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<!DOCTYPE html> <html > <head> <meta charset="utf-8"> <meta rel="search" type="application/opensearchdescription+xml" href="/open_search.xml" title="Academia.edu"> <meta content="width=device-width, initial-scale=1" name="viewport"> <meta name="google-site-verification" content="bKJMBZA7E43xhDOopFZkssMMkBRjvYERV-NaN4R6mrs"> <meta name="csrf-param" content="authenticity_token" /> <meta name="csrf-token" content="9pWFJHz9QsG6OebgsNpnAGPV7MP/twNSfIxLNHroPsyliSy8vmAStn8QK/L8OTzOC++JDz7oFXml03hyLwrQYQ==" /> <meta name="citation_title" content="Planform Geometry and Dynamics of Meandering Rivers" /> <meta name="citation_author" content="Hans Henrik Stolum" /> <meta name="twitter:card" content="summary" /> <meta name="twitter:url" content="https://www.academia.edu/12158661/Planform_Geometry_and_Dynamics_of_Meandering_Rivers" /> <meta name="twitter:title" content="Planform Geometry and Dynamics of Meandering Rivers" /> <meta name="twitter:description" content="Three freely meandering rivers in the Amazon basin were analyzed for statistical scaling properties and oxbow lake size-frequency distributions. The rivers are the Purus (central Amazon, planform data), Juruá (central Amazon, planform and oxbow lake" /> <meta name="twitter:image" content="http://a.academia-assets.com/images/twitter-card.jpeg" /> <meta property="fb:app_id" content="2369844204" /> <meta property="og:type" content="article" /> <meta property="og:url" content="https://www.academia.edu/12158661/Planform_Geometry_and_Dynamics_of_Meandering_Rivers" /> <meta property="og:title" content="Planform Geometry and Dynamics of Meandering Rivers" /> <meta property="og:image" content="http://a.academia-assets.com/images/open-graph-icons/fb-paper.gif" /> <meta property="og:description" content="Three freely meandering rivers in the Amazon basin were analyzed for statistical scaling properties and oxbow lake size-frequency distributions. The rivers are the Purus (central Amazon, planform data), Juruá (central Amazon, planform and oxbow lake" /> <meta property="article:author" content="https://independent.academia.edu/HansHenrikStolum" /> <meta name="description" content="Three freely meandering rivers in the Amazon basin were analyzed for statistical scaling properties and oxbow lake size-frequency distributions. The rivers are the Purus (central Amazon, planform data), Juruá (central Amazon, planform and oxbow lake" /> <title>(PDF) Planform Geometry and Dynamics of Meandering Rivers | Hans Henrik Stolum - Academia.edu</title> <link rel="canonical" href="https://www.academia.edu/12158661/Planform_Geometry_and_Dynamics_of_Meandering_Rivers" /> <script async src="https://www.googletagmanager.com/gtag/js?id=G-5VKX33P2DS"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-5VKX33P2DS', { cookie_domain: 'academia.edu', send_page_view: false, }); gtag('event', 'page_view', { 'controller': "single_work", 'action': "show", 'controller_action': 'single_work#show', 'logged_in': 'false', 'edge': 'unknown', // Send nil if there is no A/B test bucket, in case some records get logged // with missing data - that way we can distinguish between the two cases. // ab_test_bucket should be of the form <ab_test_name>:<bucket> 'ab_test_bucket': null, }) </script> <script> var $controller_name = 'single_work'; var $action_name = "show"; var $rails_env = 'production'; var $app_rev = '92477ec68c09d28ae4730a4143c926f074776319'; var $domain = 'academia.edu'; var $app_host = "academia.edu"; var $asset_host = "academia-assets.com"; var $start_time = new Date().getTime(); var $recaptcha_key = "6LdxlRMTAAAAADnu_zyLhLg0YF9uACwz78shpjJB"; var $recaptcha_invisible_key = "6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj"; var $disableClientRecordHit = false; </script> <script> window.require = { config: function() { return function() {} } } </script> <script> window.Aedu = window.Aedu || {}; window.Aedu.hit_data = null; window.Aedu.serverRenderTime = new Date(1732793846000); window.Aedu.timeDifference = new Date().getTime() - 1732793846000; </script> <script type="application/ld+json">{"@context":"https://schema.org","@type":"ScholarlyArticle","abstract":"Three freely meandering rivers in the Amazon basin were analyzed for statistical scaling properties and oxbow lake size-frequency distributions. The rivers are the Purus (central Amazon, planform data), Juruá (central Amazon, planform and oxbow lake data), and Madre de Dios (Peruvian Amazon, oxbow lake data). Long reaches were found to be power- law scaling over more than two orders of mag- nitude. These river planforms are self-affine fractals. Oxbow lake data suggest that the lakes are sampled from a skewed hyperbolic (Pareto) size-frequency distribution. To examine the long-term behavior of freely meandering rivers, a deterministic continuum model of meandering rivers has been used for extensive simulations of free meandering mo- tion. The simulation outcomes are consistent with a dynamical state of self-organized criticality, which has the following characteristic behavior: (1) stationary mean sinuosity of the final state; (2) robustness, in the sense that the same final state is reached from any initial conditions; and (3) formation of a spatiotemporal fractal structure. Sensitivity tests showed that this behavior is not affected by valley confinement down to a valley width of 50 w (river width), and by chute cutoffs of mature meanders up to 3 w long, but the average sinuosity value reached in the final state is sensitive to valley width less than 100 w, and chutes longer than 1.5 w. Comparison with empirical data confirmed the validity of the simulations as models of river meandering. All tests found data and simulation results to be in close agreement.","author":[{"@context":"https://schema.org","@type":"Person","name":"Hans Henrik Stolum"}],"contributor":[],"dateCreated":"2015-04-29","dateModified":"2015-04-29","datePublished":null,"headline":"Planform Geometry and Dynamics of Meandering Rivers","inLanguage":"en","keywords":["Fluvial Processes","Fluvial Geomorphology"],"locationCreated":null,"publication":null,"publisher":{"@context":"https://schema.org","@type":"Organization","name":null},"image":null,"thumbnailUrl":null,"url":"https://www.academia.edu/12158661/Planform_Geometry_and_Dynamics_of_Meandering_Rivers","sourceOrganization":[{"@context":"https://schema.org","@type":"EducationalOrganization","name":null}]}</script><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/single_work_page/loswp-102fa537001ba4d8dcd921ad9bd56c474abc201906ea4843e7e7efe9dfbf561d.css" /><link rel="stylesheet" media="all" 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The rivers are the Purus (central Amazon, planform data), Juruá (central Amazon, planform and oxbow lake data), and Madre de Dios (Peruvian Amazon, oxbow lake data). Long reaches were found to be power- law scaling over more than two orders of mag- nitude. These river planforms are self-affine fractals. Oxbow lake data suggest that the lakes are sampled from a skewed hyperbolic (Pareto) size-frequency distribution.\r\nTo examine the long-term behavior of freely meandering rivers, a deterministic continuum model of meandering rivers has been used for extensive simulations of free meandering mo- tion. The simulation outcomes are consistent with a dynamical state of self-organized criticality, which has the following characteristic behavior: (1) stationary mean sinuosity of the final state; (2) robustness, in the sense that the same final state is reached from any initial conditions; and (3) formation of a spatiotemporal fractal structure.\r\nSensitivity tests showed that this behavior is not affected by valley confinement down to a valley width of 50 w (river width), and by chute cutoffs of mature meanders up to 3 w long, but the average sinuosity value reached in the final state is sensitive to valley width less than 100 w, and chutes longer than 1.5 w.\r\nComparison with empirical data confirmed the validity of the simulations as models of river meandering. All tests found data and simulation results to be in close agreement."},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Planform Geometry and Dynamics of Meandering Rivers","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [30515984]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "full_page_mobile_sutd_modal"; window.loswp.useOptimizedScribd4genScript = false; window.loswp.appleClientId = 'edu.academia.applesignon';</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":37462278,"attachmentType":"pdf"}"><img alt="First page of “Planform Geometry and Dynamics of Meandering Rivers”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/37462278/mini_magick20190301-11794-1tlt72n.png?1551512645" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/assets/single_work_splash/adobe.icon-574afd46eb6b03a77a153a647fb47e30546f9215c0ee6a25df597a779717f9ef.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">Planform Geometry and Dynamics of Meandering Rivers</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="30515984" href="https://independent.academia.edu/HansHenrikStolum"><img alt="Profile image of Hans Henrik Stolum" class="ds-work-card--author-avatar" src="//a.academia-assets.com/images/s65_no_pic.png" />Hans Henrik Stolum</a></div><div class="ds-work-card--detail"><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">description</span><p class="ds2-5-body-sm">14 pages</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">link</span><p class="ds2-5-body-sm">1 file</p></div></div><script>(async () => { const workId = 12158661; const worksViewsPath = "/v0/works/views?subdomain_param=api&work_ids%5B%5D=12158661"; const getWorkViews = async (workId) => { const response = await fetch(worksViewsPath); if (!response.ok) { throw new Error('Failed to load work views'); } const data = await response.json(); return data.views[workId]; }; // Get the view count for the work - we send this immediately rather than waiting for // the DOM to load, so it can be available as soon as possible (but without holding up // the backend or other resource requests, because it's a bit expensive and not critical). const viewCount = await getWorkViews(workId); const updateViewCount = (viewCount) => { const viewCountNumber = Number(viewCount); if (!viewCountNumber) { throw new Error('Failed to parse view count'); } const commaizedViewCount = viewCountNumber.toLocaleString(); const viewCountBody = document.getElementById('work-metadata-view-count'); if (viewCountBody) { viewCountBody.textContent = `${commaizedViewCount} views`; } else { throw new Error('Failed to find work views element'); } }; // If the DOM is still loading, wait for it to be ready before updating the view count. if (document.readyState === "loading") { document.addEventListener('DOMContentLoaded', () => { updateViewCount(viewCount); }); // Otherwise, just update it immediately. } else { updateViewCount(viewCount); } })();</script></div><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">Three freely meandering rivers in the Amazon basin were analyzed for statistical scaling properties and oxbow lake size-frequency distributions. The rivers are the Purus (central Amazon, planform data), Juruá (central Amazon, planform and oxbow lake data), and Madre de Dios (Peruvian Amazon, oxbow lake data). Long reaches were found to be power- law scaling over more than two orders of mag- nitude. These river planforms are self-affine fractals. Oxbow lake data suggest that the lakes are sampled from a skewed hyperbolic (Pareto) size-frequency distribution. To examine the long-term behavior of freely meandering rivers, a deterministic continuum model of meandering rivers has been used for extensive simulations of free meandering mo- tion. The simulation outcomes are consistent with a dynamical state of self-organized criticality, which has the following characteristic behavior: (1) stationary mean sinuosity of the final state; (2) robustness, in the sense that the same final state is reached from any initial conditions; and (3) formation of a spatiotemporal fractal structure. Sensitivity tests showed that this behavior is not affected by valley confinement down to a valley width of 50 w (river width), and by chute cutoffs of mature meanders up to 3 w long, but the average sinuosity value reached in the final state is sensitive to valley width less than 100 w, and chutes longer than 1.5 w. Comparison with empirical data confirmed the validity of the simulations as models of river meandering. All tests found data and simulation results to be in close agreement.</p><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--work-card","attachmentId":37462278,"attachmentType":"pdf","workUrl":"https://www.academia.edu/12158661/Planform_Geometry_and_Dynamics_of_Meandering_Rivers"}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--work-card","attachmentId":37462278,"attachmentType":"pdf","workUrl":"https://www.academia.edu/12158661/Planform_Geometry_and_Dynamics_of_Meandering_Rivers"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div></div><div data-auto_select="false" data-client_id="331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b" data-doc_id="37462278" data-landing_url="https://www.academia.edu/12158661/Planform_Geometry_and_Dynamics_of_Meandering_Rivers" data-login_uri="https://www.academia.edu/registrations/google_one_tap" data-moment_callback="onGoogleOneTapEvent" id="g_id_onload"></div><div class="ds-top-related-works--grid-container"><div class="ds-related-content--container ds-top-related-works--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="0" data-entity-id="20820332" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/20820332/Influence_of_Valley_Type_on_the_Scaling_Properties_of_River_Planforms">Influence of Valley Type on the Scaling Properties of River Planforms</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="42111670" href="https://independent.academia.edu/AnicetBeauvais">Anicet Beauvais</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Water Resources Research, 1996</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Influence of Valley Type on the Scaling Properties of River Planforms","attachmentId":41580050,"attachmentType":"pdf","work_url":"https://www.academia.edu/20820332/Influence_of_Valley_Type_on_the_Scaling_Properties_of_River_Planforms","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/20820332/Influence_of_Valley_Type_on_the_Scaling_Properties_of_River_Planforms"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="1" data-entity-id="1248926" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/1248926/Models_of_Fractal_River_Basins">Models of Fractal River Basins</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="1998070" href="https://unive.academia.edu/AchilleGiacometti">Achille Giacometti</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of statistical …, 1998</p><p class="ds-related-work--abstract ds2-5-body-sm">Two distinct models for self-similar and self-affine river basins are numerically investigated. 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