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<span>Structure</span> </div> </a> <button aria-controls="toc-Structure-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 Structure subsection</span> </button> <ul id="toc-Structure-sublist" class="vector-toc-list"> <li id="toc-Source_region" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Source_region"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Source region</span> </div> </a> <ul id="toc-Source_region-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Liftoff_point" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Liftoff_point"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Liftoff point</span> </div> </a> <ul id="toc-Liftoff_point-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Near-field_region" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Near-field_region"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Near-field region</span> </div> </a> <ul id="toc-Near-field_region-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mid-field_region" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mid-field_region"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Mid-field region</span> </div> </a> <ul id="toc-Mid-field_region-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Far-field_region" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Far-field_region"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Far-field region</span> </div> </a> <ul id="toc-Far-field_region-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Advection" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Advection"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Advection</span> </div> </a> <button aria-controls="toc-Advection-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 Advection subsection</span> </button> <ul id="toc-Advection-sublist" class="vector-toc-list"> <li id="toc-Bottom-advected_plumes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bottom-advected_plumes"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Bottom-advected plumes</span> </div> </a> <ul id="toc-Bottom-advected_plumes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Surface-advected_plumes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Surface-advected_plumes"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Surface-advected plumes</span> </div> </a> <ul id="toc-Surface-advected_plumes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Intermediate_plumes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Intermediate_plumes"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Intermediate plumes</span> </div> </a> <ul id="toc-Intermediate_plumes-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Tidal_variation" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Tidal_variation"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Tidal variation</span> </div> </a> <button aria-controls="toc-Tidal_variation-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon 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</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">Mix of fresh river water and seawater</div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Kodor_river_plume.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Kodor_river_plume.jpg/250px-Kodor_river_plume.jpg" decoding="async" width="250" height="188" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Kodor_river_plume.jpg/375px-Kodor_river_plume.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Kodor_river_plume.jpg/500px-Kodor_river_plume.jpg 2x" data-file-width="4864" data-file-height="3648" /></a><figcaption><a href="/wiki/Kodori_River" class="mw-redirect" title="Kodori River">Kodor</a> river plume</figcaption></figure> <p>A <b>river plume</b> is a <a href="/wiki/Fresh_water" title="Fresh water">freshened</a> <a href="/wiki/Water_mass" title="Water mass">water mass</a> that is formed in the <a href="/wiki/Sea" title="Sea">sea</a> as a result of mixing of <a href="/wiki/Surface_runoff" title="Surface runoff">river discharge</a> and saline <a href="/wiki/Seawater" title="Seawater">seawater</a>.<sup id="cite_ref-:0_1-0" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> River plumes are formed in coastal sea areas at many regions in the World. River plumes generally occupy wide-but-shallow sea surface layers bounded by sharp <a href="/wiki/Density_gradient" title="Density gradient">density gradients</a>. The area of a river plume is 3-5 orders of magnitude greater than its depth; therefore, even small <a href="/wiki/River" title="River">rivers</a> with <a href="/wiki/Discharge_(hydrology)" title="Discharge (hydrology)">discharge</a> rates ~1–10 m/s form river plumes with horizontal spatial extents ~10–100 m. Areas of river plumes formed by the largest rivers are ~100–1000 km<sup>2</sup>. Despite the relatively small volume of total <a href="/wiki/Fresh_water" title="Fresh water">freshwater</a> <a href="/wiki/Discharge_(hydrology)" title="Discharge (hydrology)">runoff</a> to the <a href="/wiki/World_Ocean" class="mw-redirect" title="World Ocean">World Ocean</a>, river plumes occupy up to 21% of <a href="/wiki/Continental_shelf" title="Continental shelf">shelf areas</a> of the ocean, i.e., several million square kilometers.<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> </p><p>In some occasions river plumes are spoken of as <a href="/wiki/Region_of_freshwater_influence" title="Region of freshwater influence">regions of fresh water influence</a> (ROFIs), although it is preferred to use this term for regions in which multiple sources add to the <a href="/wiki/Fresh_water" title="Fresh water">fresh water</a> input of the zone or for shallow, frictional <a href="/wiki/Continental_shelf" title="Continental shelf">shelves</a>.<sup id="cite_ref-:0_1-1" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Region_of_freshwater_influence" title="Region of freshwater influence">ROFIs</a> and river plumes differ in the variation at temporal and spatial scales. The river plume can be identified as a buoyant <a href="/wiki/Water_mass" title="Water mass">water mass</a> that emerges due to <a href="/wiki/Discharge_(hydrology)" title="Discharge (hydrology)">river discharge</a> into the coastal ocean and varies over <a href="/wiki/Diurnal_cycle" title="Diurnal cycle">diurnal</a> to <a href="/wiki/Synoptic_scale_meteorology" title="Synoptic scale meteorology">synoptic</a> timescales.<sup id="cite_ref-:6_3-0" class="reference"><a href="#cite_note-:6-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> At the edges of this <a href="/wiki/Water_mass" title="Water mass">water mass</a> mixing takes place, creating a region adjacent to the river plume which is diluted and fresher compared to the open ocean, but does not have a clear boundary. This extended region is called the region of freshwater influence, <a href="/wiki/Region_of_freshwater_influence" title="Region of freshwater influence">ROFI</a>.<sup id="cite_ref-:6_3-1" class="reference"><a href="#cite_note-:6-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Due to the indirect influence of <a href="/wiki/Discharge_(hydrology)" title="Discharge (hydrology)">freshwater discharge</a>, ROFIs incorporate the dynamics and spatial extent of the river plumes but are typically assessed on seasonal, annual, and decadal timescales.<sup id="cite_ref-:6_3-2" class="reference"><a href="#cite_note-:6-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Processes">Processes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=River_plume&action=edit&section=1" title="Edit section: Processes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>River plumes play an important role in global and regional land-ocean interactions. <a href="/wiki/Discharge_(hydrology)" title="Discharge (hydrology)">River discharges</a> provide large fluxes of <a href="/wiki/Buoyancy" title="Buoyancy">buoyancy</a>, <a href="/wiki/Heat" title="Heat">heat</a>, <a href="/wiki/Suspended_load" title="Suspended load">terrigenous sediments</a>, <a href="/wiki/Biogenic_substance" title="Biogenic substance">nutrients</a>, and anthropogenic <a href="/wiki/Pollutant" title="Pollutant">pollutants</a> to the <a href="/wiki/Ocean" title="Ocean">ocean</a>. River plumes strongly influence many <a href="/wiki/Physics" title="Physics">physical</a>, <a href="/wiki/Biological" class="mw-redirect" title="Biological">biological</a>, and <a href="/wiki/Geochemistry" title="Geochemistry">geochemical</a> processes in the coastal and shelf sea areas including <a href="/wiki/Ocean_stratification" title="Ocean stratification">stratification</a> of <a href="/wiki/Seawater" title="Seawater">seawater</a>, coastal <a href="/wiki/Ocean_current" title="Ocean current">currents</a>, <a href="/wiki/Carbon_cycle" title="Carbon cycle">carbon</a> and <a href="/wiki/Biogeochemical_cycle" title="Biogeochemical cycle">biogeochemical</a> cycles, <a href="/wiki/Primary_production" title="Primary production">primary production</a>, and <a href="/wiki/Seabed" title="Seabed">seabed morphology</a>.<sup id="cite_ref-:0_1-2" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>A river plume is a dynamical system influenced by processes with a wide range of temporal and spatial scales, which depend on the size and shape of the <a href="/wiki/Estuary" title="Estuary">estuary</a> as well as on the type and variation of the forcing from the <a href="/wiki/Estuary" title="Estuary">estuary</a> and the <a href="/wiki/Ocean" title="Ocean">ocean</a>. Feedback mechanisms between <a href="/wiki/Sediment" title="Sediment">sediment</a> deposited by the plume at the <a href="/wiki/River_delta" title="River delta">submarine delta</a> and the geometry of the <a href="/wiki/River_delta" title="River delta">delta</a> make for a complex system. Due to this complexity there is not (yet) a general, simple theory that offers quantitative predictability for the motion of particles and the structure of river plumes;<sup id="cite_ref-:0_1-3" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> however, some theories incorporating simplified assumptions have helped in understanding the important aspects of <a href="/wiki/Buoyancy" title="Buoyancy">buoyancy</a>-influenced coastal flows.<sup id="cite_ref-:7_4-0" class="reference"><a href="#cite_note-:7-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> As is commonly used in <a href="/wiki/Fluid_dynamics" title="Fluid dynamics">fluid dynamics</a>, the description of these complex flows is aided by <a href="/wiki/Scale_analysis_(mathematics)" title="Scale analysis (mathematics)">scaling analysis</a> to determine the relevant processes. The primary parameters which define the structure and scale of an individual river plume are <a href="/wiki/Discharge_(hydrology)" title="Discharge (hydrology)">freshwater discharge</a>, <a href="/wiki/Tidal_Power" class="mw-redirect" title="Tidal Power">tidal energy</a>, <a href="/wiki/Coast" title="Coast">coastline</a> <a href="/wiki/Bathymetry" title="Bathymetry">bathymetry/geometry</a>, ambient <a href="/wiki/Ocean_currents" class="mw-redirect" title="Ocean currents">ocean currents</a>, <a href="/wiki/Wind" title="Wind">wind</a>, and <a href="/wiki/Coriolis_force" title="Coriolis force">the rotation of the Earth</a>.<sup id="cite_ref-:0_1-4" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Structure">Structure</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=River_plume&action=edit&section=2" title="Edit section: Structure"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div><p> The balance between the important processes varies over the position in the plume. The following regions can be distinguished: the source region, the liftoff point, the front, and the near field region. Beyond the plume itself but within its area of influence are the mid-field region and the far field region.<sup id="cite_ref-:0_1-5" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><figure typeof="mw:File/Thumb"><a href="/wiki/File:Schematic_structure_plume.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Schematic_structure_plume.png/399px-Schematic_structure_plume.png" decoding="async" width="399" height="224" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Schematic_structure_plume.png/599px-Schematic_structure_plume.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Schematic_structure_plume.png/798px-Schematic_structure_plume.png 2x" data-file-width="1280" data-file-height="720" /></a><figcaption>Schematic structure of a river plume, viewed from above. Adapted from Horner-Devine (2015).<sup id="cite_ref-:0_1-6" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Source_region">Source region</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=River_plume&action=edit&section=3" title="Edit section: Source region"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the source or estuarine region, the <a href="/wiki/Buoyancy" title="Buoyancy">buoyancy</a> and <a href="/wiki/Momentum" title="Momentum">momentum</a> of the freshwater inflow from the estuary are the dominant properties that determine the initiation of the river plume. The competition between river-induced <a href="/wiki/Stratification_(water)" title="Stratification (water)">stratification</a> and tidal mixing sets the river plume's characteristic properties. This competition can be captured in the (dimensionless) estuarine <a href="/wiki/Richardson_number" title="Richardson number">Richardson number</a>, which is defined as<sup id="cite_ref-:8_5-0" class="reference"><a href="#cite_note-:8-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </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 Ri_{E}=g_{r}'{\frac {Q_{r}}{W_{E}u_{tidal}^{3}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> <mo>′</mo> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mrow> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> </msub> <msubsup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>i</mi> <mi>d</mi> <mi>a</mi> <mi>l</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msubsup> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Ri_{E}=g_{r}'{\frac {Q_{r}}{W_{E}u_{tidal}^{3}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/19ed86617b9b1c3513bf77520063809d9c9644cc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:19.343ex; height:6.509ex;" alt="{\displaystyle Ri_{E}=g_{r}'{\frac {Q_{r}}{W_{E}u_{tidal}^{3}}},}"></span> </p><p>where </p> <ul><li>the reduced gravity <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'_{r}=g(\Delta \rho /\rho _{0})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> <mo>′</mo> </msubsup> <mo>=</mo> <mi>g</mi> <mo stretchy="false">(</mo> <mi mathvariant="normal">Δ</mi> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g'_{r}=g(\Delta \rho /\rho _{0})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d717409c3d4fd500de5b7e949dabcfcad84ef2f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.663ex; height:2.843ex;" alt="{\displaystyle g'_{r}=g(\Delta \rho /\rho _{0})}"></span> is the <a href="/wiki/Gravitational_acceleration" title="Gravitational acceleration">gravitational acceleration</a> due to the <a href="/wiki/Density" title="Density">density</a> difference between <a href="/wiki/Fresh_water" title="Fresh water">fresh river water</a> and <a href="/wiki/Seawater" title="Seawater">saline ocean water</a>,</li> <li><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_{r}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q_{r}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d499b1ea4f782a76aef1e44edceba5ba326f731d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.812ex; height:2.509ex;" alt="{\displaystyle Q_{r}}"></span> is the <a href="/wiki/Discharge_(hydrology)" title="Discharge (hydrology)">river discharge</a>,</li> <li><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_{E}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W_{E}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/55ee8cf025f8c25a50d6f5fd157abd00868cfd45" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.681ex; height:2.509ex;" alt="{\displaystyle W_{E}}"></span> is the <a href="/wiki/Estuary" title="Estuary">estuary</a> width, and</li> <li><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_{tidal}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>i</mi> <mi>d</mi> <mi>a</mi> <mi>l</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{tidal}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d3eb51e874907ee398774cda74d48d5b6317909" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.943ex; height:2.009ex;" alt="{\displaystyle u_{tidal}}"></span> is the tidal velocity.</li></ul> <p>where </p> <ul><li><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'_{r}=g(\Delta \rho /\rho _{0})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> <mo>′</mo> </msubsup> <mo>=</mo> <mi>g</mi> <mo stretchy="false">(</mo> <mi mathvariant="normal">Δ</mi> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g'_{r}=g(\Delta \rho /\rho _{0})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d717409c3d4fd500de5b7e949dabcfcad84ef2f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.663ex; height:2.843ex;" alt="{\displaystyle g'_{r}=g(\Delta \rho /\rho _{0})}"></span> is the <a href="/wiki/Gravitational_acceleration" title="Gravitational acceleration">gravitational acceleration</a> due to the <a href="/wiki/Density" title="Density">density</a> difference between <a href="/wiki/Fresh_water" title="Fresh water">fresh river water</a> and <a href="/wiki/Seawater" title="Seawater">saline ocean water</a>,</li> <li><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_{r}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q_{r}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d499b1ea4f782a76aef1e44edceba5ba326f731d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.812ex; height:2.509ex;" alt="{\displaystyle Q_{r}}"></span> is the <a href="/wiki/Discharge_(hydrology)" title="Discharge (hydrology)">river discharge</a>,</li> <li><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_{E}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W_{E}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/55ee8cf025f8c25a50d6f5fd157abd00868cfd45" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.681ex; height:2.509ex;" alt="{\displaystyle W_{E}}"></span> is the <a href="/wiki/Estuary" title="Estuary">estuary</a> width, and</li> <li><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_{tidal}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>i</mi> <mi>d</mi> <mi>a</mi> <mi>l</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{tidal}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d3eb51e874907ee398774cda74d48d5b6317909" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.943ex; height:2.009ex;" alt="{\displaystyle u_{tidal}}"></span> is the tidal velocity.</li></ul> <p>A large estuarine Richardson number (i.e. <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 Ri_{E}\gg 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> </msub> <mo>≫</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Ri_{E}\gg 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e2c631bc85f2090b18164908508596b40ec32f4a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.831ex; height:2.509ex;" alt="{\displaystyle Ri_{E}\gg 1}"></span>) indicates that <a href="/wiki/Fresh_water" title="Fresh water">freshwater</a> processes are dominant compared to the <a href="/wiki/Tide" title="Tide">tidal</a> influence, and one can expect development of a river plume.<sup id="cite_ref-:0_1-7" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Liftoff_point">Liftoff point</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=River_plume&action=edit&section=4" title="Edit section: Liftoff point"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In case of strong riverine forcing, often with a large estuarine <a href="/wiki/Richardson_number" title="Richardson number">Richardson number</a>, the front of the plume separates from the <a href="/wiki/Seabed" title="Seabed">bottom</a>. The position at which this <a href="/wiki/Flow_separation" title="Flow separation">flow separation</a> occurs is called the liftoff point and sets the landward edge of the near-field. This point is important in surface-advected river plumes.<sup id="cite_ref-:1_6-0" class="reference"><a href="#cite_note-:1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:2_7-0" class="reference"><a href="#cite_note-:2-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Near-field_region">Near-field region</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=River_plume&action=edit&section=5" title="Edit section: Near-field region"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the near-field the momentum of the plume is larger than its <a href="/wiki/Buoyancy" title="Buoyancy">buoyancy</a>. This balance is represented in the (dimensionless) <a href="/wiki/Froude_number" title="Froude number">Froude 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 Fr={u}/{\sqrt {gh}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mi>r</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>g</mi> <mi>h</mi> </msqrt> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Fr={u}/{\sqrt {gh}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f41cfa8ad35240222ef57918bc258c4cb50ff35d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:13.806ex; height:3.509ex;" alt="{\displaystyle Fr={u}/{\sqrt {gh}},}"></span> and is larger than one in the near-field, indicating <a href="/wiki/Supercritical_flow" title="Supercritical flow">supercritical flow</a>. Both the liftoff point and the outer boundary of the near-field, the plume front, are characterized by critical flow conditions (<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 Fr=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mi>r</mi> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Fr=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/14ff7b3c9a947d9ea32c6f2492072156cead83f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.05ex; height:2.176ex;" alt="{\displaystyle Fr=1}"></span>) and the flow in the near-field region shows features similar to a jet.<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> The <a href="/wiki/Momentum" title="Momentum">momentum balance</a> is dominated by <a href="/wiki/Barotropic_fluid" title="Barotropic fluid">barotropic</a> and <a href="/wiki/Baroclinity" title="Baroclinity">baroclinic</a> <a href="/wiki/Pressure" title="Pressure">pressure</a> gradients, <a href="/wiki/Turbulence" title="Turbulence">turbulent</a> shear stresses, and flow acceleration. Flow deceleration is mainly caused by the <a href="/wiki/Shear_stress" title="Shear stress">shear stresses</a> on the interface of the plume with the ambient <a href="/wiki/Ocean" title="Ocean">ocean</a>. In some cases a near-field region will not exist. This is for example the case if the width of the <a href="/wiki/River_mouth" title="River mouth">river mouth</a> is large relative to the <a href="/wiki/Rossby_radius_of_deformation" title="Rossby radius of deformation">Rossby radius of deformation</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 L_{R}={\sqrt {gh}}/{f}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>g</mi> <mi>h</mi> </msqrt> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{R}={\sqrt {gh}}/{f}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e19ada671993b23c71de8e73d9676428847ce575" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:13.381ex; height:3.509ex;" alt="{\displaystyle L_{R}={\sqrt {gh}}/{f}}"></span>, and the <a href="/wiki/Fresh_water" title="Fresh water">fresh water</a> inflow will leave the <a href="/wiki/River_mouth" title="River mouth">river mouth</a> as a far-field plume. When <a href="/wiki/Tide" title="Tide">tides</a> are large, the near-field plume is also known as the tidal plume.<sup id="cite_ref-:3_9-0" class="reference"><a href="#cite_note-:3-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Mid-field_region">Mid-field region</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=River_plume&action=edit&section=6" title="Edit section: Mid-field region"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The area at which the near-field inertial jet transfers into a flow in which <a href="/wiki/Geostrophic_current" title="Geostrophic current">geostrophic</a> or <a href="/wiki/Wind" title="Wind">wind</a>-driven processes are dominant is the midfield-area. The <a href="/wiki/Momentum" title="Momentum">momentum balance</a> of the mid-field is dominated by the rotation of the Earth (<a href="/wiki/Coriolis_force" title="Coriolis force">Coriolis effect</a>), cross-stream internal <a href="/wiki/Pressure" title="Pressure">pressure</a> gradients, and sometimes <a href="/wiki/Centripetal_force" title="Centripetal force">centripetal</a> acceleration. The initial <a href="/wiki/Momentum" title="Momentum">momentum</a> of the <a href="/wiki/Discharge_(hydrology)" title="Discharge (hydrology)">outflow</a> from the source is lost and the <a href="/wiki/Wind" title="Wind">wind</a> forcing (or <a href="/wiki/Earth%27s_rotation" title="Earth's rotation">rotation of the Earth</a> in case of small <a href="/wiki/Wind" title="Wind">wind</a> forcing) gradually takes over as the most important parameter. As a result, the flow changes its speed, direction, and spreading pattern. When the influence of <a href="/wiki/Wind" title="Wind">wind</a> forcing is small, <a href="/wiki/Discharge_(hydrology)" title="Discharge (hydrology)">outflows</a> can sometimes form a recirculating bulge;<sup id="cite_ref-:0_1-8" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:1_6-1" class="reference"><a href="#cite_note-:1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> however, evidence of such a feature in field observations is scant.<sup id="cite_ref-:17_10-0" class="reference"><a href="#cite_note-:17-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Far-field_region">Far-field region</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=River_plume&action=edit&section=7" title="Edit section: Far-field region"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Even further away from the source region is the far-field, where the plume has lost all memory of the outflow momentum. The momentum balance of the far-field is dominated by the rotation of the Earth (<a href="/wiki/Coriolis_force" title="Coriolis force">Coriolis effect</a>), <a href="/wiki/Buoyancy" title="Buoyancy">buoyancy</a>, <a href="/wiki/Wind" title="Wind">wind</a> forcing, and bottom stress. The far-field can cover large areas, up to hundreds of kilometers from its source. <a href="/wiki/Diurnal_cycle" title="Diurnal cycle">Diurnal</a> and semi-diurnal variability of the far-field region is generally governed by <a href="/wiki/Tide" title="Tide">tides</a>, synoptic variability by <a href="/wiki/Wind" title="Wind">wind</a> forcing, and seasonal variability by river discharge. In the absence of strong <a href="/wiki/Wind" title="Wind">wind</a> forcing and strong currents, the far-field plume can behave as a current of relatively <a href="/wiki/Fresh_water" title="Fresh water">fresh water</a> in the direction of a propagating <a href="/wiki/Kelvin_wave" title="Kelvin wave">Kelvin wave</a>. Examples of this can be observed in the Rhine <a href="/wiki/Region_of_freshwater_influence" title="Region of freshwater influence">ROFI</a>, where the river plume can be traced all along the Dutch coast.<sup id="cite_ref-:10_11-0" class="reference"><a href="#cite_note-:10-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> The character of this coastal current is different in the case of shallow seas, when the current occupies the whole <a href="/wiki/Water_column" title="Water column">water column</a> and its motion is affected by bottom <a href="/wiki/Friction" title="Friction">friction</a>, and in the case of a surface-advected plume whose vertical size is less than the water depth.<sup id="cite_ref-:0_1-9" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:1_6-2" class="reference"><a href="#cite_note-:1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Advection">Advection</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=River_plume&action=edit&section=8" title="Edit section: Advection"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>At the most basic and idealized level, river plumes can be classified to be either surface-<a href="/wiki/Advection" title="Advection">advected</a> or bottom-<a href="/wiki/Advection" title="Advection">advected</a>.<sup id="cite_ref-:1_6-3" class="reference"><a href="#cite_note-:1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:4_12-0" class="reference"><a href="#cite_note-:4-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> A plume is considered to be bottom-advected when it occupies the whole water column from the surface to the <a href="/wiki/Seabed" title="Seabed">seabed</a>. In this case its <a href="/wiki/Stratification_(water)" title="Stratification (water)">stratification</a> is mainly horizontal as a result of strong <a href="/wiki/Advection" title="Advection">advection</a> over the whole <a href="/wiki/Water_column" title="Water column">water column</a>, especially near the <a href="/wiki/Seabed" title="Seabed">bed</a>. A surface-advected plume does not interact with the <a href="/wiki/Seabed" title="Seabed">bottom</a> because its vertical size is less than its depth. In this case a plume is mainly vertically <a href="/wiki/Stratification_(water)" title="Stratification (water)">stratified</a>. Differentiation between these two (idealized) types of river plumes can be made by evaluating a set of parameters, as set up by Yankovsky and Chapman in their paper from 1997.<sup id="cite_ref-:1_6-4" class="reference"><a href="#cite_note-:1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> The distance up to which the <a href="/wiki/Fresh_water" title="Fresh water">fresh water</a> river plume is transported across-shelf by processes at the surface is given by </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 y_{s}={\frac {2}{f}}{\sqrt {\frac {3g'h_{0}+v_{i}^{2}}{2g'h_{0}+v_{i}^{2}}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mi>f</mi> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>3</mn> <msup> <mi>g</mi> <mo>′</mo> </msup> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> <mrow> <mn>2</mn> <msup> <mi>g</mi> <mo>′</mo> </msup> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> </mfrac> </msqrt> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y_{s}={\frac {2}{f}}{\sqrt {\frac {3g'h_{0}+v_{i}^{2}}{2g'h_{0}+v_{i}^{2}}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d02483fdd30834f67890ac5839b93c982a277048" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:21.673ex; height:7.676ex;" alt="{\displaystyle y_{s}={\frac {2}{f}}{\sqrt {\frac {3g'h_{0}+v_{i}^{2}}{2g'h_{0}+v_{i}^{2}}}},}"></span> </p><p>where </p> <ul><li><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 v_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7dffe5726650f6daac54829972a94f38eb8ec127" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.927ex; height:2.009ex;" alt="{\displaystyle v_{i}}"></span> is the inflow velocity from the source region and the near-field jet,</li> <li><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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span> is the Coriolis force,</li> <li><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"> <msup> <mi>g</mi> <mo>′</mo> </msup> </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/e7a53c0df5d85b36e3fd327c74db998f679f4f55" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.803ex; height:2.843ex;" alt="{\displaystyle g'}"></span> is the buoyancy, and</li> <li><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_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08c1c908b03c3f63383c7199465c7fd0b105030f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.393ex; height:2.509ex;" alt="{\displaystyle h_{0}}"></span> is the depth of the water column at the mouth of the <a href="/wiki/River" title="River">river</a>/<a href="/wiki/Estuary" title="Estuary">estuary</a>.</li></ul> <p>Up to the liftoff point, the plume still "feels" the bottom and one speaks of bottom-advected plumes, and the relevant processes involving bottom dynamics must be accounted for.<sup id="cite_ref-:5_13-0" class="reference"><a href="#cite_note-:5-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Vertical scales of river plumes formed by the largest rivers across the world are 10-20 m, while the vertical scale of the majority of river plumes is less than several meters. As a result, the majority of river plumes in the world are surface-advected; that is, the bottom-advected part near the estuary before the liftoff point at these plumes is much smaller than the surface-advected part. River plumes with large bottom-advected parts are formed mainly by large rivers that flow into shallow sea areas, such as the <a href="/wiki/Volga" title="Volga">Volga</a> plume in the northern part of the <a href="/wiki/Caspian_Sea" title="Caspian Sea">Caspian Sea</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Bottom-advected_plumes">Bottom-advected plumes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=River_plume&action=edit&section=9" title="Edit section: Bottom-advected plumes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Schematic_structure_bottom_advected_top.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Schematic_structure_bottom_advected_top.png/300px-Schematic_structure_bottom_advected_top.png" decoding="async" width="300" height="169" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Schematic_structure_bottom_advected_top.png/450px-Schematic_structure_bottom_advected_top.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Schematic_structure_bottom_advected_top.png/600px-Schematic_structure_bottom_advected_top.png 2x" data-file-width="1280" data-file-height="720" /></a><figcaption>Schematic structure of a bottom-advected river plume, top view. Adapted from Yankovsky and Chapman (1997)<sup id="cite_ref-:1_6-5" class="reference"><a href="#cite_note-:1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>.</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Schematic_structure_bottom_advected_side.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Schematic_structure_bottom_advected_side.png/295px-Schematic_structure_bottom_advected_side.png" decoding="async" width="295" height="166" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Schematic_structure_bottom_advected_side.png/443px-Schematic_structure_bottom_advected_side.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Schematic_structure_bottom_advected_side.png/590px-Schematic_structure_bottom_advected_side.png 2x" data-file-width="717" data-file-height="404" /></a><figcaption>Schematic structure of a bottom-advected river plume, side view. Adapted from Yankovsky and Chapman (1997)<sup id="cite_ref-:1_6-6" class="reference"><a href="#cite_note-:1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>.</figcaption></figure> <p>Bottom-advected plumes are often characterized by large discharge conditions and are generally less sensitive to <a href="/wiki/Wind" title="Wind">wind</a> forcing and corresponding advection and mixing.<sup id="cite_ref-:1_6-7" class="reference"><a href="#cite_note-:1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> This type of advection is driven by bottom <a href="/wiki/Ekman_transport" title="Ekman transport">Ekman transport</a>, which drives the fresh or brackish river outflow with 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 _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f9e51d2ad9cab8f8a5d962502ddf4189b713f7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.002ex; height:2.176ex;" alt="{\displaystyle \rho _{i}}"></span> and 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 v_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7dffe5726650f6daac54829972a94f38eb8ec127" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.927ex; height:2.009ex;" alt="{\displaystyle v_{i}}"></span> from an estuary of 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 L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}"></span> and 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 h_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08c1c908b03c3f63383c7199465c7fd0b105030f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.393ex; height:2.509ex;" alt="{\displaystyle h_{0}}"></span> to the frontal zone across the shelf. This is indicated in the figure to the right. When the frontal zone is far enough from the shore, <a href="/wiki/Thermal_wind" title="Thermal wind">thermal wind</a> dynamics can transport the complete volume flux away from the estuary. The across-shore position <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 y_{b}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y_{b}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/003a2487b07ae916ef6123320db8958f8eed6cea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.077ex; height:2.009ex;" alt="{\displaystyle y_{b}}"></span>, which denotes the width of the coastal current, and the equilibrium-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 h_{b}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{b}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/140aec52ffb1fd0966772704b2fe00827cdefa13" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.277ex; height:2.509ex;" alt="{\displaystyle h_{b}}"></span> at which the plume separates from the bottom can be calculated in equilibrium conditions with a certain bottom slope <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/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span> by </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 h_{b}={\sqrt {\frac {2fv_{i}h_{0}}{g'}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>2</mn> <mi>f</mi> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <msup> <mi>g</mi> <mo>′</mo> </msup> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{b}={\sqrt {\frac {2fv_{i}h_{0}}{g'}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6f846b87146350a9214523d47c9cd376893f40ca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:15.297ex; height:7.676ex;" alt="{\displaystyle h_{b}={\sqrt {\frac {2fv_{i}h_{0}}{g'}}}}"></span> </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 y_{b}={\frac {h_{0}}{s}}({\sqrt {\frac {2fLv_{i}}{g'h_{0}}}}-1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>s</mi> </mfrac> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>2</mn> <mi>f</mi> <mi>L</mi> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <msup> <mi>g</mi> <mo>′</mo> </msup> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </msqrt> </mrow> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y_{b}={\frac {h_{0}}{s}}({\sqrt {\frac {2fLv_{i}}{g'h_{0}}}}-1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a621aa2433a046a0a307576bcb762e978adac30" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:23.328ex; height:7.509ex;" alt="{\displaystyle y_{b}={\frac {h_{0}}{s}}({\sqrt {\frac {2fLv_{i}}{g'h_{0}}}}-1)}"></span>.<sup id="cite_ref-:1_6-8" class="reference"><a href="#cite_note-:1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>Note that this is only valid when <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_{b}>h_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>></mo> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{b}>h_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec0e1748536e02468e6e49fa1d313c02f4cf2894" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.768ex; height:2.509ex;" alt="{\displaystyle h_{b}>h_{0}}"></span>. When <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_{b}<h_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo><</mo> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{b}<h_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b16e6c16f14ebca8cf5bee68739fcc184ee894d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.768ex; height:2.509ex;" alt="{\displaystyle h_{b}<h_{0}}"></span>the bottom <a href="/wiki/Ekman_layer" title="Ekman layer">Ekman layer</a> cannot transport the river outflow offshore and another process governs the propagation. In that case, only a surface-advected plume is found.<sup id="cite_ref-:1_6-9" class="reference"><a href="#cite_note-:1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:2_7-1" class="reference"><a href="#cite_note-:2-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Surface-advected_plumes">Surface-advected plumes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=River_plume&action=edit&section=10" title="Edit section: Surface-advected plumes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Schematic_structure_surface_advected_top.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Schematic_structure_surface_advected_top.png/292px-Schematic_structure_surface_advected_top.png" decoding="async" width="292" height="164" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Schematic_structure_surface_advected_top.png/438px-Schematic_structure_surface_advected_top.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Schematic_structure_surface_advected_top.png/584px-Schematic_structure_surface_advected_top.png 2x" data-file-width="1280" data-file-height="720" /></a><figcaption>Schematic structure of a surface-advected river plume, top view. Adapted from Yankovsky and Chapman (1997)<sup id="cite_ref-:1_6-10" class="reference"><a href="#cite_note-:1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>.</figcaption></figure><figure typeof="mw:File/Thumb"><a href="/wiki/File:Schematic_structure_surface_advected_side.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Schematic_structure_surface_advected_side.png/290px-Schematic_structure_surface_advected_side.png" decoding="async" width="290" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Schematic_structure_surface_advected_side.png/435px-Schematic_structure_surface_advected_side.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Schematic_structure_surface_advected_side.png/580px-Schematic_structure_surface_advected_side.png 2x" data-file-width="770" data-file-height="397" /></a><figcaption>Schematic structure of a surface-advected river plume, side view. Adapted from Yankovsky and Chapman (1997)<sup id="cite_ref-:1_6-11" class="reference"><a href="#cite_note-:1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>.</figcaption></figure><p>Surface-advected plumes occur when the previously-defined condition 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 h_{b}<h_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo><</mo> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{b}<h_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b16e6c16f14ebca8cf5bee68739fcc184ee894d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.768ex; height:2.509ex;" alt="{\displaystyle h_{b}<h_{0}}"></span> is met. A surface-advected plume has the typical structure of a river plume as described in the section <a href="#River_plume_structure">river plume structure</a>. In the region near the mouth the initial momentum of the river outflow is the dominant mechanism, after which other processes such as <a href="/wiki/Wind" title="Wind">wind</a> forcing and the <a href="/wiki/Coriolis_force" title="Coriolis force">Coriolis effect</a> take over. In a surface-advected plume,. processes regarding interaction with the bottom such as the development of a bottom <a href="/wiki/Ekman_layer" title="Ekman layer">Ekman layer</a> are not relevant. Therefore, the defined 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 y_{b}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y_{b}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/003a2487b07ae916ef6123320db8958f8eed6cea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.077ex; height:2.009ex;" alt="{\displaystyle y_{b}}"></span>can be ignored in this approach as it has no physical basis.<sup id="cite_ref-:1_6-12" class="reference"><a href="#cite_note-:1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:2_7-2" class="reference"><a href="#cite_note-:2-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><div class="mw-heading mw-heading3"><h3 id="Intermediate_plumes">Intermediate plumes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=River_plume&action=edit&section=11" title="Edit section: Intermediate plumes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the case that the inflow 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 h_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08c1c908b03c3f63383c7199465c7fd0b105030f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.393ex; height:2.509ex;" alt="{\displaystyle h_{0}}"></span> is smaller than 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 h_{b}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{b}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/140aec52ffb1fd0966772704b2fe00827cdefa13" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.277ex; height:2.509ex;" alt="{\displaystyle h_{b}}"></span>, and the distance up to which the bottom <a href="/wiki/Ekman_layer" title="Ekman layer">Ekman layer</a> transports the river discharge is smaller than the distance up to which the surface processes transport the river outflow, (<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 y_{b}<y_{s}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo><</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y_{b}<y_{s}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3879f88d51064f1e8e50055c7f9ca0019f8b73fb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.318ex; height:2.176ex;" alt="{\displaystyle y_{b}<y_{s}}"></span>), one can find an intermediate plume. In an intermediate plume both regimes can be found. Naturally, the bottom-advected section can be found closer to the estuary mouth and the surface-advected section can be found further offshore. The liftoff point separates the regions.<sup id="cite_ref-:1_6-13" class="reference"><a href="#cite_note-:1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:2_7-3" class="reference"><a href="#cite_note-:2-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>The approach can be further generalized by non-dimensionalizing the parameters. Non-dimensional parameters have the benefit of simplifying the dynamics of the relevant processes by evaluating the magnitude of different terms. In the case of river plumes, it gives further direction to the basic classification and their different dynamics. The two most relevant non-dimensional numbers are the <a href="/w/index.php?title=Burger_number&action=edit&redlink=1" class="new" title="Burger number (page does not exist)">Burger 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 S={\sqrt {g'h_{0}}}/(fL)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>g</mi> <mo>′</mo> </msup> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </msqrt> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">(</mo> <mi>f</mi> <mi>L</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S={\sqrt {g'h_{0}}}/(fL)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/529580d31045d0dfd9fb67b83876c9d38ed052a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:16.951ex; height:4.843ex;" alt="{\displaystyle S={\sqrt {g'h_{0}}}/(fL)}"></span>, which expresses the relative importance of <a href="/wiki/Buoyancy" title="Buoyancy">buoyancy</a>, and the <a href="/wiki/Rossby_number" title="Rossby number">Rossby 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 Ro=v_{i}/(fL)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mi>o</mi> <mo>=</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">(</mo> <mi>f</mi> <mi>L</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Ro=v_{i}/(fL)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb992680303e92a49aaa1414cbb4e75282a8c0e9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.751ex; height:2.843ex;" alt="{\displaystyle Ro=v_{i}/(fL)}"></span>, which expresses the relative importance of advection. Regrouping leads to the following, non-dimensional cross-shore distances <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 Y_{b}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y_{b}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2135845f0456acaacc8fe84067f6f7a08af3c581" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.288ex; height:2.509ex;" alt="{\displaystyle Y_{b}}"></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 Y_{s}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y_{s}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b6802614359e5b2a13d3dc8cee4640865ae03d5b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.354ex; height:2.509ex;" alt="{\displaystyle Y_{s}}"></span>: </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 Y_{s}={\frac {2(3S^{2}+Ro^{2})}{\sqrt {2S^{2}+Ro^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mo stretchy="false">(</mo> <mn>3</mn> <msup> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>R</mi> <msup> <mi>o</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> <msqrt> <mn>2</mn> <msup> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>R</mi> <msup> <mi>o</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y_{s}={\frac {2(3S^{2}+Ro^{2})}{\sqrt {2S^{2}+Ro^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0b7dffe53c348ffcdcc7a9c7b7e8ee858772410" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:19.785ex; height:7.176ex;" alt="{\displaystyle Y_{s}={\frac {2(3S^{2}+Ro^{2})}{\sqrt {2S^{2}+Ro^{2}}}}}"></span> </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 Y_{b}={\frac {h_{0}}{sL}}({\frac {\sqrt {2Ro}}{S}}-1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mi>s</mi> <mi>L</mi> </mrow> </mfrac> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mn>2</mn> <mi>R</mi> <mi>o</mi> </msqrt> <mi>S</mi> </mfrac> </mrow> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y_{b}={\frac {h_{0}}{sL}}({\frac {\sqrt {2Ro}}{S}}-1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/745f021546a9c0c5697867ad92d3077072661dcb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:21.534ex; height:6.009ex;" alt="{\displaystyle Y_{b}={\frac {h_{0}}{sL}}({\frac {\sqrt {2Ro}}{S}}-1)}"></span>. </p><p>The same regimes as discussed above hold for the non-dimensional parameters. Bottom-advected plumes (<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_{b}>h_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>></mo> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{b}>h_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec0e1748536e02468e6e49fa1d313c02f4cf2894" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.768ex; height:2.509ex;" alt="{\displaystyle h_{b}>h_{0}}"></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 Y_{b}>Y_{s}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>></mo> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y_{b}>Y_{s}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a4bd330a2a4cbf3d0fcf5253c5cc113f3b025f84" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.741ex; height:2.509ex;" alt="{\displaystyle Y_{b}>Y_{s}}"></span>) in general have small <a href="/w/index.php?title=Burger_number&action=edit&redlink=1" class="new" title="Burger number (page does not exist)">Burger numbers</a> and therefore <a href="/wiki/Buoyancy" title="Buoyancy">buoyancy</a> is relatively unimportant. Surface-advected plumes (<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_{b}<h_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo><</mo> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{b}<h_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b16e6c16f14ebca8cf5bee68739fcc184ee894d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.768ex; height:2.509ex;" alt="{\displaystyle h_{b}<h_{0}}"></span>) in general have large <a href="/w/index.php?title=Burger_number&action=edit&redlink=1" class="new" title="Burger number (page does not exist)">Burger numbers</a> and therefore <a href="/wiki/Buoyancy" title="Buoyancy">buoyancy</a> is important. Furthermore, the <a href="/wiki/Rossby_number" title="Rossby number">Rossby number</a> indicates whether the plume is classified as a surface-advected plume or an intermediate plume. A relatively large <a href="/wiki/Rossby_number" title="Rossby number">Rossby number</a> compared to the <a href="/w/index.php?title=Burger_number&action=edit&redlink=1" class="new" title="Burger number (page does not exist)">Burger number</a> indicates that <a href="/wiki/Advection" title="Advection">advection</a> is important compared to <a href="/wiki/Buoyancy" title="Buoyancy">buoyancy</a> and will allow at least partial bottom-advection to occur so that one can expect an intermediate plume.<sup id="cite_ref-:1_6-14" class="reference"><a href="#cite_note-:1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:4_12-1" class="reference"><a href="#cite_note-:4-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>Note that the scheme described above was developed for idealized cases: that is, for river plumes in absence of external forcing which flow into a <a href="/wiki/Sea" title="Sea">sea</a> with idealized <a href="/wiki/Bathymetry" title="Bathymetry">bathymetry</a> and shoreline. </p> <div class="mw-heading mw-heading2"><h2 id="Tidal_variation">Tidal variation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=River_plume&action=edit&section=12" title="Edit section: Tidal variation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>River plumes vary over diurnal to <a href="/wiki/Synoptic_scale_meteorology" title="Synoptic scale meteorology">synoptic</a> temporal scales.<sup id="cite_ref-:6_3-3" class="reference"><a href="#cite_note-:6-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> In this range of temporal scales, the most important periodic variation lies within the tidal cycle, in which a <a href="/wiki/Tidal_cycle" class="mw-redirect" title="Tidal cycle">tidal cycle</a> (daily) and a spring-neap cycle (two-weekly) can be distinguished.<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> This <a href="/wiki/Barotropic_fluid" title="Barotropic fluid">barotropic</a> variation in tidal velocity magnitude and direction gives rise to variability in the strength and stability of the river plume.<sup id="cite_ref-:2_7-4" class="reference"><a href="#cite_note-:2-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> This is already clear from the competition between river discharge and tidal mixing, captured in the (dimensionless) estuarine <a href="/wiki/Richardson_number" title="Richardson number">Richardson 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 Ri_{E}=g_{r}'{Q_{r}}/W_{E}u_{tidal}^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> <mo>′</mo> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> </msub> <msubsup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>i</mi> <mi>d</mi> <mi>a</mi> <mi>l</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Ri_{E}=g_{r}'{Q_{r}}/W_{E}u_{tidal}^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90ee067389785e75a8e3218f7603e8a8a5459f25" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:21.834ex; height:3.176ex;" alt="{\displaystyle Ri_{E}=g_{r}'{Q_{r}}/W_{E}u_{tidal}^{3}}"></span>, which is used to assess in a general fashion whether a river plume can develop in a certain system.<sup id="cite_ref-:8_5-1" class="reference"><a href="#cite_note-:8-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> The tidal dynamics lead to the following general dynamics of river plumes. </p> <div class="mw-heading mw-heading3"><h3 id="Tidal_cycle">Tidal cycle</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=River_plume&action=edit&section=13" title="Edit section: Tidal cycle"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Baroclininc_schematic_tidal_straining.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/84/Baroclininc_schematic_tidal_straining.png/412px-Baroclininc_schematic_tidal_straining.png" decoding="async" width="412" height="270" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/84/Baroclininc_schematic_tidal_straining.png/618px-Baroclininc_schematic_tidal_straining.png 1.5x, //upload.wikimedia.org/wikipedia/commons/8/84/Baroclininc_schematic_tidal_straining.png 2x" data-file-width="788" data-file-height="516" /></a><figcaption>Tidal variation in plume <a href="/wiki/Stratification_(water)" title="Stratification (water)">stratification</a>. Tidal straining for ebb flows and tidal mixing for flood flows.</figcaption></figure> <p>A <a href="/wiki/Tidal_cycle" class="mw-redirect" title="Tidal cycle">tidal cycle</a> consists of a flood period or landward flow, and an ebb period or seaward flow.<sup id="cite_ref-:9_15-0" class="reference"><a href="#cite_note-:9-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> For constant <a href="/wiki/River_discharge" class="mw-redirect" title="River discharge">river discharge</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 Q_{r}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q_{r}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d499b1ea4f782a76aef1e44edceba5ba326f731d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.812ex; height:2.509ex;" alt="{\displaystyle Q_{r}}"></span> one can find a stable <a href="/wiki/Stratification_(water)" title="Stratification (water)">stratification</a> during ebb conditions and an unstable <a href="/wiki/Stratification_(water)" title="Stratification (water)">stratification</a> during flood conditions.<sup id="cite_ref-:10_11-1" class="reference"><a href="#cite_note-:10-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> This is schematically portrayed in the figure to the right. The mixing that occurs during flood conditions due to the unstable <a href="/wiki/Stratification_(water)" title="Stratification (water)">stratification</a> weakens the <a href="/wiki/Stratification_(water)" title="Stratification (water)">stratification</a> and efficient river plume advection<sup id="cite_ref-:10_11-2" class="reference"><a href="#cite_note-:10-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> and occurs in situations with low estuarine <a href="/wiki/Richardson_number" title="Richardson number">Richardson numbers</a>. </p><p>During ebb conditions the <a href="/wiki/Stratification_(water)" title="Stratification (water)">stratification</a> is enhanced. This leads to stable conditions and strong advection at the surface.<sup id="cite_ref-:10_11-3" class="reference"><a href="#cite_note-:10-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Due to mass conservation, this situation requires enhanced landward flows near the bottom. This process is called <a href="/w/index.php?title=Tidal_straining&action=edit&redlink=1" class="new" title="Tidal straining (page does not exist)">tidal straining</a>. In the case of an open coast, two-dimensional effects start playing a role. <a href="/wiki/Baroclinity" title="Baroclinity">Baroclinic</a> <a href="/wiki/Ekman_transport" title="Ekman transport">Ekman transport</a> causes <a href="/wiki/Upwelling" title="Upwelling">upwelling</a> during ebb flows and <a href="/wiki/Downwelling" title="Downwelling">downwelling</a> during flood flows.<sup id="cite_ref-:8_5-2" class="reference"><a href="#cite_note-:8-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Therefore, these <a href="/wiki/Baroclinity" title="Baroclinity">baroclinic</a> <a href="/wiki/Upwelling" title="Upwelling">upwelling</a> effects can cause ebb flows to transport nutrients and sediment towards the coast.<sup id="cite_ref-:10_11-4" class="reference"><a href="#cite_note-:10-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Spring-neap_cycle">Spring-neap cycle</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=River_plume&action=edit&section=14" title="Edit section: Spring-neap cycle"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Baroclininc_schematic_neap_spring.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Baroclininc_schematic_neap_spring.png/416px-Baroclininc_schematic_neap_spring.png" decoding="async" width="416" height="325" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Baroclininc_schematic_neap_spring.png/624px-Baroclininc_schematic_neap_spring.png 1.5x, //upload.wikimedia.org/wikipedia/commons/0/01/Baroclininc_schematic_neap_spring.png 2x" data-file-width="746" data-file-height="582" /></a><figcaption>Schematic of the spring-tide and neap-tide extremes for river plume <a href="/wiki/Stratification_(water)" title="Stratification (water)">stratification</a>. Adapted from Valle-Levinson (2010)<sup id="cite_ref-:7_4-1" class="reference"><a href="#cite_note-:7-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>.</figcaption></figure> <p>Over a spring-neap cycle the <a href="/wiki/Baroclinity" title="Baroclinity">baroclinic</a> effects over a <a href="/wiki/Tidal_cycle" class="mw-redirect" title="Tidal cycle">tidal cycle</a> amplify and favor either increased tidal straining or tidal mixing.<sup id="cite_ref-:10_11-5" class="reference"><a href="#cite_note-:10-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Spring_tides" class="mw-redirect" title="Spring tides">Spring tides</a> are characterized by relatively large tidal amplitudes and tidal flow velocities.<sup id="cite_ref-:9_15-1" class="reference"><a href="#cite_note-:9-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> This leads to increased tidal mixing over the complete <a href="/wiki/Tidal_cycle" class="mw-redirect" title="Tidal cycle">tidal cycle</a> and weakened <a href="/wiki/Stratification_(water)" title="Stratification (water)">stratification</a>.<sup id="cite_ref-:10_11-6" class="reference"><a href="#cite_note-:10-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> In some areas the <a href="/wiki/Stratification_(water)" title="Stratification (water)">stratification</a> vanishes completely, resulting in a well-mixed system, and these systems can only incorporate river plumes some of the time.<sup id="cite_ref-:2_7-5" class="reference"><a href="#cite_note-:2-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> In open-<a href="/wiki/Coast" title="Coast">coast</a> systems, <a href="/wiki/Spring_tide" class="mw-redirect" title="Spring tide">spring tide</a> conditions generally lead to increased <a href="/wiki/Downwelling" title="Downwelling">downwelling</a> effects from the <a href="/wiki/Buoyancy" title="Buoyancy">buoyant</a> river plume, causing increased seaward transport of <a href="/wiki/Sediment" title="Sediment">sediment</a> and <a href="/wiki/Nutrient" title="Nutrient">nutrients</a>.<sup id="cite_ref-:10_11-7" class="reference"><a href="#cite_note-:10-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Neap_Tides" class="mw-redirect" title="Neap Tides">Neap tides</a> are characterized by relatively low tidal amplitudes and tidal flow velocities.<sup id="cite_ref-:9_15-2" class="reference"><a href="#cite_note-:9-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> This situation favors the tidal straining effect as observed during ebb tides due to decreased tidal mixing and increased differential flow over a <a href="/wiki/Tidal_cycle" class="mw-redirect" title="Tidal cycle">tidal cycle</a>.<sup id="cite_ref-:10_11-8" class="reference"><a href="#cite_note-:10-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Due to the stronger tidal straining effect, <a href="/wiki/Neap_Tide" class="mw-redirect" title="Neap Tide">neap tide</a> conditions are generally characterized by increased landward flow near the bottom and associated increased coastal <a href="/wiki/Upwelling" title="Upwelling">upwelling</a> effects.<sup id="cite_ref-:10_11-9" class="reference"><a href="#cite_note-:10-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> In extreme cases this can lead to large depositions on the <a href="/wiki/Beach" title="Beach">beach</a>, such as the mass beaching event of <a href="/wiki/Starfish" title="Starfish">starfish</a> at the <a href="/wiki/Coast" title="Coast">coast</a> near <a href="/wiki/Scheveningen" title="Scheveningen">Scheveningen</a> January 30, 2019.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Natural_examples">Natural examples</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=River_plume&action=edit&section=15" title="Edit section: Natural examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Fraser_River">Fraser River</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=River_plume&action=edit&section=16" title="Edit section: Fraser River"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:The_Big_Muddy,_Western_Edition_(6987590721).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/af/The_Big_Muddy%2C_Western_Edition_%286987590721%29.jpg/219px-The_Big_Muddy%2C_Western_Edition_%286987590721%29.jpg" decoding="async" width="219" height="146" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/af/The_Big_Muddy%2C_Western_Edition_%286987590721%29.jpg/329px-The_Big_Muddy%2C_Western_Edition_%286987590721%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/af/The_Big_Muddy%2C_Western_Edition_%286987590721%29.jpg/438px-The_Big_Muddy%2C_Western_Edition_%286987590721%29.jpg 2x" data-file-width="5559" data-file-height="3706" /></a><figcaption>The <a href="/wiki/Fraser_River" title="Fraser River">Fraser River</a> plume</figcaption></figure><p>An example of a surface-advected plume is the <a href="/wiki/Fraser_River" title="Fraser River">Fraser River</a> plume. The <a href="/wiki/Fraser_River" title="Fraser River">Fraser River</a> plume contains all dynamical regions, clearly visible from space. The initial jet-like structure gradually transfers into a far-field plume further offshore, which is deflected to the right as would be expected on the <a href="/wiki/Northern_Hemisphere" title="Northern Hemisphere">Northern Hemisphere</a> due to the <a href="/wiki/Coriolis_force" title="Coriolis force">Coriolis effect</a>. Other similar river plumes are those of the <a href="/wiki/Columbia_River" title="Columbia River">Columbia River</a>, the <a href="/wiki/Niagara_River" title="Niagara River">Niagara River</a>, and the <a href="/wiki/Hudson_River" title="Hudson River">Hudson River</a>.<sup id="cite_ref-:0_1-10" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:3_9-1" class="reference"><a href="#cite_note-:3-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><div class="mw-heading mw-heading3"><h3 id="Amazon_River">Amazon River</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=River_plume&action=edit&section=17" title="Edit section: Amazon River"><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:Amazon_River_mouth_on_the_Atlantic.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Amazon_River_mouth_on_the_Atlantic.jpg/220px-Amazon_River_mouth_on_the_Atlantic.jpg" decoding="async" width="220" height="124" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Amazon_River_mouth_on_the_Atlantic.jpg/330px-Amazon_River_mouth_on_the_Atlantic.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/75/Amazon_River_mouth_on_the_Atlantic.jpg/440px-Amazon_River_mouth_on_the_Atlantic.jpg 2x" data-file-width="9579" data-file-height="5393" /></a><figcaption>The <a href="/wiki/Amazon_River" title="Amazon River">Amazon River</a> plume</figcaption></figure><p>The <a href="/wiki/Amazon_River" title="Amazon River">Amazon River</a> plume is an example of a river plume in which the <a href="/wiki/Earth%27s_rotation" title="Earth's rotation">Earth's rotation</a> does not play a role. Due to the high <a href="/wiki/Discharge_(hydrology)" title="Discharge (hydrology)">discharge</a>, the corresponding <a href="/wiki/Momentum" title="Momentum">momentum</a> of the <a href="/wiki/Outflow_(hydrology)" class="mw-redirect" title="Outflow (hydrology)">outflow</a>, and the equatorial latitude, the dynamics of the plume are mainly characterized by the internal <a href="/wiki/Froude_number" title="Froude number">Froude number</a>. Ambient currents transport the plume away from the mouth.<sup id="cite_ref-:0_1-11" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:5_13-1" class="reference"><a href="#cite_note-:5-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Similar plumes can be found elsewhere along the <a href="/wiki/Equator" title="Equator">Equator</a>. </p><div class="mw-heading mw-heading3"><h3 id="Mersey_River">Mersey River</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=River_plume&action=edit&section=18" title="Edit section: Mersey River"><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:Liverpool_Bay.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Liverpool_Bay.png/220px-Liverpool_Bay.png" decoding="async" width="220" height="163" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Liverpool_Bay.png/330px-Liverpool_Bay.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/60/Liverpool_Bay.png/440px-Liverpool_Bay.png 2x" data-file-width="1278" data-file-height="947" /></a><figcaption>The <a href="/wiki/River_Mersey" title="River Mersey">Mersey River</a> plume</figcaption></figure> <p>The dynamics of the <a href="/wiki/River_Mersey" title="River Mersey">Mersey River</a> plume at the mouth of <a href="/wiki/Liverpool_Bay" title="Liverpool Bay">Liverpool Bay</a> show high resemblance to a bottom-advected plume.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> This is due to strong influence of the bottom and bottom <a href="/wiki/Friction" title="Friction">friction</a> on the flow, and this controls the cross-shore spreading and length-scale. This type of plume can often be found at <a href="/wiki/Marginal_sea" class="mw-redirect" title="Marginal sea">marginal seas</a> and <a href="/wiki/Shelf_sea" class="mw-redirect" title="Shelf sea">shelf seas</a>, such as in the <a href="/wiki/North_Sea" title="North Sea">North Sea</a> at the mouth of the <a href="/wiki/Rhine" title="Rhine">Rhine</a>.<sup id="cite_ref-:0_1-12" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<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=River_plume&action=edit&section=19" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Plume_(fluid_dynamics)" title="Plume (fluid dynamics)">Plume (fluid dynamics)</a></li> <li><a href="/wiki/Region_of_freshwater_influence" title="Region of freshwater influence">Region of freshwater influence</a></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=River_plume&action=edit&section=20" 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-:0-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:0_1-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:0_1-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-:0_1-4"><sup><i><b>e</b></i></sup></a> <a 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School for Marine Science and Technology, University of Massachusetts, Dartmouth<span class="reference-accessdate">. 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title="Ayre (landform)">Ayre</a></li> <li><a href="/wiki/Barrier_island" title="Barrier island">Barrier island</a></li> <li><a href="/wiki/Bay" title="Bay">Bay</a></li> <li><a href="/wiki/Bight_(geography)" title="Bight (geography)">Bight</a></li> <li><a href="/wiki/Bodden" title="Bodden">Bodden</a></li> <li><a href="/wiki/Brackish_marsh" title="Brackish marsh">Brackish marsh</a></li> <li><a href="/wiki/Cape_(geography)" title="Cape (geography)">Cape</a></li> <li><a href="/wiki/Channel_(geography)" title="Channel (geography)">Channel</a></li> <li><a href="/wiki/Cliff" title="Cliff">Cliff</a></li> <li><a href="/wiki/Coast" title="Coast">Coast</a></li> <li><a href="/wiki/Coastal_plain" title="Coastal plain">Coastal plain</a></li> <li><a href="/wiki/Coastal_waterfall" title="Coastal waterfall">Coastal waterfall</a></li> <li><a href="/wiki/Continental_margin" title="Continental margin">Continental margin</a></li> <li><a href="/wiki/Continental_shelf" title="Continental shelf">Continental shelf</a></li> <li><a href="/wiki/Coral_reef" title="Coral reef">Coral reef</a></li> <li><a href="/wiki/Cove" title="Cove">Cove</a></li> <li><a href="/wiki/Dune" title="Dune">Dune</a> <ul><li><a href="/wiki/Cliff-top_dune" title="Cliff-top dune">cliff-top</a></li></ul></li> <li><a href="/wiki/Estuary" title="Estuary">Estuary</a></li> <li><a href="/wiki/Firth" title="Firth">Firth</a></li> <li><a href="/wiki/Fjard" title="Fjard">Fjard</a></li> <li><a href="/wiki/Fjord" title="Fjord">Fjord</a></li> <li><a href="/wiki/Freshwater_marsh" title="Freshwater marsh">Freshwater marsh</a></li> <li><a href="/wiki/Fundus_(seabed)" title="Fundus (seabed)">Fundus</a></li> <li><a href="/wiki/Gat_(landform)" title="Gat (landform)">Gat</a></li> <li><a href="/wiki/Geo_(landform)" title="Geo (landform)">Geo</a></li> <li><a href="/wiki/Gulf" title="Gulf">Gulf</a></li> <li><a href="/wiki/Gut_(coastal_geography)" title="Gut (coastal geography)">Gut</a></li> <li><a href="/wiki/Hapua" title="Hapua">Hapua</a></li> <li><a href="/wiki/Headland" title="Headland">Headland</a></li> <li><a href="/wiki/Inlet" title="Inlet">Inlet</a></li> <li><a href="/wiki/Intertidal_wetland" title="Intertidal wetland">Intertidal wetland</a></li> <li><a href="/wiki/Island" title="Island">Island</a></li> <li><a href="/wiki/Islet" title="Islet">Islet</a></li> <li><a href="/wiki/Isthmus" title="Isthmus">Isthmus</a></li> <li><a href="/wiki/Lagoon" title="Lagoon">Lagoon</a></li> <li><a href="/wiki/Machair" title="Machair">Machair</a></li> <li><a href="/wiki/Mudflat" title="Mudflat">Mudflat</a></li> <li><a href="/wiki/Natural_arch" title="Natural arch">Natural arch</a></li> <li><a href="/wiki/Peninsula" title="Peninsula">Peninsula</a></li> <li><a href="/wiki/Reef" title="Reef">Reef</a></li> <li><a href="/wiki/Ria" title="Ria">Ria</a></li> <li><a href="/wiki/Salt_marsh" title="Salt marsh">Salt marsh</a></li> <li><a href="/wiki/Shoal" title="Shoal">Shoal</a></li> <li><a href="/wiki/Skerry" title="Skerry">Skerry</a></li> <li><a href="/wiki/Sound_(geography)" title="Sound (geography)">Sound</a></li> <li><a href="/wiki/Spit_(landform)" title="Spit (landform)">Spit</a></li> <li><a href="/wiki/Stack_(geology)" title="Stack (geology)">Stack</a></li> <li><a href="/wiki/Strait" title="Strait">Strait</a></li> <li><a href="/wiki/Strand_plain" title="Strand plain">Strand plain</a></li> <li><a href="/wiki/Submarine_canyon" title="Submarine canyon">Submarine canyon</a></li> <li><a href="/wiki/Tidal_island" title="Tidal island">Tidal island</a></li> <li><a href="/wiki/Tidal_marsh" title="Tidal marsh">Tidal marsh</a></li> <li><a href="/wiki/Tide_pool" title="Tide pool">Tide pool</a></li> <li><a href="/wiki/Tied_island" title="Tied island">Tied island</a></li> <li><a href="/wiki/Tombolo" title="Tombolo">Tombolo</a></li> <li><a href="/wiki/Waituna" title="Waituna">Waituna</a></li> <li><i><a href="/wiki/Windwatt" title="Windwatt">Windwatt</a></i></li></ul> </div></td><td class="noviewer navbox-image" rowspan="6" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:Accreting_coast_Image6.svg" class="mw-file-description" title="Coastal and oceanic landforms"><img alt="Coastal and oceanic landforms" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/48/Accreting_coast_Image6.svg/140px-Accreting_coast_Image6.svg.png" decoding="async" width="140" height="66" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/48/Accreting_coast_Image6.svg/210px-Accreting_coast_Image6.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/48/Accreting_coast_Image6.svg/280px-Accreting_coast_Image6.svg.png 2x" data-file-width="1481" data-file-height="697" /></a></span><br /><br /><span typeof="mw:File"><a href="/wiki/File:Fernando_noronha.jpg" class="mw-file-description" title="Dois Irmãos - Fernando de Noronha"><img alt="Dois Irmãos - Fernando de Noronha" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/Fernando_noronha.jpg/140px-Fernando_noronha.jpg" decoding="async" width="140" height="105" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/Fernando_noronha.jpg/210px-Fernando_noronha.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/58/Fernando_noronha.jpg/280px-Fernando_noronha.jpg 2x" data-file-width="1024" data-file-height="768" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Beach" title="Beach">Beaches</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/Beach_cusps" title="Beach cusps">Beach cusps</a></li> <li><a href="/wiki/Beach_evolution" title="Beach evolution">Beach evolution</a></li> <li><a href="/wiki/Beach_ridge" title="Beach ridge">Beach ridge</a></li> <li><a href="/wiki/Beach_wrack" title="Beach wrack">Beach wrack</a></li> <li><a href="/wiki/Beaches_in_estuaries_and_bays" title="Beaches in estuaries and bays">Beaches in estuaries and bays</a></li> <li><a href="/wiki/Beachrock" title="Beachrock">Beachrock</a></li> <li><a href="/wiki/Coastal_morphodynamics" title="Coastal morphodynamics">Coastal morphodynamics</a></li> <li><a href="/wiki/Pocket_beach" title="Pocket beach">Pocket beach</a></li> <li><a href="/wiki/Raised_beach" title="Raised beach">Raised beach</a></li> <li><a href="/wiki/Modern_recession_of_beaches" class="mw-redirect" title="Modern recession of beaches">Recession</a></li> <li><a href="/wiki/Seashell" title="Seashell">Shell beach</a></li> <li><a href="/wiki/Shingle_beach" title="Shingle beach">Shingle beach</a></li> <li><a href="/wiki/Storm_beach" title="Storm beach">Storm beach</a></li> <li><a href="/wiki/Wash_margin" title="Wash margin">Wash margin</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/River_mouth" title="River mouth">River mouths</a></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/Debouch" title="Debouch">Debouch</a></li> <li><a href="/wiki/Mouth_bar" title="Mouth bar">Mouth bar</a></li> <li><a href="/wiki/River_delta" title="River delta">River delta</a> <ul><li><a href="/wiki/Mega_delta" class="mw-redirect" title="Mega delta">mega</a></li> <li><a href="/wiki/Regressive_delta" title="Regressive delta">regressive</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Large-scale_coastal_behaviour" title="Large-scale coastal behaviour">Processes</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/Blowhole_(geology)" title="Blowhole (geology)">Blowhole</a></li> <li><a href="/wiki/Cliffed_coast" title="Cliffed coast">Cliffed coast</a></li> <li><a href="/wiki/Coastal_biogeomorphology" title="Coastal biogeomorphology">Coastal biogeomorphology</a></li> <li><a href="/wiki/Coastal_erosion" title="Coastal erosion">Coastal erosion</a></li> <li><a href="/wiki/Concordant_coastline" title="Concordant coastline">Concordant coastline</a></li> <li><a href="/wiki/Current_(hydrology)" title="Current (hydrology)">Current</a></li> <li><a href="/wiki/Cuspate_foreland" title="Cuspate foreland">Cuspate foreland</a></li> <li><a href="/wiki/Discordant_coastline" title="Discordant coastline">Discordant coastline</a></li> <li><a href="/wiki/Emergent_coastline" title="Emergent coastline">Emergent coastline</a></li> <li><a href="/wiki/Feeder_bluff" title="Feeder bluff">Feeder bluff</a></li> <li><a href="/wiki/Flat_coast" title="Flat coast">Flat coast</a></li> <li><a href="/wiki/Graded_shoreline" title="Graded shoreline">Graded shoreline</a></li> <li><a href="/wiki/Ingression_coast" title="Ingression coast">Ingression coast</a></li> <li><a href="/wiki/Large-scale_coastal_behaviour" title="Large-scale coastal behaviour">Large-scale coastal behaviour</a></li> <li><a href="/wiki/Longshore_drift" title="Longshore drift">Longshore drift</a></li> <li><a href="/wiki/Marine_regression" title="Marine regression">Marine regression</a></li> <li><a href="/wiki/Marine_transgression" title="Marine transgression">Marine transgression</a></li> <li><a href="/wiki/Raised_shoreline" title="Raised shoreline">Raised shoreline</a></li> <li><a href="/wiki/Rip_current" title="Rip current">Rip current</a></li> <li><a href="/wiki/Rocky_shore" title="Rocky shore">Rocky shore</a></li> <li><a href="/wiki/Sea_cave" title="Sea cave">Sea cave</a></li> <li><a href="/wiki/Sea_foam" title="Sea foam">Sea foam</a></li> <li><a href="/wiki/Shoal" title="Shoal">Shoal</a> <ul><li><a href="/wiki/Peresyp" title="Peresyp">peresyp</a></li></ul></li> <li><a href="/wiki/Steep_coast" title="Steep coast">Steep coast</a></li> <li><a href="/wiki/Submergent_coastline" title="Submergent coastline">Submergent coastline</a></li> <li><a href="/wiki/Surf_break" title="Surf break">Surf break</a></li> <li><a href="/wiki/Surf_zone" title="Surf zone">Surf zone</a></li> <li><a href="/wiki/Surge_channel" title="Surge channel">Surge channel</a></li> <li><a href="/wiki/Swash" title="Swash">Swash</a></li> <li><a href="/wiki/Undertow_(water_waves)" title="Undertow (water waves)">Undertow</a></li> <li><a href="/wiki/Volcanic_arc" title="Volcanic arc">Volcanic arc</a></li> <li><a href="/wiki/Wave-cut_platform" title="Wave-cut platform">Wave-cut platform</a></li> <li><a href="/wiki/Wave_shoaling" title="Wave shoaling">Wave shoaling</a></li> <li><a href="/wiki/Wind_fetch" title="Wind fetch">Wind fetch</a></li> <li><a href="/wiki/Wind_wave" title="Wind wave">Wind wave</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Coastal_management" title="Coastal management">Management</a></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/Accretion_(coastal_management)" title="Accretion (coastal management)">Accretion</a></li> <li><a href="/wiki/Coastal_management" title="Coastal management">Coastal management</a></li> <li><a href="/wiki/Integrated_coastal_zone_management" title="Integrated coastal zone management">Integrated coastal zone management</a></li> <li><a href="/wiki/Submersion_(coastal_management)" title="Submersion (coastal management)">Submersion</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</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/Bulkhead_line" title="Bulkhead line">Bulkhead line</a></li> <li><a href="/wiki/Coastal_engineering" title="Coastal engineering">Coastal engineering</a></li> <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/Clay" title="Clay">clay</a></li> <li><a href="/wiki/Cobble_(geology)" title="Cobble (geology)">cobble</a></li> <li><a href="/wiki/Granule_(geology)" title="Granule (geology)">granule</a></li> <li><a href="/wiki/Gravel" title="Gravel">gravel</a></li> <li><a href="/wiki/Pebble" title="Pebble">pebble</a></li> <li><a href="/wiki/Sand" title="Sand">sand</a></li> <li><a href="/wiki/Shingle_beach" title="Shingle beach">shingle</a></li> <li><a href="/wiki/Silt" title="Silt">silt</a></li></ul></li> <li><a href="/wiki/Intertidal_zone" title="Intertidal zone">Intertidal zone</a></li> <li><a href="/wiki/Littoral_zone" title="Littoral zone">Littoral zone</a></li> <li><a href="/wiki/Physical_oceanography" title="Physical oceanography">Physical oceanography</a></li> <li><a href="/wiki/Region_of_freshwater_influence" title="Region of freshwater influence">Region of freshwater influence</a></li> <li><a class="mw-selflink selflink">River plume</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="3"><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:Coastal_geography" title="Category:Coastal geography">Category</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" 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