories_%281%29.png/220px-Modeled_Sediment_Trajectories_%281%29.png" decoding="async" width="220" height="141" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Modeled_Sediment_Trajectories_%281%29.png/330px-Modeled_Sediment_Trajectories_%281%29.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Modeled_Sediment_Trajectories_%281%29.png/440px-Modeled_Sediment_Trajectories_%281%29.png 2x" data-file-width="2330" data-file-height="1497" /></a><figcaption>For particles with a small settling velocity, diffusion will increase the complexity of the particle's path to the bottom and the time it takes to settle compared to particles with high settling velocities.</figcaption></figure> <p>The settling velocity (also called the "fall velocity" or "<a href="/wiki/Terminal_velocity" title="Terminal velocity">terminal velocity</a>") is a function of the particle <a href="/wiki/Reynolds_number" title="Reynolds number">Reynolds number</a>. Generally, for small particles (laminar approximation), it can be calculated with <a href="/wiki/Stokes%27_Law" class="mw-redirect" title="Stokes' Law">Stokes' Law</a>. For larger particles (turbulent particle Reynolds numbers), fall velocity is calculated with the turbulent <a href="/wiki/Drag_(physics)" title="Drag (physics)">drag</a> law. <a href="/wiki/William_E._Dietrich" title="William E. Dietrich">Dietrich</a> (1982) compiled a large amount of published data to which he empirically fit settling velocity curves.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> Ferguson and Church (2006) analytically combined the expressions for Stokes flow and a turbulent drag law into a single equation that works for all sizes of sediment, and successfully tested it against the data of Dietrich.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> Their equation is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w_{s}={\frac {RgD^{2}}{C_{1}\nu +(0.75C_{2}RgD^{3})^{(0.5)}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>R</mi> <mi>g</mi> <msup> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mi>ν</mi> <mo>+</mo> <mo stretchy="false">(</mo> <mn>0.75</mn> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi>R</mi> <mi>g</mi> <msup> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>0.5</mn> <mo stretchy="false">)</mo> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w_{s}={\frac {RgD^{2}}{C_{1}\nu +(0.75C_{2}RgD^{3})^{(0.5)}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e1065d4b7ce15f1a230eb3cd0d22ae65e46360da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:31.522ex; height:6.676ex;" alt="{\displaystyle w_{s}={\frac {RgD^{2}}{C_{1}\nu +(0.75C_{2}RgD^{3})^{(0.5)}}}}"></span>.</dd></dl> <p>In this equation <i>w<sub>s</sub></i> is the sediment settling velocity, <i>g</i> is acceleration due to gravity, and <i>D</i> is mean sediment diameter. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }"></span> is the <a href="/wiki/Kinematic_viscosity" class="mw-redirect" title="Kinematic viscosity">kinematic viscosity</a> of <a href="/wiki/Water" title="Water">water</a>, which is approximately 1.0 x 10<sup>−6</sup> m<sup>2</sup>/s for water at 20 °C. </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/babf569931f1a7b5182b9bec51873c2f5692fbb8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.716ex; height:2.509ex;" alt="{\displaystyle C_{1}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ec545f7870665e1028b7492746848d149878808" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.716ex; height:2.509ex;" alt="{\displaystyle C_{2}}"></span> are constants related to the shape and smoothness of the grains. </p> <table class="wikitable"> <tbody><tr> <th>Constant </th> <th>Smooth Spheres </th> <th>Natural Grains: Sieve Diameters </th> <th>Natural Grains: Nominal Diameters </th> <th>Limit for Ultra-Angular Grains </th></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/babf569931f1a7b5182b9bec51873c2f5692fbb8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.716ex; height:2.509ex;" alt="{\displaystyle C_{1}}"></span> </td> <td>18 </td> <td>18 </td> <td>20 </td> <td>24 </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ec545f7870665e1028b7492746848d149878808" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.716ex; height:2.509ex;" alt="{\displaystyle C_{2}}"></span> </td> <td>0.4 </td> <td>1.0 </td> <td>1.1 </td> <td>1.2 </td></tr></tbody></table> <p>The expression for fall velocity can be simplified so that it can be solved only in terms of <i>D</i>. We use the sieve diameters for natural grains, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g=9.8}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> <mo>=</mo> <mn>9.8</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g=9.8}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f73f08bbbd1e7ebb09ff24db591f015c8cc063df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.186ex; height:2.509ex;" alt="{\displaystyle g=9.8}"></span>, and values given above for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span>. From these parameters, the fall velocity is given by the expression: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w_{s}={\frac {16.17D^{2}}{1.8\cdot 10^{-5}+(12.1275D^{3})^{(0.5)}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>16.17</mn> <msup> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>1.8</mn> <mo>⋅</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>5</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <mn>12.1275</mn> <msup> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>0.5</mn> <mo stretchy="false">)</mo> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w_{s}={\frac {16.17D^{2}}{1.8\cdot 10^{-5}+(12.1275D^{3})^{(0.5)}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/02c548f6326c8dc780c19ef38b6adf8b84cf9767" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:34.773ex; height:6.676ex;" alt="{\displaystyle w_{s}={\frac {16.17D^{2}}{1.8\cdot 10^{-5}+(12.1275D^{3})^{(0.5)}}}}"></span></dd></dl> <p>Alternatively, settling velocity for a particle of sediment can be derived using <a href="/wiki/Stokes%27_law" title="Stokes' law">Stokes Law</a> assuming quiescent (or still) fluid in <a href="/wiki/Steady_state" title="Steady state">steady state</a>. The resulting formulation for settling velocity is, </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\displaystyle w_{s}={\frac {g~({\frac {\rho _{s}-\rho }{\rho }})~d_{sed}^{2}}{18\nu }}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>g</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>−</mo> <mi>ρ</mi> </mrow> <mi>ρ</mi> </mfrac> </mrow> <mo stretchy="false">)</mo> <mtext> </mtext> <msubsup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mi>e</mi> <mi>d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> <mrow> <mn>18</mn> <mi>ν</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\displaystyle w_{s}={\frac {g~({\frac {\rho _{s}-\rho }{\rho }})~d_{sed}^{2}}{18\nu }}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/11151dfc9f9dd0c082a63761a1c0060100203504" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:19.778ex; height:6.843ex;" alt="{\displaystyle {\displaystyle w_{s}={\frac {g~({\frac {\rho _{s}-\rho }{\rho }})~d_{sed}^{2}}{18\nu }}},}"></span> </p> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Settling_velocity.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Settling_velocity.png/352px-Settling_velocity.png" decoding="async" width="352" height="264" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Settling_velocity.png/528px-Settling_velocity.png 1.5x, //upload.wikimedia.org/wikipedia/commons/8/80/Settling_velocity.png 2x" data-file-width="640" data-file-height="480" /></a><figcaption>A plot showing the relationship between sediment particle diameter and the Stokes settling velocity</figcaption></figure> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3556280e66fe2c0d0140df20935a6f057381d77" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.116ex; height:2.009ex;" alt="{\displaystyle g}"></span> is the <a href="/wiki/Gravitational_constant" title="Gravitational constant">gravitational constant</a>; <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{s}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{s}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/93e930969b2a38890057fd45843b5d18beb0bece" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.205ex; height:2.176ex;" alt="{\displaystyle \rho _{s}}"></span> is the density of the sediment; <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span> is the density of <a href="/wiki/Water" title="Water">water</a>; <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d_{sed}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mi>e</mi> <mi>d</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d_{sed}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69640a2a162f8d9ba3b28c34d36ee918c7561bd0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.838ex; height:2.509ex;" alt="{\displaystyle d_{sed}}"></span> is the sediment particle diameter (commonly assumed to be the median particle diameter, often referred to as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d_{50}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>50</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d_{50}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d872f5c7391b5cfffaea1c4bcf55298bf635bf31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.085ex; height:2.509ex;" alt="{\displaystyle d_{50}}"></span> in field studies); and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }"></span> is the molecular viscosity of water. The Stokes settling velocity can be thought of as the terminal velocity resulting from balancing a particle's buoyant force (proportional to the cross-sectional area) with the gravitational force (proportional to the mass). Small particles will have a slower settling velocity than heavier particles, as seen in the figure. This has implications for many aspects of sediment transport, for example, how far downstream a particle might be advected in a river. </p> <div class="mw-heading mw-heading2"><h2 id="Hjulström–Sundborg_diagram"><span id="Hjulstr.C3.B6m.E2.80.93Sundborg_diagram"></span>Hjulström–Sundborg diagram</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=23" title="Edit section: Hjulström–Sundborg diagram"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Hjulstr%C3%B6m_curve" title="Hjulström curve">Hjulström curve</a></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Hjulstr%C3%B6ms_diagram_en.PNG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Hjulstr%C3%B6ms_diagram_en.PNG/300px-Hjulstr%C3%B6ms_diagram_en.PNG" decoding="async" width="300" height="218" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Hjulstr%C3%B6ms_diagram_en.PNG/450px-Hjulstr%C3%B6ms_diagram_en.PNG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/60/Hjulstr%C3%B6ms_diagram_en.PNG/600px-Hjulstr%C3%B6ms_diagram_en.PNG 2x" data-file-width="744" data-file-height="540" /></a><figcaption>The <a href="/wiki/Logarithmic_scale" title="Logarithmic scale">logarithmic</a> Hjulström curve</figcaption></figure> <p>In 1935, <a href="/wiki/Filip_Hjulstr%C3%B6m" title="Filip Hjulström">Filip Hjulström</a> created the <a href="/wiki/Hjulstr%C3%B6m_curve" title="Hjulström curve">Hjulström curve</a>, a graph which shows the relationship between the size of sediment and the velocity required to erode (lift it), transport it, or deposit it.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> The graph is <a href="/wiki/Logarithmic_scale" title="Logarithmic scale">logarithmic</a>. </p><p><a href="/wiki/%C3%85ke_Sundborg" title="Åke Sundborg">Åke Sundborg</a> later modified the Hjulström curve to show separate curves for the movement threshold corresponding to several water depths, as is necessary if the flow velocity rather than the boundary shear stress (as in the Shields diagram) is used for the flow strength.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p><p>This curve has no more than a historical value nowadays, although its simplicity is still attractive. Among the drawbacks of this curve are that it does not take the water depth into account and more importantly, that it does not show that sedimentation is caused by flow velocity <i>deceleration</i> and erosion is caused by flow <i>acceleration</i>. The dimensionless Shields diagram is now unanimously accepted for initiation of sediment motion in rivers. </p> <div class="mw-heading mw-heading2"><h2 id="Transport_rate">Transport rate</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=24" title="Edit section: Transport rate"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Stream_Load.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Stream_Load.gif/500px-Stream_Load.gif" decoding="async" width="500" height="268" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/9/9c/Stream_Load.gif 1.5x" data-file-width="686" data-file-height="368" /></a><figcaption>A schematic diagram of where the different types of sediment load are carried in the flow. <a href="/wiki/Dissolved_load" title="Dissolved load">Dissolved load</a> is not sediment: it is composed of disassociated <a href="/wiki/Ion" title="Ion">ions</a> moving along with the flow. It may, however, constitute a significant proportion (often several percent, but occasionally greater than half) of the total amount of material being transported by the stream.</figcaption></figure> <p>Formulas to calculate sediment transport rate exist for sediment moving in several different parts of the flow. These formulas are often segregated into <a href="/wiki/Bed_load" title="Bed load">bed load</a>, <a href="/wiki/Suspended_load" title="Suspended load">suspended load</a>, and <a href="/wiki/Wash_load" title="Wash load">wash load</a>. They may sometimes also be segregated into <a href="/wiki/Bed_material_load" title="Bed material load">bed material load</a> and wash load. </p> <div class="mw-heading mw-heading3"><h3 id="Bed_load">Bed load</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=25" title="Edit section: Bed load"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Bed load moves by rolling, sliding, and hopping (or <a href="/wiki/Saltation_(geology)" title="Saltation (geology)">saltating</a>) over the bed, and moves at a small fraction of the fluid flow velocity. Bed load is generally thought to constitute 5–10% of the total sediment load in a stream, making it less important in terms of mass balance. However, the <a href="/wiki/Bed_material_load" title="Bed material load">bed material load</a> (the bed load plus the portion of the suspended load which comprises material derived from the bed) is often dominated by bed load, especially in gravel-bed rivers. This bed material load is the only part of the sediment load that actively interacts with the bed. As the bed load is an important component of that, it plays a major role in controlling the morphology of the channel. </p><p>Bed load transport rates are usually expressed as being related to excess dimensionless shear stress raised to some power. Excess dimensionless shear stress is a nondimensional measure of bed shear stress about the threshold for motion. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (\tau _{b}^{*}-\tau _{c}^{*})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msubsup> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\tau _{b}^{*}-\tau _{c}^{*})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7894ae36296de038425db48dd4f0cbfc86a9b204" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:9.274ex; height:3.009ex;" alt="{\displaystyle (\tau _{b}^{*}-\tau _{c}^{*})}"></span>,</dd></dl> <p>Bed load transport rates may also be given by a ratio of bed shear stress to critical shear stress, which is equivalent in both the dimensional and nondimensional cases. This ratio is called the "transport stage" <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (T_{s}{\text{ or }}\phi )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mtext> or </mtext> </mrow> <mi>ϕ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (T_{s}{\text{ or }}\phi )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/13ee6007c8f36d6b5f4a8796c5ed0f5346931c59" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.791ex; height:2.843ex;" alt="{\displaystyle (T_{s}{\text{ or }}\phi )}"></span> and is an important in that it shows bed shear stress as a multiple of the value of the criterion for the initiation of motion. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{s}=\phi ={\frac {\tau _{b}}{\tau _{c}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mi>ϕ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{s}=\phi ={\frac {\tau _{b}}{\tau _{c}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d2b3f9ea48be96d4695d6a4e392898a81cc3f9a0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:12.74ex; height:5.009ex;" alt="{\displaystyle T_{s}=\phi ={\frac {\tau _{b}}{\tau _{c}}}}"></span></dd></dl> <p>When used for sediment transport formulae, this ratio is typically raised to a power. </p><p>The majority of the published relations for bedload transport are given in dry sediment weight per unit channel width, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> ("<a href="/wiki/Breadth" class="mw-redirect" title="Breadth">breadth</a>"): </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q_{s}={\frac {Q_{s}}{b}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mi>b</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{s}={\frac {Q_{s}}{b}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ea44b188340b4bc8c0af2e954af6d69fcb7aa27b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.817ex; height:5.509ex;" alt="{\displaystyle q_{s}={\frac {Q_{s}}{b}}}"></span>.</dd></dl> <p>Due to the difficulty of estimating bed load transport rates, these equations are typically only suitable for the situations for which they were designed. </p> <div class="mw-heading mw-heading4"><h4 id="Notable_bed_load_transport_formulae">Notable bed load transport formulae</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=26" title="Edit section: Notable bed load transport formulae"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading5"><h5 id="Meyer-Peter_Müller_and_derivatives"><span id="Meyer-Peter_M.C3.BCller_and_derivatives"></span>Meyer-Peter Müller and derivatives</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=27" title="Edit section: Meyer-Peter Müller and derivatives"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The transport formula of Meyer-Peter and Müller, originally developed in 1948,<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> was designed for well-<a href="/wiki/Sorting_(sediment)" title="Sorting (sediment)">sorted</a> <a href="/wiki/Particle_size_(grain_size)" class="mw-redirect" title="Particle size (grain size)">fine</a> <a href="/wiki/Gravel" title="Gravel">gravel</a> at a transport stage of about 8.<sup id="cite_ref-whipple_sed_trans_19-2" class="reference"><a href="#cite_note-whipple_sed_trans-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> The formula uses the above nondimensionalization for shear stress,<sup id="cite_ref-whipple_sed_trans_19-3" class="reference"><a href="#cite_note-whipple_sed_trans-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau *={\frac {\tau }{(\rho _{s}-\rho )(g)(D)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> <mo>∗</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>τ</mi> <mrow> <mo stretchy="false">(</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>−</mo> <mi>ρ</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>g</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>D</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau *={\frac {\tau }{(\rho _{s}-\rho )(g)(D)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ccc59604ae3aec4fa3be925f34f72e7a8d1392c6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:21.015ex; height:5.509ex;" alt="{\displaystyle \tau *={\frac {\tau }{(\rho _{s}-\rho )(g)(D)}}}"></span>,</dd></dl> <p>and <a href="/wiki/Hans_Albert_Einstein" title="Hans Albert Einstein">Hans Einstein's</a> nondimensionalization for sediment volumetric discharge per unit width<sup id="cite_ref-whipple_sed_trans_19-4" class="reference"><a href="#cite_note-whipple_sed_trans-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q_{s}*={\frac {q_{s}}{D{\sqrt {{\frac {\rho _{s}-\rho }{\rho }}gD}}}}={\frac {q_{s}}{Re_{p}\nu }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>∗</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mrow> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>−</mo> <mi>ρ</mi> </mrow> <mi>ρ</mi> </mfrac> </mrow> <mi>g</mi> <mi>D</mi> </msqrt> </mrow> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mrow> <mi>R</mi> <msub> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mi>ν</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{s}*={\frac {q_{s}}{D{\sqrt {{\frac {\rho _{s}-\rho }{\rho }}gD}}}}={\frac {q_{s}}{Re_{p}\nu }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c214dc5d709218b4dba34bf0aba2b259bc360c96" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.671ex; width:28.104ex; height:7.676ex;" alt="{\displaystyle q_{s}*={\frac {q_{s}}{D{\sqrt {{\frac {\rho _{s}-\rho }{\rho }}gD}}}}={\frac {q_{s}}{Re_{p}\nu }}}"></span>.</dd></dl> <p>Their formula reads: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q_{s}*=8\left(\tau *-\tau *_{c}\right)^{3/2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>∗</mo> <mo>=</mo> <mn>8</mn> <msup> <mrow> <mo>(</mo> <mrow> <mi>τ</mi> <mo>∗</mo> <mo>−</mo> <mi>τ</mi> <msub> <mo>∗</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{s}*=8\left(\tau *-\tau *_{c}\right)^{3/2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ae0599a795a9f19b32e83e5ba842a0fb66b7492" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.485ex; height:3.509ex;" alt="{\displaystyle q_{s}*=8\left(\tau *-\tau *_{c}\right)^{3/2}}"></span>.<sup id="cite_ref-whipple_sed_trans_19-5" class="reference"><a href="#cite_note-whipple_sed_trans-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup></dd></dl> <p>Their experimentally determined value for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau *_{c}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> <msub> <mo>∗</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau *_{c}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49fde89acb808672f65920196f5c89a0bdc6b0f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.309ex; height:2.009ex;" alt="{\displaystyle \tau *_{c}}"></span> is 0.047, and is the third commonly used value for this (in addition to Parker's 0.03 and Shields' 0.06). </p><p>Because of its broad use, some revisions to the formula have taken place over the years that show that the coefficient on the left ("8" above) is a function of the transport stage:<sup id="cite_ref-whipple_sed_trans_19-6" class="reference"><a href="#cite_note-whipple_sed_trans-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-f-l_26-0" class="reference"><a href="#cite_note-f-l-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-cheng_27-0" class="reference"><a href="#cite_note-cheng-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-wilson_28-0" class="reference"><a href="#cite_note-wilson-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{s}\approx 2\rightarrow q_{s}*=5.7\left(\tau *-0.047\right)^{3/2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>≈</mo> <mn>2</mn> <mo stretchy="false">→</mo> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>∗</mo> <mo>=</mo> <mn>5.7</mn> <msup> <mrow> <mo>(</mo> <mrow> <mi>τ</mi> <mo>∗</mo> <mo>−</mo> <mn>0.047</mn> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{s}\approx 2\rightarrow q_{s}*=5.7\left(\tau *-0.047\right)^{3/2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf1f9862128855e9a9e96be1301bd1168edd3566" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:34.518ex; height:3.509ex;" alt="{\displaystyle T_{s}\approx 2\rightarrow q_{s}*=5.7\left(\tau *-0.047\right)^{3/2}}"></span><sup id="cite_ref-f-l_26-1" class="reference"><a href="#cite_note-f-l-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{s}\approx 100\rightarrow q_{s}*=12.1\left(\tau *-0.047\right)^{3/2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>≈</mo> <mn>100</mn> <mo stretchy="false">→</mo> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>∗</mo> <mo>=</mo> <mn>12.1</mn> <msup> <mrow> <mo>(</mo> <mrow> <mi>τ</mi> <mo>∗</mo> <mo>−</mo> <mn>0.047</mn> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{s}\approx 100\rightarrow q_{s}*=12.1\left(\tau *-0.047\right)^{3/2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5fa79b011deec0bd2cc7a55207967ff300a1cfc8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:38.005ex; height:3.509ex;" alt="{\displaystyle T_{s}\approx 100\rightarrow q_{s}*=12.1\left(\tau *-0.047\right)^{3/2}}"></span><sup id="cite_ref-cheng_27-1" class="reference"><a href="#cite_note-cheng-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-wilson_28-1" class="reference"><a href="#cite_note-wilson-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup></dd></dl> <p>The variations in the coefficient were later generalized as a function of dimensionless shear stress:<sup id="cite_ref-whipple_sed_trans_19-7" class="reference"><a href="#cite_note-whipple_sed_trans-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-wiberg_smith_29-0" class="reference"><a href="#cite_note-wiberg_smith-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{cases}q_{s}*=\alpha _{s}\left(\tau *-\tau _{c}*\right)^{n}\\n={\frac {3}{2}}\\\alpha _{s}=1.6\ln \left(\tau *\right)+9.8\approx 9.64\tau *^{0.166}\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>∗</mo> <mo>=</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mrow> <mi>τ</mi> <mo>∗</mo> <mo>−</mo> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>∗</mo> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mtd> </mtr> <mtr> <mtd> <mi>n</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mn>1.6</mn> <mi>ln</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mi>τ</mi> <mo>∗</mo> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mn>9.8</mn> <mo>≈</mo> <mn>9.64</mn> <mi>τ</mi> <msup> <mo>∗</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0.166</mn> </mrow> </msup> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{cases}q_{s}*=\alpha _{s}\left(\tau *-\tau _{c}*\right)^{n}\\n={\frac {3}{2}}\\\alpha _{s}=1.6\ln \left(\tau *\right)+9.8\approx 9.64\tau *^{0.166}\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b5aae0ecdd1800d332776a0e2acc38f81d42d621" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.171ex; width:37.266ex; height:9.509ex;" alt="{\displaystyle {\begin{cases}q_{s}*=\alpha _{s}\left(\tau *-\tau _{c}*\right)^{n}\\n={\frac {3}{2}}\\\alpha _{s}=1.6\ln \left(\tau *\right)+9.8\approx 9.64\tau *^{0.166}\end{cases}}}"></span><sup id="cite_ref-wiberg_smith_29-1" class="reference"><a href="#cite_note-wiberg_smith-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup></dd></dl> <div class="mw-heading mw-heading5"><h5 id="Wilcock_and_Crowe">Wilcock and Crowe</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=28" title="Edit section: Wilcock and Crowe"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 2003, <a href="/w/index.php?title=Peter_Wilcock_(scientist)&action=edit&redlink=1" class="new" title="Peter Wilcock (scientist) (page does not exist)">Peter Wilcock</a> and Joanna Crowe (now Joanna Curran) published a sediment transport formula that works with multiple grain sizes across the sand and gravel range.<sup id="cite_ref-wilcock_crowe_30-0" class="reference"><a href="#cite_note-wilcock_crowe-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> Their formula works with surface grain size distributions, as opposed to older models which use subsurface grain size distributions (and thereby implicitly infer a surface grain <a href="/wiki/Sorting_(sediment)" title="Sorting (sediment)">sorting</a>). </p><p>Their expression is more complicated than the basic sediment transport rules (such as that of Meyer-Peter and Müller) because it takes into account multiple grain sizes: this requires consideration of reference shear stresses for each grain size, the fraction of the total sediment supply that falls into each grain size class, and a "hiding function". </p><p>The "hiding function" takes into account the fact that, while small grains are inherently more mobile than large grains, on a mixed-grain-size bed, they may be trapped in deep pockets between large grains. Likewise, a large grain on a bed of small particles will be stuck in a much smaller pocket than if it were on a bed of grains of the same size. In gravel-bed rivers, this can cause "equal mobility", in which small grains can move just as easily as large ones.<sup id="cite_ref-parker_etal_1982_31-0" class="reference"><a href="#cite_note-parker_etal_1982-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> As sand is added to the system, it moves away from the "equal mobility" portion of the hiding function to one in which grain size again matters.<sup id="cite_ref-wilcock_crowe_30-1" class="reference"><a href="#cite_note-wilcock_crowe-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p><p>Their model is based on the transport stage, or ratio of bed shear stress to critical shear stress for the initiation of grain motion. Because their formula works with several grain sizes simultaneously, they define the critical shear stress for each grain size class, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{c,D_{i}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>,</mo> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{c,D_{i}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c02b02447cf110dfd72ffe3fe19363373f1bcc2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.403ex; height:2.343ex;" alt="{\displaystyle \tau _{c,D_{i}}}"></span>, to be equal to a "reference shear stress", <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{ri}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{ri}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3239b78a40fccfcf3858fd6cbb0fc87303894996" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.557ex; height:2.009ex;" alt="{\displaystyle \tau _{ri}}"></span>.<sup id="cite_ref-wilcock_crowe_30-2" class="reference"><a href="#cite_note-wilcock_crowe-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p><p>They express their equations in terms of a dimensionless transport parameter, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W_{i}^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W_{i}^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/529019d6e7f633d4fb3b053ae0ab8916c8582d7f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.562ex; height:2.843ex;" alt="{\displaystyle W_{i}^{*}}"></span> (with the "<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle *}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle *}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e9972f426d9e07855984f73ee195a21dbc21755" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.079ex; margin-bottom: -0.25ex; width:1.162ex; height:1.509ex;" alt="{\displaystyle *}"></span>" indicating nondimensionality and the "<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97c3604a1807e9a8da4212370a9af82776197dbd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:0.8ex; height:1.676ex;" alt="{\displaystyle _{i}}"></span>" indicating that it is a function of grain size): </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W_{i}^{*}={\frac {Rgq_{bi}}{F_{i}u*^{3}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>R</mi> <mi>g</mi> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mi>u</mi> <msup> <mo>∗</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W_{i}^{*}={\frac {Rgq_{bi}}{F_{i}u*^{3}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa19d92af90e4937b4d52d47b35ef3d5b730eac2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:13.337ex; height:6.009ex;" alt="{\displaystyle W_{i}^{*}={\frac {Rgq_{bi}}{F_{i}u*^{3}}}}"></span></dd></dl> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q_{bi}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{bi}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1db97329b6679d3de36fcbd0f5b7d6333d5b599a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.542ex; height:2.009ex;" alt="{\displaystyle q_{bi}}"></span> is the volumetric bed load transport rate of size class <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> per unit channel width <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span>. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18f9a5ed62f131c8ad9acdf7f8539f103f1e0ec9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.294ex; height:2.509ex;" alt="{\displaystyle F_{i}}"></span> is the proportion of size class <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> that is present on the bed. </p><p>They came up with two equations, depending on the transport stage, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="{\displaystyle \phi }"></span>. For <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi <1.35}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> <mo><</mo> <mn>1.35</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi <1.35}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8e6e24195928f19a4c927914df4b7c747cc6e2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.618ex; height:2.509ex;" alt="{\displaystyle \phi <1.35}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W_{i}^{*}=0.002\phi ^{7.5}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>=</mo> <mn>0.002</mn> <msup> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>7.5</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W_{i}^{*}=0.002\phi ^{7.5}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2e8d49ffa35a81183850cf6a8e555c5ea9440308" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:15.676ex; height:3.343ex;" alt="{\displaystyle W_{i}^{*}=0.002\phi ^{7.5}}"></span></dd></dl> <p>and for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi \geq 1.35}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> <mo>≥</mo> <mn>1.35</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi \geq 1.35}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c42db783828df708f77ecf47f088a8d649fe66e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.618ex; height:2.509ex;" alt="{\displaystyle \phi \geq 1.35}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W_{i}^{*}=14\left(1-{\frac {0.894}{\phi ^{0.5}}}\right)^{4.5}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>=</mo> <mn>14</mn> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>0.894</mn> <msup> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0.5</mn> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4.5</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W_{i}^{*}=14\left(1-{\frac {0.894}{\phi ^{0.5}}}\right)^{4.5}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2545053fc807d5c215a7b4c4b6f846276e5ea10e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:24.876ex; height:6.676ex;" alt="{\displaystyle W_{i}^{*}=14\left(1-{\frac {0.894}{\phi ^{0.5}}}\right)^{4.5}}"></span>.</dd></dl> <p>This equation asymptotically reaches a constant value of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W_{i}^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W_{i}^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/529019d6e7f633d4fb3b053ae0ab8916c8582d7f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.562ex; height:2.843ex;" alt="{\displaystyle W_{i}^{*}}"></span> as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="{\displaystyle \phi }"></span> becomes large. </p> <div class="mw-heading mw-heading5"><h5 id="Wilcock_and_Kenworthy">Wilcock and Kenworthy</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=29" title="Edit section: Wilcock and Kenworthy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 2002, <a href="/w/index.php?title=Peter_Wilcock_(scientist)&action=edit&redlink=1" class="new" title="Peter Wilcock (scientist) (page does not exist)">Peter Wilcock</a> and T. A. Kenworthy, following Peter Wilcock (1998),<sup id="cite_ref-Wilcock_Science_32-0" class="reference"><a href="#cite_note-Wilcock_Science-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> published a sediment bed-load transport formula that works with only two sediments fractions, i.e. sand and gravel fractions.<sup id="cite_ref-wilcock_Kenworthy_33-0" class="reference"><a href="#cite_note-wilcock_Kenworthy-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> A mixed-sized sediment bed-load transport model using only two fractions offers practical advantages in terms of both computational and conceptual modeling by taking into account the nonlinear effects of sand presence in gravel beds on bed-load transport rate of both fractions. In fact, in the two-fraction bed load formula appears a new ingredient with respect to that of Meyer-Peter and Müller that is the proportion <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18f9a5ed62f131c8ad9acdf7f8539f103f1e0ec9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.294ex; height:2.509ex;" alt="{\displaystyle F_{i}}"></span> of fraction <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> on the bed surface where the subscript <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97c3604a1807e9a8da4212370a9af82776197dbd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:0.8ex; height:1.676ex;" alt="{\displaystyle _{i}}"></span> represents either the sand (s) or gravel (g) fraction. The proportion <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18f9a5ed62f131c8ad9acdf7f8539f103f1e0ec9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.294ex; height:2.509ex;" alt="{\displaystyle F_{i}}"></span>, as a function of sand content <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{s}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{s}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/34f933ad7a8dc310b3fa8e9f7b0b2558cba136db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.143ex; height:2.509ex;" alt="{\displaystyle f_{s}}"></span>, physically represents the relative influence of the mechanisms controlling sand and gravel transport, associated with the change from a clast-supported to matrix-supported gravel bed. Moreover, since <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{s}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{s}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/34f933ad7a8dc310b3fa8e9f7b0b2558cba136db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.143ex; height:2.509ex;" alt="{\displaystyle f_{s}}"></span> spans between 0 and 1, phenomena that vary with <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{s}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{s}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/34f933ad7a8dc310b3fa8e9f7b0b2558cba136db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.143ex; height:2.509ex;" alt="{\displaystyle f_{s}}"></span> include the relative size effects producing "hiding" of fine grains and "exposure" of coarse grains. The "hiding" effect takes into account the fact that, while small grains are inherently more mobile than large grains, on a mixed-grain-size bed, they may be trapped in deep pockets between large grains. Likewise, a large grain on a bed of small particles will be stuck in a much smaller pocket than if it were on a bed of grains of the same size, which the Meyer-Peter and Müller formula refers to. In gravel-bed rivers, this can cause "equal mobility", in which small grains can move just as easily as large ones.<sup id="cite_ref-parker_etal_1982_31-1" class="reference"><a href="#cite_note-parker_etal_1982-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> As sand is added to the system, it moves away from the "equal mobility" portion of the hiding function to one in which grain size again matters.<sup id="cite_ref-wilcock_Kenworthy_33-1" class="reference"><a href="#cite_note-wilcock_Kenworthy-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> </p><p>Their model is based on the transport stage, <i>i.e.</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="{\displaystyle \phi }"></span>, or ratio of bed shear stress to critical shear stress for the initiation of grain motion. Because their formula works with only two fractions simultaneously, they define the critical shear stress for each of the two grain size classes, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{ri}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{ri}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3239b78a40fccfcf3858fd6cbb0fc87303894996" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.557ex; height:2.009ex;" alt="{\displaystyle \tau _{ri}}"></span>, where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97c3604a1807e9a8da4212370a9af82776197dbd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:0.8ex; height:1.676ex;" alt="{\displaystyle _{i}}"></span> represents either the sand (s) or gravel (g) fraction. The critical shear stress that represents the incipient motion for each of the two fractions is consistent with established values in the limit of pure sand and gravel beds and shows a sharp change with increasing sand content over the transition from a clast- to matrix-supported bed.<sup id="cite_ref-wilcock_Kenworthy_33-2" class="reference"><a href="#cite_note-wilcock_Kenworthy-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> </p><p>They express their equations in terms of a dimensionless transport parameter, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W_{i}^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W_{i}^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/529019d6e7f633d4fb3b053ae0ab8916c8582d7f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.562ex; height:2.843ex;" alt="{\displaystyle W_{i}^{*}}"></span> (with the "<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle *}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle *}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e9972f426d9e07855984f73ee195a21dbc21755" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.079ex; margin-bottom: -0.25ex; width:1.162ex; height:1.509ex;" alt="{\displaystyle *}"></span>" indicating nondimensionality and the "<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97c3604a1807e9a8da4212370a9af82776197dbd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:0.8ex; height:1.676ex;" alt="{\displaystyle _{i}}"></span>" indicating that it is a function of grain size): </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W_{i}^{*}={\frac {Rgq_{bi}}{F_{i}u*^{3}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>R</mi> <mi>g</mi> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mi>u</mi> <msup> <mo>∗</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W_{i}^{*}={\frac {Rgq_{bi}}{F_{i}u*^{3}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa19d92af90e4937b4d52d47b35ef3d5b730eac2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:13.337ex; height:6.009ex;" alt="{\displaystyle W_{i}^{*}={\frac {Rgq_{bi}}{F_{i}u*^{3}}}}"></span></dd></dl> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q_{bi}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{bi}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1db97329b6679d3de36fcbd0f5b7d6333d5b599a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.542ex; height:2.009ex;" alt="{\displaystyle q_{bi}}"></span> is the volumetric bed load transport rate of size class <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> per unit channel width <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span>. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18f9a5ed62f131c8ad9acdf7f8539f103f1e0ec9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.294ex; height:2.509ex;" alt="{\displaystyle F_{i}}"></span> is the proportion of size class <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> that is present on the bed. </p><p>They came up with two equations, depending on the transport stage, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="{\displaystyle \phi }"></span>. For <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi <\phi ^{'}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> <mo><</mo> <msup> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi></mi> <mo>′</mo> </msup> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi <\phi ^{'}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/102061dbed9b7aff5a7f05cdffbc1443e27db1f6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.633ex; height:3.176ex;" alt="{\displaystyle \phi <\phi ^{'}}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W_{i}^{*}=0.002\phi ^{7.5}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>=</mo> <mn>0.002</mn> <msup> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>7.5</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W_{i}^{*}=0.002\phi ^{7.5}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2e8d49ffa35a81183850cf6a8e555c5ea9440308" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:15.676ex; height:3.343ex;" alt="{\displaystyle W_{i}^{*}=0.002\phi ^{7.5}}"></span></dd></dl> <p>and for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi \geq \phi ^{'}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> <mo>≥</mo> <msup> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi></mi> <mo>′</mo> </msup> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi \geq \phi ^{'}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd6f3f45e7d872d8aa5e6bb930a4d3f0f4221fbb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.633ex; height:3.176ex;" alt="{\displaystyle \phi \geq \phi ^{'}}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W_{i}^{*}=A\left(1-{\frac {\chi }{\phi ^{0.5}}}\right)^{4.5}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>=</mo> <mi>A</mi> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>χ</mi> <msup> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0.5</mn> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4.5</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W_{i}^{*}=A\left(1-{\frac {\chi }{\phi ^{0.5}}}\right)^{4.5}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b288b93531e6f4fd60e76372b1a23acefa3f33c5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:22.716ex; height:6.676ex;" alt="{\displaystyle W_{i}^{*}=A\left(1-{\frac {\chi }{\phi ^{0.5}}}\right)^{4.5}}"></span>.</dd></dl> <p>This equation asymptotically reaches a constant value of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W_{i}^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W_{i}^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/529019d6e7f633d4fb3b053ae0ab8916c8582d7f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.562ex; height:2.843ex;" alt="{\displaystyle W_{i}^{*}}"></span> as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="{\displaystyle \phi }"></span> becomes large and the symbols <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A,\phi ^{'},\chi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>,</mo> <msup> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi></mi> <mo>′</mo> </msup> </mrow> </msup> <mo>,</mo> <mi>χ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A,\phi ^{'},\chi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5aeecb11b64f060ce3d3d49246eb1898391b9fbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.415ex; height:3.176ex;" alt="{\displaystyle A,\phi ^{'},\chi }"></span> have the following values: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A=70,\phi ^{'}=1.19,\chi =0.908,{\text{laboratory}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mn>70</mn> <mo>,</mo> <msup> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi></mi> <mo>′</mo> </msup> </mrow> </msup> <mo>=</mo> <mn>1.19</mn> <mo>,</mo> <mi>χ</mi> <mo>=</mo> <mn>0.908</mn> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>laboratory</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=70,\phi ^{'}=1.19,\chi =0.908,{\text{laboratory}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74199c11c1b130c4c6f1d20917eff136f4c51919" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:40.045ex; height:3.176ex;" alt="{\displaystyle A=70,\phi ^{'}=1.19,\chi =0.908,{\text{laboratory}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A=115,\phi ^{'}=1.27,\chi =0.923,{\text{field}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mn>115</mn> <mo>,</mo> <msup> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi></mi> <mo>′</mo> </msup> </mrow> </msup> <mo>=</mo> <mn>1.27</mn> <mo>,</mo> <mi>χ</mi> <mo>=</mo> <mn>0.923</mn> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>field</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=115,\phi ^{'}=1.27,\chi =0.923,{\text{field}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0cfd5b25e27dd25ffa54dc88740ff474c700d404" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:34.993ex; height:3.176ex;" alt="{\displaystyle A=115,\phi ^{'}=1.27,\chi =0.923,{\text{field}}}"></span></dd></dl> <p>In order to apply the above formulation, it is necessary to specify the characteristic grain sizes <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{s}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{s}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d298c806ea05a75b31dd782bf7b362c169547ad3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.928ex; height:2.509ex;" alt="{\displaystyle D_{s}}"></span> for the sand portion and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{g}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{g}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6f5626aa4260303f293c7ebaa4786e38440557c9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.946ex; height:2.843ex;" alt="{\displaystyle D_{g}}"></span> for the gravel portion of the surface layer, the fractions <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{s}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{s}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5f8fe463c9e2d708fff2d0e450a73b8875313a3d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.498ex; height:2.509ex;" alt="{\displaystyle F_{s}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{g}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{g}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/03cf1bda064b272b4a9aff2baab298c67c3d7a38" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.516ex; height:2.843ex;" alt="{\displaystyle F_{g}}"></span> of sand and gravel, respectively in the surface layer, the submerged specific gravity of the sediment R and shear velocity associated with skin friction <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u_{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53f06376827f0e844992e08986763b37f6f771d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.293ex; margin-bottom: -0.379ex; width:2.384ex; height:2.009ex;" alt="{\displaystyle u_{*}}"></span> . </p> <div class="mw-heading mw-heading5"><h5 id="Kuhnle_et_al.">Kuhnle <i>et al.</i></h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=30" title="Edit section: Kuhnle et al."><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For the case in which sand fraction is transported by the current over and through an immobile gravel bed, Kuhnle <i>et al.</i>(2013),<sup id="cite_ref-Kuhnle_34-0" class="reference"><a href="#cite_note-Kuhnle-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> following the theoretical analysis done by Pellachini (2011),<sup id="cite_ref-Pellachini_35-0" class="reference"><a href="#cite_note-Pellachini-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> provides a new relationship for the bed load transport of the sand fraction when gravel particles remain at rest. It is worth mentioning that Kuhnle <i>et al.</i> (2013)<sup id="cite_ref-Kuhnle_34-1" class="reference"><a href="#cite_note-Kuhnle-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> applied the Wilcock and Kenworthy (2002)<sup id="cite_ref-wilcock_Kenworthy_33-3" class="reference"><a href="#cite_note-wilcock_Kenworthy-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> formula to their experimental data and found out that predicted bed load rates of sand fraction were about 10 times greater than measured and approached 1 as the sand elevation became near the top of the gravel layer.<sup id="cite_ref-Kuhnle_34-2" class="reference"><a href="#cite_note-Kuhnle-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> They, also, hypothesized that the mismatch between predicted and measured sand bed load rates is due to the fact that the bed shear stress used for the Wilcock and Kenworthy (2002)<sup id="cite_ref-wilcock_Kenworthy_33-4" class="reference"><a href="#cite_note-wilcock_Kenworthy-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> formula was larger than that available for transport within the gravel bed because of the sheltering effect of the gravel particles.<sup id="cite_ref-Kuhnle_34-3" class="reference"><a href="#cite_note-Kuhnle-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> To overcome this mismatch, following Pellachini (2011),<sup id="cite_ref-Pellachini_35-1" class="reference"><a href="#cite_note-Pellachini-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> they assumed that the variability of the bed shear stress available for the sand to be transported by the current would be some function of the so-called "Roughness Geometry Function" (RGF),<sup id="cite_ref-Nikora_36-0" class="reference"><a href="#cite_note-Nikora-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> which represents the gravel bed elevations distribution. Therefore, the sand bed load formula follows as:<sup id="cite_ref-Kuhnle_34-4" class="reference"><a href="#cite_note-Kuhnle-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q_{s}^{*}=2.29*10^{-5}A(z_{s})^{2.14}\left({\frac {\tau _{b}}{\tau _{cs}}}\right)^{3.49}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>=</mo> <mn>2.29</mn> <mo>∗</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>5</mn> </mrow> </msup> <mi>A</mi> <mo stretchy="false">(</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2.14</mn> </mrow> </msup> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mi>s</mi> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3.49</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{s}^{*}=2.29*10^{-5}A(z_{s})^{2.14}\left({\frac {\tau _{b}}{\tau _{cs}}}\right)^{3.49}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66161e3cd356fce3a38aca647220b0fcfdcfa499" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:35.156ex; height:6.676ex;" alt="{\displaystyle q_{s}^{*}=2.29*10^{-5}A(z_{s})^{2.14}\left({\frac {\tau _{b}}{\tau _{cs}}}\right)^{3.49}}"></span></dd></dl> <p>where </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q_{s}^{*}={\frac {q_{s}}{[(s-1)gD_{s}]^{0.5}\rho _{s}D_{s}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mrow> <mo stretchy="false">[</mo> <mo stretchy="false">(</mo> <mi>s</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mi>g</mi> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <msup> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0.5</mn> </mrow> </msup> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{s}^{*}={\frac {q_{s}}{[(s-1)gD_{s}]^{0.5}\rho _{s}D_{s}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0b941a46e531dce0d12e72663b1713e0b7c7abb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:25.775ex; height:5.676ex;" alt="{\displaystyle q_{s}^{*}={\frac {q_{s}}{[(s-1)gD_{s}]^{0.5}\rho _{s}D_{s}}}}"></span></dd></dl> <p>the subscript <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle _{s}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle _{s}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9cde2b6337649f8fa1fc0358c098e25b4736d0c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.003ex; height:1.343ex;" alt="{\displaystyle _{s}}"></span> refers to the sand fraction, s represents the ratio <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{s}/\rho _{w}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>w</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{s}/\rho _{w}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ec6ed8ac2889881e8406fff317919f1519d9619" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.979ex; height:2.843ex;" alt="{\displaystyle \rho _{s}/\rho _{w}}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{s}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{s}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/93e930969b2a38890057fd45843b5d18beb0bece" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.205ex; height:2.176ex;" alt="{\displaystyle \rho _{s}}"></span> is the sand fraction density, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A(z_{s})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo stretchy="false">(</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A(z_{s})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/89f8f1156435b099a3c7e0ad2749fea1e5ed9bf5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.637ex; height:2.843ex;" alt="{\displaystyle A(z_{s})}"></span> is the RGF as a function of the sand level <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z_{s}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z_{s}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/890b60b1fc36eae52dc9ca6f8a80cc9996853f7e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.084ex; height:2.009ex;" alt="{\displaystyle z_{s}}"></span> within the gravel bed, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{b}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{b}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/721b220270c8a21caf5bc857eb43133412b20f97" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.954ex; height:2.009ex;" alt="{\displaystyle \tau _{b}}"></span> is the bed shear stress available for sand transport and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{cs}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{cs}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/796ae45a28465729647f664a60fd1346a6828dee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.731ex; height:2.009ex;" alt="{\displaystyle \tau _{cs}}"></span> is the critical shear stress for incipient motion of the sand fraction, which was calculated graphically using the updated Shields-type relation of Miller <i>et al.</i>(1977)<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0" /> </mrow> <annotation encoding="application/x-tex">{\displaystyle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df4dcd61276328f7c7ec5bdc399b6e11114a2c68" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:0; height:0.343ex;" alt="{\displaystyle }"></span>.<sup id="cite_ref-Miller_37-0" class="reference"><a href="#cite_note-Miller-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Suspended_load">Suspended load</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=31" title="Edit section: Suspended load"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Suspended_load" title="Suspended load">Suspended load</a></div> <p>Suspended load is carried in the lower to middle parts of the flow, and moves at a large fraction of the mean flow velocity in the stream. </p><p>A common characterization of suspended sediment concentration in a flow is given by the Rouse Profile. This characterization works for the situation in which sediment concentration <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1882ba8f1dc60f0c68a642abb5af093c73910921" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.061ex; height:2.009ex;" alt="{\displaystyle c_{0}}"></span> at one particular elevation above the bed <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e72d1d86e86355892b39b8eb32b964834e113bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.135ex; height:2.009ex;" alt="{\displaystyle z_{0}}"></span> can be quantified. It is given by the expression: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {c_{s}}{c_{0}}}=\left[{\frac {z\left(h-z_{0}\right)}{z_{0}\left(h-z\right)}}\right]^{-P/\alpha }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <msup> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>z</mi> <mrow> <mo>(</mo> <mrow> <mi>h</mi> <mo>−</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mi>h</mi> <mo>−</mo> <mi>z</mi> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> <mo>]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>α</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {c_{s}}{c_{0}}}=\left[{\frac {z\left(h-z_{0}\right)}{z_{0}\left(h-z\right)}}\right]^{-P/\alpha }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/02d612f774bb3a3032da73ccee944e2c0868f228" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:23.505ex; height:7.009ex;" alt="{\displaystyle {\frac {c_{s}}{c_{0}}}=\left[{\frac {z\left(h-z_{0}\right)}{z_{0}\left(h-z\right)}}\right]^{-P/\alpha }}"></span></dd></dl> <p>Here, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf368e72c009decd9b6686ee84a375632e11de98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.088ex; height:1.676ex;" alt="{\displaystyle z}"></span> is the elevation above the bed, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{s}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{s}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75b83e050da28fa0d83e2aa786963805742ab756" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.01ex; height:2.009ex;" alt="{\displaystyle c_{s}}"></span> is the concentration of suspended sediment at that elevation, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b26be3e694314bc90c3215047e4a2010c6ee184a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.339ex; height:2.176ex;" alt="{\displaystyle h}"></span> is the flow depth, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span> is the Rouse number, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span> relates the eddy viscosity for momentum <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{m}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{m}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d4b81165d9cdc72a3cc30acf9bc34e81292268a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.648ex; height:2.509ex;" alt="{\displaystyle K_{m}}"></span> to the eddy diffusivity for sediment, which is approximately equal to one.<sup id="cite_ref-harris_sus_sed_38-0" class="reference"><a href="#cite_note-harris_sus_sed-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha ={\frac {K_{s}}{K_{m}}}\approx 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> </mfrac> </mrow> <mo>≈</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha ={\frac {K_{s}}{K_{m}}}\approx 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/613baa02d70d17b9027d6ff3cb073cfe1aca8c2b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:13.331ex; height:5.676ex;" alt="{\displaystyle \alpha ={\frac {K_{s}}{K_{m}}}\approx 1}"></span></dd></dl> <p>Experimental work has shown that <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span> ranges from 0.93 to 1.10 for sands and silts.<sup id="cite_ref-moore_sus_sed_39-0" class="reference"><a href="#cite_note-moore_sus_sed-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> </p><p>The Rouse profile characterizes sediment concentrations because the Rouse number includes both turbulent mixing and settling under the weight of the particles. Turbulent mixing results in the net motion of particles from regions of high concentrations to low concentrations. Because particles settle downward, for all cases where the particles are not neutrally buoyant or sufficiently light that this settling velocity is negligible, there is a net negative concentration gradient as one goes upward in the flow. The Rouse Profile therefore gives the concentration profile that provides a balance between turbulent mixing (net upwards) of sediment and the downwards settling velocity of each particle. </p> <div class="mw-heading mw-heading3"><h3 id="Bed_material_load">Bed material load</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=32" title="Edit section: Bed material load"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Bed material load comprises the bed load and the portion of the suspended load that is sourced from the bed. </p><p>Three common bed material transport relations are the "Ackers-White",<sup id="cite_ref-ackers-white_40-0" class="reference"><a href="#cite_note-ackers-white-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> "Engelund-Hansen", "Yang" formulae. The first is for <a href="/wiki/Sand" title="Sand">sand</a> to <a href="/wiki/Granule_(geology)" title="Granule (geology)">granule</a>-size gravel, and the second and third are for sand<sup id="cite_ref-bm_eval_41-0" class="reference"><a href="#cite_note-bm_eval-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> though Yang later expanded his formula to include fine gravel. That all of these formulae cover the sand-size range and two of them are exclusively for sand is that the sediment in sand-bed rivers is commonly moved simultaneously as bed and suspended load. </p> <div class="mw-heading mw-heading4"><h4 id="Engelund–Hansen"><span id="Engelund.E2.80.93Hansen"></span>Engelund–Hansen</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=33" title="Edit section: Engelund–Hansen"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The bed material load formula of Engelund and Hansen is the only one to not include some kind of critical value for the initiation of sediment transport. It reads: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q_{s}*={\frac {0.05}{c_{f}}}\tau *^{2.5}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>∗</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>0.05</mn> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mfrac> </mrow> <mi>τ</mi> <msup> <mo>∗</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2.5</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{s}*={\frac {0.05}{c_{f}}}\tau *^{2.5}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b17a652eca74af3ccf7c502b828157e1f519234" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:15.97ex; height:5.843ex;" alt="{\displaystyle q_{s}*={\frac {0.05}{c_{f}}}\tau *^{2.5}}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q_{s}*}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{s}*}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8867602cedc3d8ae451f9d031ff7856610cfb11e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.203ex; height:2.009ex;" alt="{\displaystyle q_{s}*}"></span> is the Einstein nondimensionalization for sediment volumetric discharge per unit width, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{f}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{f}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbd9627ee62d4ecd080c2331ff404bf08fa2e5f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.143ex; height:2.343ex;" alt="{\displaystyle c_{f}}"></span> is a friction factor, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau *}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau *}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df6ef55b609bc41060a8ff820c86e3f2458196e9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.364ex; height:1.676ex;" alt="{\displaystyle \tau *}"></span> is the Shields stress. The Engelund–Hansen formula is one of the few sediment transport formulae in which a threshold "critical shear stress" is absent. </p> <div class="mw-heading mw-heading3"><h3 id="Wash_load">Wash load</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=34" title="Edit section: Wash load"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Wash load is carried within the water column as part of the flow, and therefore moves with the mean velocity of main stream. Wash load concentrations are approximately uniform in the water column. This is described by the endmember case in which the Rouse number is equal to 0 (i.e. the settling velocity is far less than the turbulent mixing velocity), which leads to a prediction of a perfectly uniform vertical concentration profile of material. </p> <div class="mw-heading mw-heading3"><h3 id="Total_load">Total load</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=35" title="Edit section: Total load"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Some authors have attempted formulations for the total <a href="/wiki/Sediment" title="Sediment">sediment</a> load carried in water.<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> These formulas are designed largely for sand, as (depending on flow conditions) sand often can be carried as both bed load and suspended load in the same stream or shoreface. </p> <div class="mw-heading mw-heading2"><h2 id="Bed_load_sediment_mitigation_at_intake_structures">Bed load sediment mitigation at intake structures</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=36" title="Edit section: Bed load sediment mitigation at intake structures"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Riverside intake structures used in <a href="/wiki/Water_supply" title="Water supply">water supply</a>, <a href="/wiki/Canal" title="Canal">canal</a> diversions, and <a href="/wiki/Water_cooling" title="Water cooling">water cooling</a> can experience entrainment of bed load (sand-size) sediments. These entrained sediments produce multiple deleterious effects such as reduction or blockage of intake capacity, feedwater <a href="/wiki/Pump" title="Pump">pump</a> <a href="/wiki/Impeller" title="Impeller">impeller</a> damage or vibration, and result in sediment deposition in downstream pipelines and canals. Structures that modify local near-field secondary currents are useful to mitigate these effects and limit or prevent bed load sediment entry.<sup id="cite_ref-sediment_control_44-0" class="reference"><a href="#cite_note-sediment_control-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=37" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Sedimentology" title="Sedimentology">Sedimentology</a> – Study of natural sediments and their formation processes</li> <li><a href="/wiki/Exner_equation" title="Exner equation">Exner equation</a> – Law of sediment aggradation</li> <li><a href="/wiki/Hydrology" title="Hydrology">Hydrology</a> – Science of the movement, distribution, and quality of water on Earth</li> <li><a href="/wiki/Sediment_gravity_flow" title="Sediment gravity flow">Sediment gravity flow</a> – Sediment transport mechanism</li> <li><a href="/wiki/Stream_capacity" title="Stream capacity">Stream capacity</a> – Total amount of sediment a stream can transport</li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=38" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFAnderson1990" class="citation journal cs1">Anderson, R (1990). "Eolian ripples as examples of self-organization in geomorphological systems". <i>Earth-Science Reviews</i>. <b>29</b> (1–4): 77. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0012-8252%280%2990029-U">10.1016/0012-8252(0)90029-U</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Earth-Science+Reviews&rft.atitle=Eolian+ripples+as+examples+of+self-organization+in+geomorphological+systems&rft.volume=29&rft.issue=1%E2%80%934&rft.pages=77&rft.date=1990&rft_id=info%3Adoi%2F10.1016%2F0012-8252%280%2990029-U&rft.aulast=Anderson&rft.aufirst=R&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKocurekEwing2005" class="citation journal cs1">Kocurek, Gary; Ewing, Ryan C. (2005). "Aeolian dune field self-organization – implications for the formation of simple versus complex dune-field patterns". <i>Geomorphology</i>. <b>72</b> (1–4): 94. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2005Geomo..72...94K">2005Geomo..72...94K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.geomorph.2005.05.005">10.1016/j.geomorph.2005.05.005</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Geomorphology&rft.atitle=Aeolian+dune+field+self-organization+%E2%80%93+implications+for+the+formation+of+simple+versus+complex+dune-field+patterns&rft.volume=72&rft.issue=1%E2%80%934&rft.pages=94&rft.date=2005&rft_id=info%3Adoi%2F10.1016%2Fj.geomorph.2005.05.005&rft_id=info%3Abibcode%2F2005Geomo..72...94K&rft.aulast=Kocurek&rft.aufirst=Gary&rft.au=Ewing%2C+Ryan+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGoudie,_AMiddleton2001" class="citation journal cs1">Goudie, A; Middleton, N.J. (2001). "Saharan dust storms: nature and consequences". <i>Earth-Science Reviews</i>. <b>56</b> (1–4): 179. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2001ESRv...56..179G">2001ESRv...56..179G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0012-8252%2801%2900067-8">10.1016/S0012-8252(01)00067-8</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Earth-Science+Reviews&rft.atitle=Saharan+dust+storms%3A+nature+and+consequences&rft.volume=56&rft.issue=1%E2%80%934&rft.pages=179&rft.date=2001&rft_id=info%3Adoi%2F10.1016%2FS0012-8252%2801%2900067-8&rft_id=info%3Abibcode%2F2001ESRv...56..179G&rft.au=Goudie%2C+A&rft.au=Middleton%2C+N.J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://earthobservatory.nasa.gov/IOTD/view.php?id=6458">"Dust Storm Spreads Out of Gobi Desert"</a>. Earthobservatory.nasa.gov. 13 April 2006<span class="reference-accessdate">. Retrieved <span class="nowrap">2022-05-08</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Dust+Storm+Spreads+Out+of+Gobi+Desert&rft.pub=Earthobservatory.nasa.gov&rft.date=2006-04-13&rft_id=http%3A%2F%2Fearthobservatory.nasa.gov%2FIOTD%2Fview.php%3Fid%3D6458&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNeuendorfMehlJackson2011" class="citation book cs1">Neuendorf, Klaus K.E.; Mehl, James P. Jr; Jackson, Julia A., eds. (2011). <a rel="nofollow" class="external text" href="https://store.americangeosciences.org/glossary-of-geology-fifth-edition-revised.html"><i>Glossary of Geology</i></a> (5th revised ed.). Alexandria, Virginia: American Geological Institute. p. 800. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-642-06621-4" title="Special:BookSources/978-3-642-06621-4"><bdi>978-3-642-06621-4</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/751527782">751527782</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Glossary+of+Geology&rft.place=Alexandria%2C+Virginia&rft.pages=800&rft.edition=5th+revised&rft.pub=American+Geological+Institute&rft.date=2011&rft_id=info%3Aoclcnum%2F751527782&rft.isbn=978-3-642-06621-4&rft_id=https%3A%2F%2Fstore.americangeosciences.org%2Fglossary-of-geology-fifth-edition-revised.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://books.google.com/books?id=if-PaNVS7cAC&pg=PA84&dq=fluvioglacial+definition&lr=&ei=KaQrSpnHMIncygTF_fScBw">Wilson, W.E. & Moore, J.E. 2003. Glossary of Hydrology, American Geological Institute, Springer, 248pp.</a></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCharlton2008" class="citation book cs1">Charlton, Ro (2008). <span class="id-lock-limited" title="Free access subject to limited trial, subscription normally required"><a rel="nofollow" class="external text" href="https://archive.org/details/fundamentalsfluv00char"><i>Fundamentals of fluvial geomorphology</i></a></span>. London: Rutledge. p. <a rel="nofollow" class="external text" href="https://archive.org/details/fundamentalsfluv00char/page/n274">234</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-415-33454-9" title="Special:BookSources/978-0-415-33454-9"><bdi>978-0-415-33454-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamentals+of+fluvial+geomorphology&rft.place=London&rft.pages=234&rft.pub=Rutledge&rft.date=2008&rft.isbn=978-0-415-33454-9&rft.aulast=Charlton&rft.aufirst=Ro&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Ffundamentalsfluv00char&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWohl2014" class="citation book cs1">Wohl, Ellen (2014). <i>Rivers in the Landscape: Science and Management</i>. Wiley-Blackwell. p. 330. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-118-41489-7" title="Special:BookSources/978-1-118-41489-7"><bdi>978-1-118-41489-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Rivers+in+the+Landscape%3A+Science+and+Management&rft.pages=330&rft.pub=Wiley-Blackwell&rft.date=2014&rft.isbn=978-1-118-41489-7&rft.aulast=Wohl&rft.aufirst=Ellen&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAshtonMurrayArnault2001" class="citation journal cs1">Ashton, Andrew; Murray, A. Brad; Arnault, Olivier (2001). "Formation of coastline features by large-scale instabilities induced by high-angle waves". <i>Nature</i>. <b>414</b> (6861): 296–300. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2001Natur.414..296A">2001Natur.414..296A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F35104541">10.1038/35104541</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/11713526">11713526</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:205023325">205023325</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Formation+of+coastline+features+by+large-scale+instabilities+induced+by+high-angle+waves&rft.volume=414&rft.issue=6861&rft.pages=296-300&rft.date=2001&rft_id=info%3Adoi%2F10.1038%2F35104541&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A205023325%23id-name%3DS2CID&rft_id=info%3Apmid%2F11713526&rft_id=info%3Abibcode%2F2001Natur.414..296A&rft.aulast=Ashton&rft.aufirst=Andrew&rft.au=Murray%2C+A.+Brad&rft.au=Arnault%2C+Olivier&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRoeringKirchnerDietrich1999" class="citation journal cs1">Roering, Joshua J.; Kirchner, James W.; Dietrich, William E. (1999). <a rel="nofollow" class="external text" href="https://doi.org/10.1029%2F1998WR900090">"Evidence for nonlinear, diffusive sediment transport on hillslopes and implications for landscape morphology"</a>. <i>Water Resources Research</i>. <b>35</b> (3): 853. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1999WRR....35..853R">1999WRR....35..853R</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1029%2F1998WR900090">10.1029/1998WR900090</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Water+Resources+Research&rft.atitle=Evidence+for+nonlinear%2C+diffusive+sediment+transport+on+hillslopes+and+implications+for+landscape+morphology&rft.volume=35&rft.issue=3&rft.pages=853&rft.date=1999&rft_id=info%3Adoi%2F10.1029%2F1998WR900090&rft_id=info%3Abibcode%2F1999WRR....35..853R&rft.aulast=Roering&rft.aufirst=Joshua+J.&rft.au=Kirchner%2C+James+W.&rft.au=Dietrich%2C+William+E.&rft_id=https%3A%2F%2Fdoi.org%2F10.1029%252F1998WR900090&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrantWalkerHillLintern2013" class="citation journal cs1">Grant, J.; Walker, T.R.; Hill, P.S.; Lintern, D.G. (2013). "BEAST-A portable device for quantification of erosion in intact sediment cores". <i>Methods in Oceanography</i>. <b>5</b>: 39–55. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.mio.2013.03.001">10.1016/j.mio.2013.03.001</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Methods+in+Oceanography&rft.atitle=BEAST-A+portable+device+for+quantification+of+erosion+in+intact+sediment+cores&rft.volume=5&rft.pages=39-55&rft.date=2013&rft_id=info%3Adoi%2F10.1016%2Fj.mio.2013.03.001&rft.aulast=Grant&rft.aufirst=J.&rft.au=Walker%2C+T.R.&rft.au=Hill%2C+P.S.&rft.au=Lintern%2C+D.G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">Shields, A. (1936) Anwendung der Ähnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung; In Mitteilungen der Preussischen Versuchsanstalt für Wasserbau und Schiffbau, Heft 26 (<a rel="nofollow" class="external text" href="http://repository.tudelft.nl/assets/uuid:61a19716-a994-4942-9906-f680eb9952d6/Shields.pdf">Online</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110718072601/http://repository.tudelft.nl/assets/uuid:61a19716-a994-4942-9906-f680eb9952d6/Shields.pdf">Archived</a> 2011-07-18 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>; PDF; 3,8 MB)</span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSharmeenWillgoose2006" class="citation journal cs1">Sharmeen, Saniya; Willgoose, Garry R. (2006). <a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fesp.1397">"The interaction between armouring and particle weathering for eroding landscapes"</a>. <i><a href="/wiki/Earth_Surface_Processes_and_Landforms" title="Earth Surface Processes and Landforms">Earth Surface Processes and Landforms</a></i>. <b>31</b> (10): 1195–1210. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2006ESPL...31.1195S">2006ESPL...31.1195S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fesp.1397">10.1002/esp.1397</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:91175516">91175516</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Earth+Surface+Processes+and+Landforms&rft.atitle=The+interaction+between+armouring+and+particle+weathering+for+eroding+landscapes&rft.volume=31&rft.issue=10&rft.pages=1195-1210&rft.date=2006&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A91175516%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1002%2Fesp.1397&rft_id=info%3Abibcode%2F2006ESPL...31.1195S&rft.aulast=Sharmeen&rft.aufirst=Saniya&rft.au=Willgoose%2C+Garry+R.&rft_id=https%3A%2F%2Fdoi.org%2F10.1002%252Fesp.1397&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWalkerGrant2009" class="citation journal cs1">Walker, T.R.; Grant, J. (2009). "Quantifying erosion rates and stability of bottom sediments at mussel aquaculture sites in Prince Edward Island, Canada". <i>Journal of Marine Systems</i>. <b>75</b> (1–2): 46–55. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2009JMS....75...46W">2009JMS....75...46W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.jmarsys.2008.07.009">10.1016/j.jmarsys.2008.07.009</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Marine+Systems&rft.atitle=Quantifying+erosion+rates+and+stability+of+bottom+sediments+at+mussel+aquaculture+sites+in+Prince+Edward+Island%2C+Canada&rft.volume=75&rft.issue=1%E2%80%932&rft.pages=46-55&rft.date=2009&rft_id=info%3Adoi%2F10.1016%2Fj.jmarsys.2008.07.009&rft_id=info%3Abibcode%2F2009JMS....75...46W&rft.aulast=Walker&rft.aufirst=T.R.&rft.au=Grant%2C+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text">Dey S. (1999) Sediment threshold. <i>Applied Mathematical Modelling</i>, Elsevier, Vol. 23, No. 5, 399-417.</span> </li> <li id="cite_note-Chanson-16"><span class="mw-cite-backlink">^ <a href="#cite_ref-Chanson_16-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Chanson_16-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHubert_Chanson2004" class="citation book cs1"><a href="/wiki/Hubert_Chanson" title="Hubert Chanson">Hubert Chanson</a> (2004). <i>The Hydraulics of Open Channel Flow: An Introduction</i>. Butterworth-Heinemann, 2nd edition, Oxford, UK, 630 pages. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7506-5978-9" title="Special:BookSources/978-0-7506-5978-9"><bdi>978-0-7506-5978-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Hydraulics+of+Open+Channel+Flow%3A+An+Introduction&rft.pub=Butterworth-Heinemann%2C+2nd+edition%2C+Oxford%2C+UK%2C+630+pages&rft.date=2004&rft.isbn=978-0-7506-5978-9&rft.au=Hubert+Chanson&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-whipple_roughness-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-whipple_roughness_17-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWhipple2004" class="citation web cs1">Whipple, Kelin (2004). <a rel="nofollow" class="external text" href="http://ocw.mit.edu/courses/earth-atmospheric-and-planetary-sciences/12-163-surface-processes-and-landscape-evolution-fall-2004/labs/roughnes_handout.pdf">"Hydraulic Roughness"</a> <span class="cs1-format">(PDF)</span>. <i>12.163: Surface processes and landscape evolution</i>. MIT OCW<span class="reference-accessdate">. Retrieved <span class="nowrap">2009-03-27</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=12.163%3A+Surface+processes+and+landscape+evolution&rft.atitle=Hydraulic+Roughness&rft.date=2004&rft.aulast=Whipple&rft.aufirst=Kelin&rft_id=http%3A%2F%2Focw.mit.edu%2Fcourses%2Fearth-atmospheric-and-planetary-sciences%2F12-163-surface-processes-and-landscape-evolution-fall-2004%2Flabs%2Froughnes_handout.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-Parker1990-18"><span class="mw-cite-backlink">^ <a href="#cite_ref-Parker1990_18-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Parker1990_18-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFParker1990" class="citation journal cs1">Parker, G (1990). "Surface-based bedload transport relation for gravel rivers". <i>Journal of Hydraulic Research</i>. <b>28</b> (4): 417–436. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1990JHydR..28..417P">1990JHydR..28..417P</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F00221689009499058">10.1080/00221689009499058</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Hydraulic+Research&rft.atitle=Surface-based+bedload+transport+relation+for+gravel+rivers&rft.volume=28&rft.issue=4&rft.pages=417-436&rft.date=1990&rft_id=info%3Adoi%2F10.1080%2F00221689009499058&rft_id=info%3Abibcode%2F1990JHydR..28..417P&rft.aulast=Parker&rft.aufirst=G&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-whipple_sed_trans-19"><span class="mw-cite-backlink">^ <a href="#cite_ref-whipple_sed_trans_19-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-whipple_sed_trans_19-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-whipple_sed_trans_19-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-whipple_sed_trans_19-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-whipple_sed_trans_19-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-whipple_sed_trans_19-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-whipple_sed_trans_19-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-whipple_sed_trans_19-7"><sup><i><b>h</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWhipple2004" class="citation web cs1">Whipple, Kelin (September 2004). <a rel="nofollow" class="external text" href="https://ocw.mit.edu/courses/earth-atmospheric-and-planetary-sciences/12-163-surface-processes-and-landscape-evolution-fall-2004/lecture-notes/4_sediment_transport_edited.pdf">"IV. Essentials of Sediment Transport"</a> <span class="cs1-format">(PDF)</span>. <i>12.163/12.463 Surface Processes and Landscape Evolution: Course Notes</i>. <a href="/wiki/MIT_OpenCourseWare" title="MIT OpenCourseWare">MIT OpenCourseWare</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2009-10-11</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=12.163%2F12.463+Surface+Processes+and+Landscape+Evolution%3A+Course+Notes&rft.atitle=IV.+Essentials+of+Sediment+Transport&rft.date=2004-09&rft.aulast=Whipple&rft.aufirst=Kelin&rft_id=https%3A%2F%2Focw.mit.edu%2Fcourses%2Fearth-atmospheric-and-planetary-sciences%2F12-163-surface-processes-and-landscape-evolution-fall-2004%2Flecture-notes%2F4_sediment_transport_edited.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-moore_loose_ends-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-moore_loose_ends_20-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMoore" class="citation web cs1">Moore, Andrew. <a rel="nofollow" class="external text" href="http://www.personal.kent.edu/~amoore5/FST_L_20.pdf">"Lecture 20—Some Loose Ends"</a> <span class="cs1-format">(PDF)</span>. <i>Lecture Notes: Fluvial Sediment Transport</i>. Kent State<span class="reference-accessdate">. Retrieved <span class="nowrap">23 December</span> 2009</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Lecture+Notes%3A+Fluvial+Sediment+Transport&rft.atitle=Lecture+20%E2%80%94Some+Loose+Ends&rft.aulast=Moore&rft.aufirst=Andrew&rft_id=http%3A%2F%2Fwww.personal.kent.edu%2F~amoore5%2FFST_L_20.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDietrich1982" class="citation journal cs1">Dietrich, W. E. (1982). <a rel="nofollow" class="external text" href="https://www.sfu.ca/~jvenditt/geog413_613/readings/1982_Dietrich_settling_velocity.pdf">"Settling Velocity of Natural Particles"</a> <span class="cs1-format">(PDF)</span>. <i>Water Resources Research</i>. <b>18</b> (6): 1615–1626. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1982WRR....18.1615D">1982WRR....18.1615D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1029%2FWR018i006p01615">10.1029/WR018i006p01615</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:128625889">128625889</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Water+Resources+Research&rft.atitle=Settling+Velocity+of+Natural+Particles&rft.volume=18&rft.issue=6&rft.pages=1615-1626&rft.date=1982&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A128625889%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1029%2FWR018i006p01615&rft_id=info%3Abibcode%2F1982WRR....18.1615D&rft.aulast=Dietrich&rft.aufirst=W.+E.&rft_id=https%3A%2F%2Fwww.sfu.ca%2F~jvenditt%2Fgeog413_613%2Freadings%2F1982_Dietrich_settling_velocity.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFergusonChurch2006" class="citation journal cs1">Ferguson, R. I.; Church, M. (2006). "A Simple Universal Equation for Grain Settling Velocity". <i>Journal of Sedimentary Research</i>. <b>74</b> (6): 933–937. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1306%2F051204740933">10.1306/051204740933</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Sedimentary+Research&rft.atitle=A+Simple+Universal+Equation+for+Grain+Settling+Velocity&rft.volume=74&rft.issue=6&rft.pages=933-937&rft.date=2006&rft_id=info%3Adoi%2F10.1306%2F051204740933&rft.aulast=Ferguson&rft.aufirst=R.+I.&rft.au=Church%2C+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.coolgeography.co.uk/A-level/AQA/Year%2012/Rivers,%20Floods/Long%20profile/Hjulstrom.htm">The long profile – changing processes: types of erosion, transportation and deposition, types of load; the Hjulstrom curve</a>. coolgeography.co.uk. Last accessed 26 Dec 2011.</span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://ocw.mit.edu/courses/earth-atmospheric-and-planetary-sciences/12-090-special-topics-an-introduction-to-fluid-motions-sediment-transport-and-current-generated-sedimentary-structures-fall-2006/lecture-notes/ch9.pdf">Special Topics: An Introduction to Fluid Motions, Sediment Transport, and Current-generated Sedimentary Structures; As taught in: Fall 2006</a>. <a href="/wiki/Massachusetts_Institute_of_Technology" title="Massachusetts Institute of Technology">Massachusetts Institute of Technology</a>. 2006. Last accessed 26 Dec 2011.</span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMeyer-PeterMüller,_R.1948" class="citation book cs1">Meyer-Peter, E; Müller, R. (1948). <i>Formulas for bed-load transport</i>. Proceedings of the 2nd Meeting of the International Association for Hydraulic Structures Research. pp. 39–64.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Formulas+for+bed-load+transport&rft.series=Proceedings+of+the+2nd+Meeting+of+the+International+Association+for+Hydraulic+Structures+Research&rft.pages=39-64&rft.date=1948&rft.aulast=Meyer-Peter&rft.aufirst=E&rft.au=M%C3%BCller%2C+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-f-l-26"><span class="mw-cite-backlink">^ <a href="#cite_ref-f-l_26-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-f-l_26-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFernandez-Luquevan_Beek,_R1976" class="citation journal cs1">Fernandez-Luque, R; van Beek, R (1976). <a rel="nofollow" class="external text" href="http://resolver.tudelft.nl/uuid:2627433e-275e-4327-8841-ae998a6c525c">"Erosion and transport of bedload sediment"</a>. <i>J. Hydrol. Res</i>. <b>14</b> (2): 127–144. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1976JHydR..14..127F">1976JHydR..14..127F</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F00221687609499677">10.1080/00221687609499677</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=J.+Hydrol.+Res.&rft.atitle=Erosion+and+transport+of+bedload+sediment&rft.volume=14&rft.issue=2&rft.pages=127-144&rft.date=1976&rft_id=info%3Adoi%2F10.1080%2F00221687609499677&rft_id=info%3Abibcode%2F1976JHydR..14..127F&rft.aulast=Fernandez-Luque&rft.aufirst=R&rft.au=van+Beek%2C+R&rft_id=http%3A%2F%2Fresolver.tudelft.nl%2Fuuid%3A2627433e-275e-4327-8841-ae998a6c525c&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-cheng-27"><span class="mw-cite-backlink">^ <a href="#cite_ref-cheng_27-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-cheng_27-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCheng2002" class="citation journal cs1">Cheng, Nian-Sheng (2002). "Exponential Formula for Bedload Transport". <i>Journal of Hydraulic Engineering</i>. <b>128</b> (10): 942. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1061%2F%28ASCE%290733-9429%282002%29128%3A10%28942%29">10.1061/(ASCE)0733-9429(2002)128:10(942)</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/10356%2F83917">10356/83917</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Hydraulic+Engineering&rft.atitle=Exponential+Formula+for+Bedload+Transport&rft.volume=128&rft.issue=10&rft.pages=942&rft.date=2002&rft_id=info%3Ahdl%2F10356%2F83917&rft_id=info%3Adoi%2F10.1061%2F%28ASCE%290733-9429%282002%29128%3A10%28942%29&rft.aulast=Cheng&rft.aufirst=Nian-Sheng&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-wilson-28"><span class="mw-cite-backlink">^ <a href="#cite_ref-wilson_28-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-wilson_28-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilson1966" class="citation journal cs1">Wilson, K. C. (1966). "Bed-load transport at high shear stress". <i>J. Hydraul. Div</i>. <b>92</b> (6). ASCE: 49–59. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1061%2FJYCEAJ.0001562">10.1061/JYCEAJ.0001562</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=J.+Hydraul.+Div.&rft.atitle=Bed-load+transport+at+high+shear+stress&rft.volume=92&rft.issue=6&rft.pages=49-59&rft.date=1966&rft_id=info%3Adoi%2F10.1061%2FJYCEAJ.0001562&rft.aulast=Wilson&rft.aufirst=K.+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-wiberg_smith-29"><span class="mw-cite-backlink">^ <a href="#cite_ref-wiberg_smith_29-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-wiberg_smith_29-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWibergDungan_Smith1989" class="citation journal cs1"><a href="/wiki/Patricia_Wiberg" title="Patricia Wiberg">Wiberg, Patricia L.</a>; Dungan Smith, J. (1989). "Model for Calculating Bed Load Transport of Sediment". <i>Journal of Hydraulic Engineering</i>. <b>115</b>: 101. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1061%2F%28ASCE%290733-9429%281989%29115%3A1%28101%29">10.1061/(ASCE)0733-9429(1989)115:1(101)</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Hydraulic+Engineering&rft.atitle=Model+for+Calculating+Bed+Load+Transport+of+Sediment&rft.volume=115&rft.pages=101&rft.date=1989&rft_id=info%3Adoi%2F10.1061%2F%28ASCE%290733-9429%281989%29115%3A1%28101%29&rft.aulast=Wiberg&rft.aufirst=Patricia+L.&rft.au=Dungan+Smith%2C+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-wilcock_crowe-30"><span class="mw-cite-backlink">^ <a href="#cite_ref-wilcock_crowe_30-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-wilcock_crowe_30-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-wilcock_crowe_30-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilcockCrowe2003" class="citation journal cs1">Wilcock, Peter R.; Crowe, Joanna C. (2003). "Surface-based Transport Model for Mixed-Size Sediment". <i>Journal of Hydraulic Engineering</i>. <b>129</b> (2): 120. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1061%2F%28ASCE%290733-9429%282003%29129%3A2%28120%29">10.1061/(ASCE)0733-9429(2003)129:2(120)</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:40651180">40651180</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Hydraulic+Engineering&rft.atitle=Surface-based+Transport+Model+for+Mixed-Size+Sediment&rft.volume=129&rft.issue=2&rft.pages=120&rft.date=2003&rft_id=info%3Adoi%2F10.1061%2F%28ASCE%290733-9429%282003%29129%3A2%28120%29&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A40651180%23id-name%3DS2CID&rft.aulast=Wilcock&rft.aufirst=Peter+R.&rft.au=Crowe%2C+Joanna+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-parker_etal_1982-31"><span class="mw-cite-backlink">^ <a href="#cite_ref-parker_etal_1982_31-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-parker_etal_1982_31-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFParkerKlingeman,_P._C.McLean,_D._G.1982" class="citation journal cs1">Parker, G.; Klingeman, P. C.; McLean, D. G. (1982). <a rel="nofollow" class="external text" href="http://cedb.asce.org/cgi/WWWdisplay.cgi?8200331">"Bedload and Size Distribution in Paved Gravel-Bed Streams"</a>. <i>Journal of the Hydraulics Division</i>. <b>108</b> (4). <a href="/wiki/American_Society_of_Civil_Engineers" title="American Society of Civil Engineers">ASCE</a>: 544–571. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1061%2FJYCEAJ.0005854">10.1061/JYCEAJ.0005854</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+Hydraulics+Division&rft.atitle=Bedload+and+Size+Distribution+in+Paved+Gravel-Bed+Streams&rft.volume=108&rft.issue=4&rft.pages=544-571&rft.date=1982&rft_id=info%3Adoi%2F10.1061%2FJYCEAJ.0005854&rft.aulast=Parker&rft.aufirst=G.&rft.au=Klingeman%2C+P.+C.&rft.au=McLean%2C+D.+G.&rft_id=http%3A%2F%2Fcedb.asce.org%2Fcgi%2FWWWdisplay.cgi%3F8200331&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-Wilcock_Science-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-Wilcock_Science_32-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilcock1998" class="citation journal cs1">Wilcock, P. R. (1998). "Two-fraction model of initial sediment motion in gravel-bed rivers". <i>Science</i>. <b>280</b> (5362): 410–412. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1998Sci...280..410W">1998Sci...280..410W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fscience.280.5362.410">10.1126/science.280.5362.410</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/9545213">9545213</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Science&rft.atitle=Two-fraction+model+of+initial+sediment+motion+in+gravel-bed+rivers&rft.volume=280&rft.issue=5362&rft.pages=410-412&rft.date=1998&rft_id=info%3Apmid%2F9545213&rft_id=info%3Adoi%2F10.1126%2Fscience.280.5362.410&rft_id=info%3Abibcode%2F1998Sci...280..410W&rft.aulast=Wilcock&rft.aufirst=P.+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-wilcock_Kenworthy-33"><span class="mw-cite-backlink">^ <a href="#cite_ref-wilcock_Kenworthy_33-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-wilcock_Kenworthy_33-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-wilcock_Kenworthy_33-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-wilcock_Kenworthy_33-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-wilcock_Kenworthy_33-4"><sup><i><b>e</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilcockKenworthy2002" class="citation journal cs1">Wilcock, Peter R.; Kenworthy, T. (2002). <a rel="nofollow" class="external text" href="https://digitalcommons.usu.edu/wats_facpub/640">"A two-fraction model for the transport of sand/gravel mixtures"</a>. <i>Water Resour. Res</i>. <b>38</b> (10): 1194. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2002WRR....38.1194W">2002WRR....38.1194W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1029%2F2001WR000684">10.1029/2001WR000684</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Water+Resour.+Res.&rft.atitle=A+two-fraction+model+for+the+transport+of+sand%2Fgravel+mixtures&rft.volume=38&rft.issue=10&rft.pages=1194&rft.date=2002&rft_id=info%3Adoi%2F10.1029%2F2001WR000684&rft_id=info%3Abibcode%2F2002WRR....38.1194W&rft.aulast=Wilcock&rft.aufirst=Peter+R.&rft.au=Kenworthy%2C+T.&rft_id=https%3A%2F%2Fdigitalcommons.usu.edu%2Fwats_facpub%2F640&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-Kuhnle-34"><span class="mw-cite-backlink">^ <a href="#cite_ref-Kuhnle_34-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Kuhnle_34-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Kuhnle_34-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Kuhnle_34-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-Kuhnle_34-4"><sup><i><b>e</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKuhnleWrenLangendoenRigby2013" class="citation journal cs1">Kuhnle, R. A.; Wren, D. G.; Langendoen, E. J.; Rigby, J. R. (2013). <a rel="nofollow" class="external text" href="https://zenodo.org/record/1236032">"Sand Transport over an Immobile Gravel Substrate"</a>. <i>Journal of Hydraulic Engineering</i>. <b>139</b> (2): 167–176. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1061%2F%28ASCE%29HY.1943-7900.0000615">10.1061/(ASCE)HY.1943-7900.0000615</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Hydraulic+Engineering&rft.atitle=Sand+Transport+over+an+Immobile+Gravel+Substrate&rft.volume=139&rft.issue=2&rft.pages=167-176&rft.date=2013&rft_id=info%3Adoi%2F10.1061%2F%28ASCE%29HY.1943-7900.0000615&rft.aulast=Kuhnle&rft.aufirst=R.+A.&rft.au=Wren%2C+D.+G.&rft.au=Langendoen%2C+E.+J.&rft.au=Rigby%2C+J.+R.&rft_id=https%3A%2F%2Fzenodo.org%2Frecord%2F1236032&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-Pellachini-35"><span class="mw-cite-backlink">^ <a href="#cite_ref-Pellachini_35-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Pellachini_35-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPellachini2011" class="citation thesis cs1">Pellachini, Corrado (2011). <a rel="nofollow" class="external text" href="http://eprints-phd.biblio.unitn.it/605/"><i>Modelling fine sediment transport over an immobile gravel bed</i></a> (phd). Trento: Unitn-eprints.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adissertation&rft.title=Modelling+fine+sediment+transport+over+an+immobile+gravel+bed&rft.inst=Unitn-eprints&rft.date=2011&rft.aulast=Pellachini&rft.aufirst=Corrado&rft_id=http%3A%2F%2Feprints-phd.biblio.unitn.it%2F605%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-Nikora-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-Nikora_36-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNikoraGoringMcEwanGriffiths2001" class="citation journal cs1">Nikora, V; Goring, D; McEwan, I; Griffiths, G (2001). "Spatially averaged open-channel flow over rough bed". <i>J. Hydraul. Eng</i>. <b>127</b> (2): 123–133. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1061%2F%28ASCE%290733-9429%282001%29127%3A2%28123%29">10.1061/(ASCE)0733-9429(2001)127:2(123)</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=J.+Hydraul.+Eng.&rft.atitle=Spatially+averaged+open-channel+flow+over+rough+bed&rft.volume=127&rft.issue=2&rft.pages=123-133&rft.date=2001&rft_id=info%3Adoi%2F10.1061%2F%28ASCE%290733-9429%282001%29127%3A2%28123%29&rft.aulast=Nikora&rft.aufirst=V&rft.au=Goring%2C+D&rft.au=McEwan%2C+I&rft.au=Griffiths%2C+G&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-Miller-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-Miller_37-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMillerMcCaveKomar1977" class="citation journal cs1">Miller, M.C.; McCave, I.N.; Komar, P.D. (1977). "Threshold of sediment motion under unidirectional currents". <i>Sedimentology</i>. <b>24</b> (4): 507–527. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1977Sedim..24..507M">1977Sedim..24..507M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fj.1365-3091.1977.tb00136.x">10.1111/j.1365-3091.1977.tb00136.x</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Sedimentology&rft.atitle=Threshold+of+sediment+motion+under+unidirectional+currents.&rft.volume=24&rft.issue=4&rft.pages=507-527&rft.date=1977&rft_id=info%3Adoi%2F10.1111%2Fj.1365-3091.1977.tb00136.x&rft_id=info%3Abibcode%2F1977Sedim..24..507M&rft.aulast=Miller&rft.aufirst=M.C.&rft.au=McCave%2C+I.N.&rft.au=Komar%2C+P.D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-harris_sus_sed-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-harris_sus_sed_38-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHarris2003" class="citation web cs1">Harris, Courtney K. (March 18, 2003). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100528054103/http://www.vims.edu/~ckharris/MS698_03/lecture_09.pdf">"Lecture 9: Suspended Sediment Transport II"</a> <span class="cs1-format">(PDF)</span>. <i>Sediment transport processes in coastal environments</i>. <a href="/wiki/Virginia_Institute_of_Marine_Science" title="Virginia Institute of Marine Science">Virginia Institute of Marine Science</a>. Archived from <a rel="nofollow" class="external text" href="http://www.vims.edu/~ckharris/MS698_03/lecture_09.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 28 May 2010<span class="reference-accessdate">. Retrieved <span class="nowrap">23 December</span> 2009</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Sediment+transport+processes+in+coastal+environments&rft.atitle=Lecture+9%3A+Suspended+Sediment+Transport+II&rft.date=2003-03-18&rft.aulast=Harris&rft.aufirst=Courtney+K.&rft_id=http%3A%2F%2Fwww.vims.edu%2F~ckharris%2FMS698_03%2Flecture_09.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-moore_sus_sed-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-moore_sus_sed_39-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMoore" class="citation web cs1">Moore, Andrew. <a rel="nofollow" class="external text" href="http://www.personal.kent.edu/~amoore5/FST_L_21.pdf">"Lecture 21—Suspended Sediment Transport"</a> <span class="cs1-format">(PDF)</span>. <i>Lecture Notes: Fluvial Sediment Transport</i>. Kent State<span class="reference-accessdate">. Retrieved <span class="nowrap">25 December</span> 2009</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Lecture+Notes%3A+Fluvial+Sediment+Transport&rft.atitle=Lecture+21%E2%80%94Suspended+Sediment+Transport&rft.aulast=Moore&rft.aufirst=Andrew&rft_id=http%3A%2F%2Fwww.personal.kent.edu%2F~amoore5%2FFST_L_21.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-ackers-white-40"><span class="mw-cite-backlink"><b><a href="#cite_ref-ackers-white_40-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAckersWhite,_W.R.1973" class="citation journal cs1">Ackers, P.; White, W.R. (1973). <a rel="nofollow" class="external text" href="http://cedb.asce.org/cgi/WWWdisplay.cgi?7300122">"Sediment Transport: New Approach and Analysis"</a>. <i><a href="/wiki/Journal_of_the_Hydraulics_Division" class="mw-redirect" title="Journal of the Hydraulics Division">Journal of the Hydraulics Division</a></i>. <b>99</b> (11). <a href="/wiki/American_Society_of_Civil_Engineers" title="American Society of Civil Engineers">ASCE</a>: 2041–2060. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1061%2FJYCEAJ.0003791">10.1061/JYCEAJ.0003791</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+Hydraulics+Division&rft.atitle=Sediment+Transport%3A+New+Approach+and+Analysis&rft.volume=99&rft.issue=11&rft.pages=2041-2060&rft.date=1973&rft_id=info%3Adoi%2F10.1061%2FJYCEAJ.0003791&rft.aulast=Ackers&rft.aufirst=P.&rft.au=White%2C+W.R.&rft_id=http%3A%2F%2Fcedb.asce.org%2Fcgi%2FWWWdisplay.cgi%3F7300122&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-bm_eval-41"><span class="mw-cite-backlink"><b><a href="#cite_ref-bm_eval_41-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAriffinA.A._GhaniN.A._ZakairaA.H._Yahya2002" class="citation journal cs1">Ariffin, J.; A.A. Ghani; N.A. Zakaira; A.H. Yahya (14–16 October 2002). <a rel="nofollow" class="external text" href="http://redac.eng.usm.my/html/publish/2002_07.pdf">"Evaluation of equations on total bed material load"</a> <span class="cs1-format">(PDF)</span>. <i>International Conference on Urban Hydrology for the 21st Century</i>. <a href="/wiki/Kuala_Lumpur" title="Kuala Lumpur">Kuala Lumpur</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Conference+on+Urban+Hydrology+for+the+21st+Century&rft.atitle=Evaluation+of+equations+on+total+bed+material+load&rft.date=2002-10-14%2F2002-10-16&rft.aulast=Ariffin&rft.aufirst=J.&rft.au=A.A.+Ghani&rft.au=N.A.+Zakaira&rft.au=A.H.+Yahya&rft_id=http%3A%2F%2Fredac.eng.usm.my%2Fhtml%2Fpublish%2F2002_07.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-42"><span class="mw-cite-backlink"><b><a href="#cite_ref-42">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFYang1979" class="citation journal cs1">Yang, C (1979). "Unit stream power equations for total load". <i>Journal of Hydrology</i>. <b>40</b> (1–2): 123. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1979JHyd...40..123Y">1979JHyd...40..123Y</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0022-1694%2879%2990092-1">10.1016/0022-1694(79)90092-1</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Hydrology&rft.atitle=Unit+stream+power+equations+for+total+load&rft.volume=40&rft.issue=1%E2%80%932&rft.pages=123&rft.date=1979&rft_id=info%3Adoi%2F10.1016%2F0022-1694%2879%2990092-1&rft_id=info%3Abibcode%2F1979JHyd...40..123Y&rft.aulast=Yang&rft.aufirst=C&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-43">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBailard1981" class="citation journal cs1">Bailard, James A. (1981). "An Energetics Total Load Sediment Transport Model For a Plane Sloping Beach". <i>Journal of Geophysical Research</i>. <b>86</b> (C11): 10938. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1981JGR....8610938B">1981JGR....8610938B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1029%2FJC086iC11p10938">10.1029/JC086iC11p10938</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Geophysical+Research&rft.atitle=An+Energetics+Total+Load+Sediment+Transport+Model+For+a+Plane+Sloping+Beach&rft.volume=86&rft.issue=C11&rft.pages=10938&rft.date=1981&rft_id=info%3Adoi%2F10.1029%2FJC086iC11p10938&rft_id=info%3Abibcode%2F1981JGR....8610938B&rft.aulast=Bailard&rft.aufirst=James+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> <li id="cite_note-sediment_control-44"><span class="mw-cite-backlink"><b><a href="#cite_ref-sediment_control_44-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNatatoOgden1998" class="citation journal cs1">Natato, T.; Ogden, F.L. (1998). "Sediment control at water intakes along sand-bed rivers". <i>Journal of Hydraulic Engineering</i>. <b>126</b> (6): 589–596. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1061%2F%28ASCE%290733-9429%281998%29124%3A6%28589%29">10.1061/(ASCE)0733-9429(1998)124:6(589)</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Hydraulic+Engineering&rft.atitle=Sediment+control+at+water+intakes+along+sand-bed+rivers&rft.volume=126&rft.issue=6&rft.pages=589-596&rft.date=1998&rft_id=info%3Adoi%2F10.1061%2F%28ASCE%290733-9429%281998%29124%3A6%28589%29&rft.aulast=Natato&rft.aufirst=T.&rft.au=Ogden%2C+F.L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASediment+transport" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sediment_transport&action=edit&section=39" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Liu, Z. (2001), <a rel="nofollow" class="external text" href="http://lvov.weizmann.ac.il/lvov/Literature-Online/Literature/Books/2001_Sediment_Transport.pdf">Sediment Transport</a>.</li> <li>Moore, A. <a rel="nofollow" class="external text" href="https://www.personal.kent.edu/~amoore5/html/fst_lecture_notes.html">Fluvial sediment transport lecture notes</a>, Kent State.</li> <li>Wilcock, P. <a rel="nofollow" class="external text" href="http://calm.geo.berkeley.edu/geomorph/wilcock/wilcock.html">Sediment Transport Seminar</a>, January 26–28, 2004, University of California at Berkeley</li> <li>Southard, J. B. (2007), <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080714180813/http://ocw.mit.edu/OcwWeb/Earth--Atmospheric--and-Planetary-Sciences/12-090Fall-2006/CourseHome/index.htm">Sediment Transport and Sedimentary Structures</a></li> <li>Linwood, J. G., <a rel="nofollow" class="external text" href="https://www.geocities.ws/linwood/suds/">Suspended Sediment Concentration and Discharge in a West London River.</a></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Sediment_transport" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Sediment_transport" title="Template:Sediment transport"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Sediment_transport" title="Template talk:Sediment transport"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Sediment_transport" title="Special:EditPage/Template:Sediment transport"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Sediment_transport" style="font-size:114%;margin:0 4em"><a class="mw-selflink selflink">Sediment transport</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Water</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Armored_mud_ball" title="Armored mud ball">Armored mud ball</a></li> <li><a href="/wiki/Coastal_sediment_transport" title="Coastal sediment transport">Coastal sediment transport</a></li> <li><a href="/wiki/Fluvial_processes" class="mw-redirect" title="Fluvial processes">Fluvial processes</a></li> <li><a href="/wiki/Bed_load" title="Bed load">Bed load</a></li> <li><a href="/wiki/Suspended_load" title="Suspended load">Suspended load</a></li> <li><a href="/wiki/Bed_material_load" title="Bed material load">Bed material load</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Glacial</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Glacial_flour" class="mw-redirect" title="Glacial flour">Glacial flour</a></li> <li><a href="/wiki/Glacial_outwash" class="mw-redirect" title="Glacial outwash">Glacial outwash</a></li> <li><a href="/wiki/Braided_river" title="Braided river">Braided river</a></li> <li><a href="/wiki/Moraine" title="Moraine">Moraine</a></li> <li><a href="/wiki/Esker" title="Esker">Esker</a></li> <li><a href="/wiki/Drumlin" title="Drumlin">Drumlin</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Hillslope</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Soil_creep" class="mw-redirect" title="Soil creep">Soil creep</a></li> <li><a href="/wiki/Landslide" title="Landslide">Landslide</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Aeolian_processes" title="Aeolian processes">Aeolian</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Dune" title="Dune">Dune</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="River_morphology" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:River_morphology" title="Template:River morphology"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:River_morphology" title="Template talk:River morphology"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:River_morphology" title="Special:EditPage/Template:River morphology"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="River_morphology" style="font-size:114%;margin:0 4em"><a href="/wiki/River_morphology" title="River morphology">River morphology</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Large-scale features</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Alluvial_plain" title="Alluvial plain">Alluvial plain</a></li> <li><a href="/wiki/Drainage_basin" title="Drainage basin">Drainage basin</a></li> <li><a href="/wiki/Drainage_system_(geomorphology)" title="Drainage system (geomorphology)">Drainage system (geomorphology)</a></li> <li><a href="/wiki/Estuary" title="Estuary">Estuary</a></li> <li><a href="/wiki/Strahler_number" title="Strahler number">Strahler number (stream order)</a></li> <li><a href="/wiki/River_valley" class="mw-redirect" title="River valley">River valley</a></li> <li><a href="/wiki/River_delta" title="River delta">River delta</a></li> <li><a href="/wiki/River_sinuosity" class="mw-redirect" title="River sinuosity">River sinuosity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Alluvial_river" title="Alluvial river">Alluvial rivers</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Anabranch" title="Anabranch">Anabranch</a></li> <li><a href="/wiki/Avulsion_(river)" title="Avulsion (river)">Avulsion (river)</a></li> <li><a href="/wiki/Bar_(river_morphology)" title="Bar (river morphology)">Bar (river morphology)</a></li> <li><a href="/wiki/Braided_river" title="Braided river">Braided river</a></li> <li><a href="/wiki/Channel_pattern" title="Channel pattern">Channel pattern</a></li> <li><a href="/wiki/Cut_bank" title="Cut bank">Cut bank</a></li> <li><a href="/wiki/Floodplain" title="Floodplain">Floodplain</a></li> <li><a href="/wiki/Meander" title="Meander">Meander</a></li> <li><a href="/wiki/Meander_cutoff" title="Meander cutoff">Meander cutoff</a></li> <li><a href="/wiki/Mouth_bar" title="Mouth bar">Mouth bar</a></li> <li><a href="/wiki/Oxbow_lake" title="Oxbow lake">Oxbow lake</a></li> <li><a href="/wiki/Point_bar" title="Point bar">Point bar</a></li> <li><a href="/wiki/Riffle" title="Riffle">Riffle</a></li> <li><a href="/wiki/Rapids" title="Rapids">Rapids</a></li> <li><a href="/wiki/Riparian_zone" title="Riparian zone">Riparian zone</a></li> <li><a href="/wiki/River_bifurcation" title="River bifurcation">River bifurcation</a></li> <li><a href="/wiki/River_channel_migration" title="River channel migration">River channel migration</a></li> <li><a href="/wiki/River_mouth" title="River mouth">River mouth</a></li> <li><a href="/wiki/Slip-off_slope" title="Slip-off slope">Slip-off slope</a></li> <li><a href="/wiki/Stream_pool" title="Stream pool">Stream pool</a></li> <li><a href="/wiki/Thalweg" title="Thalweg">Thalweg</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Bedrock_river" title="Bedrock river">Bedrock river</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Canyon" title="Canyon">Canyon</a></li> <li><a href="/wiki/Knickpoint" title="Knickpoint">Knickpoint</a></li> <li><a href="/wiki/Plunge_pool" title="Plunge pool">Plunge pool</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Bedform" title="Bedform">Bedforms</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ait" title="Ait">Ait</a></li> <li><a href="/wiki/Antidune" title="Antidune">Antidune</a></li> <li><a href="/wiki/Dune" title="Dune">Dune</a></li> <li><a href="/wiki/Ripple_marks" title="Ripple marks">Current ripple</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Regional processes</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Aggradation" title="Aggradation">Aggradation</a></li> <li><a href="/wiki/Base_level" title="Base level">Base level</a></li> <li><a href="/wiki/Degradation_(geology)" title="Degradation (geology)">Degradation (geology)</a></li> <li><a href="/wiki/Erosion_and_tectonics" title="Erosion and tectonics">Erosion and tectonics</a></li> <li><a href="/wiki/River_rejuvenation" title="River rejuvenation">River rejuvenation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Mechanics</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Deposition_(geology)" title="Deposition (geology)">Deposition (geology)</a></li> <li><a href="/wiki/Erosion#Water" title="Erosion">Water erosion</a></li> <li><a href="/wiki/Exner_equation" title="Exner equation">Exner equation</a></li> <li><a href="/wiki/Hack%27s_law" title="Hack's law">Hack's law</a></li> <li><a href="/wiki/Helicoidal_flow" title="Helicoidal flow">Helicoidal flow</a></li> <li><a href="/wiki/Playfair%27s_law" title="Playfair's law">Playfair's law</a></li> <li><a class="mw-selflink selflink">Sediment transport</a></li> <li><a href="/wiki/List_of_rivers_that_have_reversed_direction" title="List of rivers that have reversed direction">List of rivers that have reversed direction</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow hlist" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:River_morphology" title="Category:River morphology">Category</a></li></ul> </div></td></tr></tbody></table></div> <p><a href="/wiki/Special:Contributions/2601:247:C400:5E0:B9C2:ADE9:5C57:AF41" title="Special:Contributions/2601:247:C400:5E0:B9C2:ADE9:5C57:AF41">2601:247:C400:5E0:B9C2:ADE9:5C57:AF41</a> (<a href="/w/index.php?title=User_talk:2601:247:C400:5E0:B9C2:ADE9:5C57:AF41&action=edit&redlink=1" class="new" title="User talk:2601:247:C400:5E0:B9C2:ADE9:5C57:AF41 (page does not exist)">talk</a>) 20:47, 3 December 2024 (UTC)<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><a href="/wiki/Special:Contributions/2601:247:C400:5E0:B9C2:ADE9:5C57:AF41" title="Special:Contributions/2601:247:C400:5E0:B9C2:ADE9:5C57:AF41">2601:247:C400:5E0:B9C2:ADE9:5C57:AF41</a> (<a href="/w/index.php?title=User_talk:2601:247:C400:5E0:B9C2:ADE9:5C57:AF41&action=edit&redlink=1" class="new" title="User talk:2601:247:C400:5E0:B9C2:ADE9:5C57:AF41 (page does not exist)">talk</a>) 20:47, 3 December 2024 (UTC) </p> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Geologic_principles_and_processes" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Geologic_Principles" title="Template:Geologic Principles"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Geologic_Principles" title="Template talk:Geologic Principles"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Geologic_Principles" title="Special:EditPage/Template:Geologic Principles"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Geologic_principles_and_processes" style="font-size:114%;margin:0 4em"><a href="/wiki/Geology" title="Geology"> Geologic</a> principles and processes</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Stratigraphy" title="Stratigraphy">Stratigraphic principles</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Principle_of_original_horizontality" title="Principle of original horizontality">Principle of original horizontality</a></li> <li><a href="/wiki/Law_of_superposition" title="Law of superposition">Law of superposition</a></li> <li><a href="/wiki/Principle_of_lateral_continuity" title="Principle of lateral continuity">Principle of lateral continuity</a></li> <li><a href="/wiki/Principle_of_cross-cutting_relationships" class="mw-redirect" title="Principle of cross-cutting relationships">Principle of cross-cutting relationships</a></li> <li><a href="/wiki/Principle_of_faunal_succession" title="Principle of faunal succession">Principle of faunal succession</a></li> <li><a href="/wiki/Law_of_included_fragments" title="Law of included fragments">Principle of inclusions and components</a></li> <li><a href="/wiki/Walther%27s_law" class="mw-redirect" title="Walther's law">Walther's law</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="4" style="width:1px;padding:0 0 0 2px"><div><figure class="mw-halign-right" typeof="mw:File"><a href="/wiki/File:Wallula-Gap-the-sisters.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/Wallula-Gap-the-sisters.JPG/50px-Wallula-Gap-the-sisters.JPG" decoding="async" width="50" height="67" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/Wallula-Gap-the-sisters.JPG/75px-Wallula-Gap-the-sisters.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/Wallula-Gap-the-sisters.JPG/100px-Wallula-Gap-the-sisters.JPG 2x" data-file-width="1339" data-file-height="1786" /></a><figcaption></figcaption></figure></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Petrology" title="Petrology">Petrologic principles</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Intrusive_rock" title="Intrusive rock">Intrusive</a></li> <li><a href="/wiki/Extrusive_rock" title="Extrusive rock">Extrusive</a></li> <li><a href="/wiki/Volcanic_rock" title="Volcanic rock">Volcanic</a></li> <li><a href="/wiki/Exfoliation_joint" title="Exfoliation joint">Exfoliation</a></li> <li><a href="/wiki/Weathering" title="Weathering">Weathering</a></li> <li><a href="/wiki/Soil_formation" title="Soil formation">Soil formation</a></li> <li><a href="/wiki/Diagenesis" title="Diagenesis">Diagenesis</a></li> <li><a href="/wiki/Compaction_(geology)" title="Compaction (geology)">Compaction</a></li> <li><a href="/wiki/Metamorphism" title="Metamorphism">Metamorphism</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Geomorphology" title="Geomorphology">Geomorphologic processes</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Plate_tectonics" title="Plate tectonics">Plate tectonics</a></li> <li><a href="/wiki/Salt_tectonics" title="Salt tectonics">Salt tectonics</a></li> <li><a href="/wiki/Tectonic_uplift" title="Tectonic uplift">Tectonic uplift</a></li> <li><a href="/wiki/Subsidence" title="Subsidence">Subsidence</a></li> <li><a href="/wiki/Marine_transgression" title="Marine transgression">Marine transgression</a></li> <li><a href="/wiki/Marine_regression" title="Marine regression">Marine regression</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a class="mw-selflink selflink">Sediment transport</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Fluvial" class="mw-redirect" title="Fluvial">Fluvial processes</a></li> <li><a href="/wiki/Aeolian_processes" title="Aeolian processes">Aeolian processes</a></li> <li><a href="/wiki/Glacier" title="Glacier">Glacial processes</a></li> <li><a href="/wiki/Mass_wasting" title="Mass wasting">Mass wasting processes</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="3"><div><b><span class="nowrap"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:WikiProject_Geology.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/WikiProject_Geology.svg/16px-WikiProject_Geology.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/WikiProject_Geology.svg/24px-WikiProject_Geology.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e7/WikiProject_Geology.svg/32px-WikiProject_Geology.svg.png 2x" data-file-width="327" data-file-height="328" /></a></span> </span><a href="/wiki/Portal:Geology" title="Portal:Geology">Geology portal</a></b></div></td></tr></tbody></table></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-45"><span class="mw-cite-backlink"><b><a href="#cite_ref-45">^</a></b></span> <span class="reference-text">←Ĥľôŝşǣæżžźȳÿŷýŵűųŭǜǚǘūǖūǔůũüûùúťțșšşŝśřŗŕőǫŏō→</span> </li> </ol></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Sediment_transport&oldid=1257556380">https://en.wikipedia.org/w/index.php?title=Sediment_transport&oldid=1257556380</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Fluid_mechanics" title="Category:Fluid mechanics">Fluid mechanics</a></li><li><a href="/wiki/Category:Sedimentology" title="Category:Sedimentology">Sedimentology</a></li><li><a href="/wiki/Category:Environmental_engineering" title="Category:Environmental engineering">Environmental engineering</a></li><li><a href="/wiki/Category:Hydrology" title="Category:Hydrology">Hydrology</a></li><li><a href="/wiki/Category:Physical_geography" title="Category:Physical geography">Physical geography</a></li><li><a href="/wiki/Category:Geological_processes" title="Category:Geological processes">Geological processes</a></li><li><a href="/wiki/Category:Transport_phenomena" title="Category:Transport phenomena">Transport phenomena</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Webarchive_template_wayback_links" title="Category:Webarchive template wayback links">Webarchive template wayback links</a></li><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_matches_Wikidata" title="Category:Short description matches Wikidata">Short description matches Wikidata</a></li><li><a href="/wiki/Category:Articles_with_excerpts" title="Category:Articles with excerpts">Articles with excerpts</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 15 November 2024, at 15:06<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. By using this site, you agree to the <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use" class="extiw" title="foundation:Special:MyLanguage/Policy:Terms of Use">Terms of Use</a> and <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy" class="extiw" title="foundation:Special:MyLanguage/Policy:Privacy policy">Privacy Policy</a>. Wikipedia® is a registered trademark of the <a rel="nofollow" class="external text" href="https://wikimediafoundation.org/">Wikimedia Foundation, Inc.</a>, a non-profit organization.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Privacy policy</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:About">About Wikipedia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:General_disclaimer">Disclaimers</a></li> <li id="footer-places-contact"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us">Contact Wikipedia</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Code of Conduct</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Developers</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/en.wikipedia.org">Statistics</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookie statement</a></li> <li id="footer-places-mobileview"><a href="//en.m.wikipedia.org/w/index.php?title=Sediment_transport&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobile view</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-5f58cd8b6-dxlh5","wgBackendResponseTime":167,"wgPageParseReport":{"limitreport":{"cputime":"0.925","walltime":"1.164","ppvisitednodes":{"value":5165,"limit":1000000},"postexpandincludesize":{"value":148134,"limit":2097152},"templateargumentsize":{"value":9370,"limit":2097152},"expansiondepth":{"value":8,"limit":100},"expensivefunctioncount":{"value":11,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":337209,"limit":5000000},"entityaccesscount":{"value":0,"limit":400},"timingprofile":["100.00% 744.623 1 -total"," 40.94% 304.820 1 Template:Reflist"," 28.32% 210.867 27 Template:Cite_journal"," 14.80% 110.207 5 Template:Annotated_link"," 12.55% 93.421 1 Template:Sediment_sidebar"," 9.19% 68.450 1 Template:Short_description"," 8.06% 59.983 1 Template:Excerpt"," 6.19% 46.096 2 Template:Pagetype"," 5.70% 42.439 3 Template:Navbox"," 4.18% 31.108 29 Template:Flatlist"]},"scribunto":{"limitreport-timeusage":{"value":"0.483","limit":"10.000"},"limitreport-memusage":{"value":20815117,"limit":52428800},"limitreport-logs":"table#1 {\n [\"size\"] = \"tiny\",\n}\n"},"cachereport":{"origin":"mw-api-int.codfw.main-5f78b95b56-jz4j9","timestamp":"20241203204804","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Sediment transport","url":"https:\/\/en.wikipedia.org\/wiki\/Sediment_transport","sameAs":"http:\/\/www.wikidata.org\/entity\/Q7445303","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q7445303","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2006-11-18T13:48:09Z","dateModified":"2024-11-15T15:06:04Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/b\/b9\/Wafrica_amo_2007209_lrg.jpg","headline":"movement of solid particles, typically by gravity and fluid entrainment"}</script> </body> </html>