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typeof="mw:File/Thumb"><a href="/wiki/File:Langmuir_Circulation.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Langmuir_Circulation.jpg/220px-Langmuir_Circulation.jpg" decoding="async" width="220" height="112" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Langmuir_Circulation.jpg/330px-Langmuir_Circulation.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Langmuir_Circulation.jpg/440px-Langmuir_Circulation.jpg 2x" data-file-width="1129" data-file-height="573" /></a><figcaption>Langmuir circulation</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Rodeo_Lagoon_From_Trail.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Rodeo_Lagoon_From_Trail.JPG/220px-Rodeo_Lagoon_From_Trail.JPG" decoding="async" width="220" height="130" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Rodeo_Lagoon_From_Trail.JPG/330px-Rodeo_Lagoon_From_Trail.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Rodeo_Lagoon_From_Trail.JPG/440px-Rodeo_Lagoon_From_Trail.JPG 2x" data-file-width="3040" data-file-height="1793" /></a><figcaption>White streaks in this lagoon are due to the Langmuir circulation.</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Lines_of_sargassum_Sargasso_Sea.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Lines_of_sargassum_Sargasso_Sea.jpg/220px-Lines_of_sargassum_Sargasso_Sea.jpg" decoding="async" width="220" height="293" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Lines_of_sargassum_Sargasso_Sea.jpg/330px-Lines_of_sargassum_Sargasso_Sea.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Lines_of_sargassum_Sargasso_Sea.jpg/440px-Lines_of_sargassum_Sargasso_Sea.jpg 2x" data-file-width="600" data-file-height="800" /></a><figcaption>These lines of <a href="/wiki/Sargassum" title="Sargassum">sargassum</a> can stretch for miles along the surface. The clumps of floating <a href="/wiki/Algae" title="Algae">algae</a> are often concentrated by the strong winds and wave action associated with the <a href="/wiki/Gulf_Stream" title="Gulf Stream">Gulf Stream</a>.</figcaption></figure> <p>In <a href="/wiki/Physical_oceanography" title="Physical oceanography">physical oceanography</a>, <b>Langmuir circulation</b> consists of a series of shallow, slow, counter-rotating <a href="/wiki/Vortex" title="Vortex">vortices</a> at the ocean's surface aligned with the wind. These circulations are developed when wind blows steadily over the sea surface. <a href="/wiki/Irving_Langmuir" title="Irving Langmuir">Irving Langmuir</a> discovered this phenomenon after observing <a href="/wiki/Windrow" title="Windrow">windrows</a> of seaweed in the <a href="/wiki/Sargasso_Sea" title="Sargasso Sea">Sargasso Sea</a> in 1927.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Langmuir circulations circulate within the <a href="/wiki/Mixed_layer" title="Mixed layer">mixed layer</a>; however, it is not yet so clear how strongly they can cause mixing at the base of the mixed layer. <sup id="cite_ref-thorpe2004_2-0" class="reference"><a href="#cite_note-thorpe2004-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Theory">Theory</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Langmuir_circulation&action=edit&section=1" title="Edit section: Theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The driving force of these circulations is an interaction of the mean flow with wave averaged flows of the surface waves. <a href="/wiki/Stokes_drift" title="Stokes drift">Stokes drift velocity</a> of the waves stretches and tilts the vorticity of the flow near the surface. The production of vorticity in the upper ocean is balanced by downward (often turbulent) diffusion <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu _{T}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu _{T}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/05f1c9e973def4abb53b3d6193a61ee58c4c3c63" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.538ex; height:2.009ex;" alt="{\displaystyle \nu _{T}}"></span>. For a flow driven by a wind <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38a7dcde9730ef0853809fefc18d88771f95206c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.202ex; height:1.676ex;" alt="{\displaystyle \tau }"></span> characterized by <a href="/wiki/Friction_velocity" class="mw-redirect" title="Friction velocity">friction velocity</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u_{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53f06376827f0e844992e08986763b37f6f771d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.293ex; margin-bottom: -0.379ex; width:2.384ex; height:2.009ex;" alt="{\displaystyle u_{*}}"></span> the ratio of vorticity diffusion and production defines the Langmuir number <sup id="cite_ref-thorpe2004_2-1" class="reference"><a href="#cite_note-thorpe2004-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {La} ={\sqrt {\frac {\nu _{T}^{3}k^{6}}{\sigma a^{2}u_{*}^{2}k^{4}}}}~{\text{ or }}~{\sqrt {\frac {\nu _{T}^{3}\beta ^{6}}{u_{*}^{2}S_{0}\beta ^{3}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">L</mi> <mi mathvariant="normal">a</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <msubsup> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msubsup> <msup> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> </mrow> <mrow> <mi>σ</mi> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msubsup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <msup> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mrow> </mfrac> </msqrt> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext> or </mtext> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <msubsup> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msubsup> <msup> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> </mrow> <mrow> <msubsup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {La} ={\sqrt {\frac {\nu _{T}^{3}k^{6}}{\sigma a^{2}u_{*}^{2}k^{4}}}}~{\text{ or }}~{\sqrt {\frac {\nu _{T}^{3}\beta ^{6}}{u_{*}^{2}S_{0}\beta ^{3}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95163ae65de3ad623c7e6d819c133df1231261a9" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:31.948ex; height:7.676ex;" alt="{\displaystyle \mathrm {La} ={\sqrt {\frac {\nu _{T}^{3}k^{6}}{\sigma a^{2}u_{*}^{2}k^{4}}}}~{\text{ or }}~{\sqrt {\frac {\nu _{T}^{3}\beta ^{6}}{u_{*}^{2}S_{0}\beta ^{3}}}}}"></span> where the first definition is for a monochromatic wave field of amplitude <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span>, frequency <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 \sigma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59f59b7c3e6fdb1d0365a494b81fb9a696138c36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle \sigma }"></span>, and wavenumber <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}"></span> and the second uses a generic inverse length scale <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 \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }"></span>, and Stokes velocity scale <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_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebe0ac45a38c4437bd2689a14ec434cd499e7e49" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.479ex; height:2.509ex;" alt="{\displaystyle S_{0}}"></span>. This is exemplified by the <a href="/wiki/Craik%E2%80%93Leibovich_vortex_force" title="Craik–Leibovich vortex force">Craik–Leibovich equations</a><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> which are an approximation of the <a href="/wiki/Generalized_Lagrangian_mean" title="Generalized Lagrangian mean">Lagrangian mean</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> In the <a href="/wiki/Boussinesq_approximation_(buoyancy)" title="Boussinesq approximation (buoyancy)">Boussinesq approximation</a> the governing equations can be written <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\partial u_{i}}{\partial t}}+u_{j}\,\nabla _{j}u_{i}=-2\varepsilon _{ijk}\Omega _{j}(u_{k}^{s}+u_{k})-\nabla _{i}\left({\frac {P}{\rho _{0}}}+{\frac {1}{2}}u_{j}^{s}u_{j}^{s}+u_{j}^{s}u_{j}\right)+\varepsilon _{ijk}u_{j}^{s}\varepsilon _{k\ell m}\,\nabla _{\ell }u_{m}+g_{i}{\frac {\rho }{\rho _{0}}}+\nabla _{j}\nu \,\nabla _{j}u_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mspace width="thinmathspace" /> <msub> <mi mathvariant="normal">∇</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mn>2</mn> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> <msub> <mi mathvariant="normal">Ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msubsup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msubsup> <mo>+</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>−</mo> <msub> <mi mathvariant="normal">∇</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>P</mi> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msubsup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msubsup> <msubsup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msubsup> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> </msub> <msubsup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msubsup> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mi>ℓ</mi> <mi>m</mi> </mrow> </msub> <mspace width="thinmathspace" /> <msub> <mi mathvariant="normal">∇</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ℓ</mi> </mrow> </msub> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ρ</mi> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>+</mo> <msub> <mi mathvariant="normal">∇</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mi>ν</mi> <mspace width="thinmathspace" /> <msub> <mi mathvariant="normal">∇</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial u_{i}}{\partial t}}+u_{j}\,\nabla _{j}u_{i}=-2\varepsilon _{ijk}\Omega _{j}(u_{k}^{s}+u_{k})-\nabla _{i}\left({\frac {P}{\rho _{0}}}+{\frac {1}{2}}u_{j}^{s}u_{j}^{s}+u_{j}^{s}u_{j}\right)+\varepsilon _{ijk}u_{j}^{s}\varepsilon _{k\ell m}\,\nabla _{\ell }u_{m}+g_{i}{\frac {\rho }{\rho _{0}}}+\nabla _{j}\nu \,\nabla _{j}u_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f402cc66ffbb589bf16e73ad1dd1d268ecd1e95" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:104.939ex; height:6.176ex;" alt="{\displaystyle {\frac {\partial u_{i}}{\partial t}}+u_{j}\,\nabla _{j}u_{i}=-2\varepsilon _{ijk}\Omega _{j}(u_{k}^{s}+u_{k})-\nabla _{i}\left({\frac {P}{\rho _{0}}}+{\frac {1}{2}}u_{j}^{s}u_{j}^{s}+u_{j}^{s}u_{j}\right)+\varepsilon _{ijk}u_{j}^{s}\varepsilon _{k\ell m}\,\nabla _{\ell }u_{m}+g_{i}{\frac {\rho }{\rho _{0}}}+\nabla _{j}\nu \,\nabla _{j}u_{i}}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nabla _{i}u_{i}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">∇</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla _{i}u_{i}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cee70291aa288b323295c39379f115b86432ea90" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.126ex; height:2.509ex;" alt="{\displaystyle \nabla _{i}u_{i}=0}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\partial \rho }{\partial t}}+u_{j}\,\nabla _{j}\rho =\nabla _{i}\kappa \,\nabla _{i}\rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>ρ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mspace width="thinmathspace" /> <msub> <mi mathvariant="normal">∇</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mi>ρ</mi> <mo>=</mo> <msub> <mi mathvariant="normal">∇</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mi>κ</mi> <mspace width="thinmathspace" /> <msub> <mi mathvariant="normal">∇</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial \rho }{\partial t}}+u_{j}\,\nabla _{j}\rho =\nabla _{i}\kappa \,\nabla _{i}\rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e57f736ea0056f7d513b6749a13137dbae12cadb" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:24.368ex; height:5.676ex;" alt="{\displaystyle {\frac {\partial \rho }{\partial t}}+u_{j}\,\nabla _{j}\rho =\nabla _{i}\kappa \,\nabla _{i}\rho }"></span> 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 u_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/14f13cb025ff2e136dcbd2fc81ddf965b728e3d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.129ex; height:2.009ex;" alt="{\displaystyle u_{i}}"></span> is the fluid velocity,</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 \Omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24b0d5ca6f381068d756f6337c08e0af9d1eeb6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Omega }"></span> is planetary rotation,</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_{i}^{s}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{i}^{s}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f8bf186263cd9ac5ca626ac9f6a97a726f2e53dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.333ex; height:2.843ex;" alt="{\displaystyle u_{i}^{s}}"></span> is the Stokes drift velocity of the surface wave field,</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 P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span> is the pressure,</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_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ce36142a0a1c6660e82bdf3ef3f1551317efe0c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.909ex; height:2.009ex;" alt="{\displaystyle g_{i}}"></span> is the acceleration due to gravity,</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 \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span> is the density,</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 \rho _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9c04a9d26b86af8c6205ba2a6287fd655b6b714" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.256ex; height:2.176ex;" alt="{\displaystyle \rho _{0}}"></span> is the reference density,</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 \nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }"></span> is the viscosity, 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 \kappa }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>κ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \kappa }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54ddec2e922c5caea4e47d04feef86e782dc8e6d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.339ex; height:1.676ex;" alt="{\displaystyle \kappa }"></span> is the diffusivity.</li></ul> <p>In the open ocean conditions where there may not be a dominant length scale controlling the scale of the Langmuir cells the concept of <a href="/wiki/Langmuir_Turbulence" class="mw-redirect" title="Langmuir Turbulence">Langmuir Turbulence</a> is advanced.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Observations">Observations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Langmuir_circulation&action=edit&section=2" title="Edit section: Observations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The circulation has been observed to be between 0°–20° to the right of the wind in the <a href="/wiki/Northern_hemisphere" class="mw-redirect" title="Northern hemisphere">northern hemisphere</a> <sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> and the <a href="/wiki/Helix" title="Helix">helix</a> forming bands of <a href="/wiki/Divergence" title="Divergence">divergence</a> and <a href="/wiki/Convergence_zone" title="Convergence zone">convergence</a> at the surface. At the convergence zones, there are commonly concentrations of floating seaweed, foam and debris along these bands. Along these divergent zones, the ocean surface is typically clear of debris since diverging currents force material out of this zone and into adjacent converging zones. At the surface the circulation will set a current from the divergence zone to the convergence zone and the spacing between these zones are of the order of 1–300 m (3–1,000 ft). Below convergence zones narrow jets of downward flow form and the magnitude of the current will be comparable to the horizontal flow. The downward propagation will typically be in the order of meters or tenths of meters and will not penetrate the <a href="/wiki/Pycnocline" title="Pycnocline">pycnocline</a>. The <a href="/wiki/Upwelling" title="Upwelling">upwelling</a> is less intense and takes place over a wider band under the divergence zone. In wind speeds ranging from 2–12 m/s (6.6–39.4 ft/s) the maximum vertical velocity ranged from 2–10 cm/s (0.79–3.94 in/s) with a ratio of down-welling to wind velocities ranging from −0.0025 to −0.0085. <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> </p> <div class="mw-heading mw-heading2"><h2 id="Biological_effects">Biological effects</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Langmuir_circulation&action=edit&section=3" title="Edit section: Biological effects"><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:Windward_velocity_profile_in_Langmuir_cells.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Windward_velocity_profile_in_Langmuir_cells.jpg/220px-Windward_velocity_profile_in_Langmuir_cells.jpg" decoding="async" width="220" height="154" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Windward_velocity_profile_in_Langmuir_cells.jpg/330px-Windward_velocity_profile_in_Langmuir_cells.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Windward_velocity_profile_in_Langmuir_cells.jpg/440px-Windward_velocity_profile_in_Langmuir_cells.jpg 2x" data-file-width="1216" data-file-height="850" /></a><figcaption>Higher windward velocity in convergent zones of Langmuir cells</figcaption></figure><p>Langmuir circulations (LCs), which are counter-rotating cylindrical roll vortices in the upper ocean, have significant role in vertical mixing. Though they are transient and their strength as well as direction depend on wind and wave properties, they facilitate mixing of nutrients and affect the distribution of marine organisms like <a href="/wiki/Plankton" title="Plankton">plankton</a> in the upper <a href="/wiki/Mixed_layer" title="Mixed layer">mixed layer</a> of ocean.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:0_10-0" class="reference"><a href="#cite_note-:0-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> The wind-generated roll <a href="/wiki/Vortex" title="Vortex">vortices</a> create regions where organisms of different <a href="/wiki/Buoyancy" title="Buoyancy">buoyancy</a>, orientation and swimming behavior can aggregate, resulting in patchiness.<sup id="cite_ref-:1_11-0" class="reference"><a href="#cite_note-:1-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Indeed, LC can produce significant aggregation of <a href="/wiki/Algae" title="Algae">algae</a> during events like <a href="/wiki/Red_tide" class="mw-redirect" title="Red tide">red tide</a>.<sup id="cite_ref-:0_10-1" class="reference"><a href="#cite_note-:0-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> Theoretically, LC size increases with the wind speed unless limited by density discontinuities by <a href="/wiki/Pycnocline" title="Pycnocline">pycnocline</a>. But the visibility of surface effects of LC could be limited by the <a href="/wiki/Breaking_wave" title="Breaking wave">breaking waves</a> during strong winds that disperse the materials present at the surface.<sup id="cite_ref-:2_12-0" class="reference"><a href="#cite_note-:2-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> So, the surface effects of LC are more likely to be visible during winds stronger than critical wind speed of 3 m/s but not too strong. </p><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:PIV_vectors_of_counter_rotating_vortices.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/PIV_vectors_of_counter_rotating_vortices.jpg/220px-PIV_vectors_of_counter_rotating_vortices.jpg" decoding="async" width="220" height="137" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/PIV_vectors_of_counter_rotating_vortices.jpg/330px-PIV_vectors_of_counter_rotating_vortices.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/de/PIV_vectors_of_counter_rotating_vortices.jpg/440px-PIV_vectors_of_counter_rotating_vortices.jpg 2x" data-file-width="1209" data-file-height="755" /></a><figcaption>PIV vectors of counter rotating vortices</figcaption></figure><p>Moreover, previous studies have shown that organisms and materials can aggregate at different regions within LC like downwelling current in convergent zone, upwelling current in divergent zone, retention zone in LC vortex and region between upwelling and downwelling zones.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Similarly, LC are found to have higher <a href="/wiki/Windward_and_leeward" title="Windward and leeward">windward</a> surface current in convergent zones due to jet like flow. This faster moving convergent region in water surface can enhance the transport of organisms and materials in the direction of wind. </p><div class="mw-heading mw-heading3"><h3 id="Effect_on_plants">Effect on plants</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Langmuir_circulation&action=edit&section=4" title="Edit section: Effect on plants"><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:Aggregation_of_particles_within_Langmuir_Circulation.tif" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/Aggregation_of_particles_within_Langmuir_Circulation.tif/lossy-page1-220px-Aggregation_of_particles_within_Langmuir_Circulation.tif.jpg" decoding="async" width="220" height="129" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/Aggregation_of_particles_within_Langmuir_Circulation.tif/lossy-page1-330px-Aggregation_of_particles_within_Langmuir_Circulation.tif.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/08/Aggregation_of_particles_within_Langmuir_Circulation.tif/lossy-page1-440px-Aggregation_of_particles_within_Langmuir_Circulation.tif.jpg 2x" data-file-width="1103" data-file-height="645" /></a><figcaption>Distribution of particles within Langmuir cells</figcaption></figure> <p>In 1927, Langmuir saw the organized rows of <i><a href="/wiki/Sargassum" title="Sargassum">Sargassum</a></i> <i>natans</i> while crossing the <a href="/wiki/Sargasso_Sea" title="Sargasso Sea">Sargasso Sea</a> in the <a href="/wiki/Atlantic_Ocean" title="Atlantic Ocean">Atlantic Ocean</a>. Unlike active swimmers like animals and zooplankton, plants and phytoplankton are usually passive bodies in water and their aggregation are determined by the flow behavior. In windrows, concentrated planktonic organisms color the water and indicate the presence of LC. There has been observation of greater variability in plankton tows collected along the wind direction than samples collected perpendicular to the wind.<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> And one of the reason for such variation could be due to LC that results convergence (high sample) or in between (low sample) zones in alongwind tow.<sup id="cite_ref-Stommel,_H._1949_15-0" class="reference"><a href="#cite_note-Stommel,_H._1949-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> Similarly, such converging effect of LC has also been observed as high chlorophyll zone at about 100 m in <a href="/wiki/Lake_Tahoe" title="Lake Tahoe">Lake Tahoe</a> which could be due to oblique towing through LC.<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> In addition, <i>Sargassum</i> get carried from surface to <a href="/wiki/Benthos" title="Benthos">benthos</a> in downwelling zone of LC and can lose buoyancy after sinking at depth for enough time.<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> Some of the plants that are usually observed floating in water could get submerged during high wind conditions due to downwelling current of LC. Besides, LC could also lead to patchiness of positively buoyant dinoflagellates (including toxic <a href="/wiki/Red_tide" class="mw-redirect" title="Red tide">red tide</a> organisms) during blooms.<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> Moreover, the negatively buoyant phytoplankters which would sink slowly in still water has been observed to get retained in <a href="/wiki/Photic_zone" title="Photic zone">euphotic</a> zone which may be due to suspension created by vertical convection cells.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p><p>Furthermore, a broader study on the Langmuir supercells in which the circulation can reach the seafloor observed the aggregation of <a href="/wiki/Seaweed" title="Seaweed">macroalgae</a> <i><a href="/wiki/Colpomenia" title="Colpomenia">Colpomenia</a> sp.</i> in the sea floor of <a href="/wiki/Shallow_water_marine_environment" title="Shallow water marine environment">shallow waters</a> (~5 m) in <a href="/wiki/Bahama_Banks" title="Bahama Banks">Great Bahama Bank</a> due to local wind speed of around 8 to 13 m/s.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> Such LC could be responsible for transport of carbon biomass from shallow water to <a href="/wiki/Deep_sea" title="Deep sea">deep sea</a>. This effect was evident as the concentration of the <a href="/wiki/Algae" title="Algae">algae</a> were found to reduce dramatically after the occurrence of LC as observed from ocean color <a href="/wiki/Satellite_imagery" title="Satellite imagery">satellite imagery</a> (<a href="/wiki/NASA" title="NASA">NASA</a>) during the period of the study. Such aggregation of negatively buoyant <a href="/wiki/Seaweed" title="Seaweed">macroalgae</a> on <a href="/wiki/Seabed" title="Seabed">sea floor</a> is similar to windrows of positively buoyant particles on water surface due to LC. </p> <div class="mw-heading mw-heading3"><h3 id="Effect_on_animals">Effect on animals</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Langmuir_circulation&action=edit&section=5" title="Edit section: Effect on animals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>While plants have passive reaction to LC, animals can react to both the LC, presence of plant/food aggregation and light. One of such observation was the adaptation of <i><a href="/wiki/Portuguese_man_o%27_war" title="Portuguese man o' war">Physalia</a></i> to windrows containing entangling <i><a href="/wiki/Sargassum" title="Sargassum">Sargassum</a></i>. <i>Physalia</i> tend to drift across the <a href="/wiki/Windrow" title="Windrow">windrows</a> which also increased food or zooplankter availability in divergent zones.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p><p>Moreover, studies in Lake Mendota have shown good correlation between <i><a href="/wiki/Daphnia_pulex" title="Daphnia pulex">Daphnia pulex</a></i> concentration and the appearance of foam lines. Similarly, significant differences were observed in catches of <i><a href="/wiki/Daphnia" title="Daphnia">Daphnia</a></i> <i>hyaline</i> when sampling in and out of <a href="/wiki/Foam_line" title="Foam line">foamlines</a> in South Wales lake, with greater number appearing in divergent zone.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> Such distribution of particles and animals can be described using mathematical model developed by Stommel that suggested area of retention on upwelling zone for sinking particles and on downwelling zone for positively buoyant particles.<sup id="cite_ref-Stommel,_H._1949_15-1" class="reference"><a href="#cite_note-Stommel,_H._1949-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> Actually, the <a href="/wiki/Zooplankton" title="Zooplankton">zooplankton</a> could become trapped in upwelling zones to a point where animals are stimulated to swim downwards.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> A more detailed model was later developed by Stavn describing the zooplankton aggregation where the animal orientation, dorsal light reaction and current velocity determined their region of concentration in either downwelling (due to slow current), upwelling (due to high current) and in between latter two zones (due to intermediate currents).<sup id="cite_ref-:1_11-1" class="reference"><a href="#cite_note-:1-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> There has been further improvement in such models like the modification of Stommel's model by Titman & Kilham in order to consider the difference in maximum downwelling and upwelling velocities<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> and by Evans & Taylor that discussed the instability of Stommel's regions due to varying swimming speed with depth which produced spiral trajectories affecting accumulation region.<sup id="cite_ref-:0_10-2" class="reference"><a href="#cite_note-:0-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>Nevertheless, high concentration of planktonic organisms within LC can attract birds and fish. Schools of <a href="/wiki/White_bass" title="White bass">White Bass</a> <i>Roccus chrysops</i> were observed feeding upon <i><a href="/wiki/Daphnia" title="Daphnia">Daphnia</a></i> along the foam track.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> In contrast, lesser <a href="/wiki/Flamingo" title="Flamingo">Flamingoes</a> <i>Phoeniconaias minor</i> were observed feeding on bubble lines containing concentrated <a href="/wiki/Cyanobacteria" title="Cyanobacteria">blue-green algae</a>.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> Similarly, medusae were found to aggregate in linear pattern (average spacing of 129 m) parallel with wind in the Bering Sea which could be due to large LCs.<sup id="cite_ref-:2_12-1" class="reference"><a href="#cite_note-:2-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> Such aggregation can affect the feeding and predation of <a href="/wiki/Jellyfish" title="Jellyfish">medusae</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Effect_on_surface_tension">Effect on surface tension</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Langmuir_circulation&action=edit&section=6" title="Edit section: Effect on surface tension"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>High concentration of surfactants (surface-active substances) produced by phytoplanktons can result higher Marangoni stress in converging regions in LC. Numerical simulation suggest that such Marangoni stress due to surfactant can increase the size of vortical structures, vertical velocity and remixing of water and biological/chemical components in the local region compared to that without surfactant.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p><p>Finally, more theoretical and experimental investigations are needed to confirm the significance of LC. </p> <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=Langmuir_circulation&action=edit&section=7" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"> <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFOpen_University2001" class="citation cs2">Open University (2001), <i>Ocean Circulation</i> (2nd ed.), Butterworth-Heinemann, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780750652780" title="Special:BookSources/9780750652780"><bdi>9780750652780</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Ocean+Circulation&rft.edition=2nd&rft.pub=Butterworth-Heinemann&rft.date=2001&rft.isbn=9780750652780&rft.au=Open+University&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALangmuir+circulation" class="Z3988"></span></span> </li> <li id="cite_note-thorpe2004-2"><span class="mw-cite-backlink">^ <a 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(2004), "Langmuir circulation", <i>Annual Review of Fluid Mechanics</i>, <b>36</b>: 55–79, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2004AnRFM..36...55T">2004AnRFM..36...55T</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1146%2Fannurev.fluid.36.052203.071431">10.1146/annurev.fluid.36.052203.071431</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annual+Review+of+Fluid+Mechanics&rft.atitle=Langmuir+circulation&rft.volume=36&rft.pages=55-79&rft.date=2004&rft_id=info%3Adoi%2F10.1146%2Fannurev.fluid.36.052203.071431&rft_id=info%3Abibcode%2F2004AnRFM..36...55T&rft.aulast=Thorpe&rft.aufirst=S.A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALangmuir+circulation" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCraikLeibovich1976" class="citation cs2">Craik, A.D.D.; Leibovich, S. 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(1980), "On wave-current interactions theories of Langmuir circulations", <i>Journal of Fluid Mechanics</i>, <b>99</b> (4): 715–724, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1980JFM....99..715L">1980JFM....99..715L</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FS0022112080000857">10.1017/S0022112080000857</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:14996095">14996095</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Fluid+Mechanics&rft.atitle=On+wave-current+interactions+theories+of+Langmuir+circulations&rft.volume=99&rft.issue=4&rft.pages=715-724&rft.date=1980&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A14996095%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1017%2FS0022112080000857&rft_id=info%3Abibcode%2F1980JFM....99..715L&rft.aulast=Leibovich&rft.aufirst=S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALangmuir+circulation" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcWilliamsSullivanMoeng1997" class="citation cs2">McWilliams, J.; Sullivan, P.; Moeng, C. (1997), "Langmuir turbulence in the ocean", <i>Journal of Fluid Mechanics</i>, <b>334</b> (1): 1–30, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1997JFM...334....1M">1997JFM...334....1M</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FS0022112096004375">10.1017/S0022112096004375</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:76650016">76650016</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Fluid+Mechanics&rft.atitle=Langmuir+turbulence+in+the+ocean&rft.volume=334&rft.issue=1&rft.pages=1-30&rft.date=1997&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A76650016%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1017%2FS0022112096004375&rft_id=info%3Abibcode%2F1997JFM...334....1M&rft.aulast=McWilliams&rft.aufirst=J.&rft.au=Sullivan%2C+P.&rft.au=Moeng%2C+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALangmuir+circulation" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStewart2002" class="citation cs2">Stewart, Robert H. 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(1961). <a rel="nofollow" class="external text" href="https://doi.org/10.4319%2Flo.1961.6.1.0053">"Surface Schooling and Feeding Behavior in the White Bass, Roccus Chrysops (Rafinesque), in Lake Mendota"</a>. <i>Limnology and Oceanography</i>. <b>6</b> (1): 53–60. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1961LimOc...6...53M">1961LimOc...6...53M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.4319%2Flo.1961.6.1.0053">10.4319/lo.1961.6.1.0053</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0024-3590">0024-3590</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Limnology+and+Oceanography&rft.atitle=Surface+Schooling+and+Feeding+Behavior+in+the+White+Bass%2C+Roccus+Chrysops+%28Rafinesque%29%2C+in+Lake+Mendota&rft.volume=6&rft.issue=1&rft.pages=53-60&rft.date=1961&rft.issn=0024-3590&rft_id=info%3Adoi%2F10.4319%2Flo.1961.6.1.0053&rft_id=info%3Abibcode%2F1961LimOc...6...53M&rft.aulast=McNaught&rft.aufirst=Donald+C.&rft.au=Hasler%2C+Arthur+D.&rft_id=https%3A%2F%2Fdoi.org%2F10.4319%252Flo.1961.6.1.0053&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALangmuir+circulation" class="Z3988"></span></span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTuite1981" class="citation journal cs1">Tuite, C. H. (1981). "Standing crop densities and distribution of Spirulina and benthic diatoms in East African alkaline saline lakes". <i>Freshwater Biology</i>. <b>11</b> (4): 345–360. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1981FrBio..11..345T">1981FrBio..11..345T</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fj.1365-2427.1981.tb01266.x">10.1111/j.1365-2427.1981.tb01266.x</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0046-5070">0046-5070</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Freshwater+Biology&rft.atitle=Standing+crop+densities+and+distribution+of+Spirulina+and+benthic+diatoms+in+East+African+alkaline+saline+lakes&rft.volume=11&rft.issue=4&rft.pages=345-360&rft.date=1981&rft.issn=0046-5070&rft_id=info%3Adoi%2F10.1111%2Fj.1365-2427.1981.tb01266.x&rft_id=info%3Abibcode%2F1981FrBio..11..345T&rft.aulast=Tuite&rft.aufirst=C.+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALangmuir+circulation" class="Z3988"></span></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBotteMansutti2012" class="citation journal cs1">Botte, Vincenzo; Mansutti, Daniela (August 2012). "A numerical estimate of the plankton-induced sea surface tension effects in a Langmuir circulation". <i>Mathematics and Computers in Simulation</i>. <b>82</b> (12): 2916–2928. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.matcom.2012.07.014">10.1016/j.matcom.2012.07.014</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematics+and+Computers+in+Simulation&rft.atitle=A+numerical+estimate+of+the+plankton-induced+sea+surface+tension+effects+in+a+Langmuir+circulation&rft.volume=82&rft.issue=12&rft.pages=2916-2928&rft.date=2012-08&rft_id=info%3Adoi%2F10.1016%2Fj.matcom.2012.07.014&rft.aulast=Botte&rft.aufirst=Vincenzo&rft.au=Mansutti%2C+Daniela&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALangmuir+circulation" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Langmuir_circulation&action=edit&section=8" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Media related to <a href="https://commons.wikimedia.org/wiki/Category:Langmuir_circulation" class="extiw" title="commons:Category:Langmuir 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model">model</a></li></ul></li></ul> </div></td><td class="noviewer navbox-image" rowspan="10" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:Upwelling.svg" class="mw-file-description" title="Upwelling"><img alt="Upwelling" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Upwelling.svg/120px-Upwelling.svg.png" decoding="async" width="120" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Upwelling.svg/180px-Upwelling.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Upwelling.svg/240px-Upwelling.svg.png 2x" data-file-width="365" data-file-height="242" /></a></span><br /><br /><br /><br /><br /><br /><span typeof="mw:File"><a href="/wiki/File:Antarctic_bottom_water.svg" class="mw-file-description" title="Antarctic bottom water"><img alt="Antarctic bottom water" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Antarctic_bottom_water.svg/120px-Antarctic_bottom_water.svg.png" decoding="async" width="120" height="76" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Antarctic_bottom_water.svg/180px-Antarctic_bottom_water.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Antarctic_bottom_water.svg/240px-Antarctic_bottom_water.svg.png 2x" data-file-width="745" data-file-height="470" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Ocean_current" title="Ocean current">Circulation</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/Atmospheric_circulation" title="Atmospheric circulation">Atmospheric circulation</a></li> <li><a href="/wiki/Baroclinity" title="Baroclinity">Baroclinity</a></li> <li><a href="/wiki/Boundary_current" title="Boundary current">Boundary current</a></li> <li><a href="/wiki/Coriolis_force" title="Coriolis force">Coriolis force</a></li> <li><a href="/wiki/Coriolis%E2%80%93Stokes_force" title="Coriolis–Stokes force">Coriolis–Stokes force</a></li> <li><a href="/wiki/Craik%E2%80%93Leibovich_vortex_force" title="Craik–Leibovich vortex force">Craik–Leibovich vortex force</a></li> <li><a href="/wiki/Downwelling" title="Downwelling">Downwelling</a></li> <li><a href="/wiki/Eddy_(fluid_dynamics)" title="Eddy (fluid dynamics)">Eddy</a></li> <li><a href="/wiki/Ekman_layer" title="Ekman layer">Ekman layer</a></li> <li><a href="/wiki/Ekman_spiral" title="Ekman spiral">Ekman spiral</a></li> <li><a href="/wiki/Ekman_transport" title="Ekman transport">Ekman transport</a></li> <li><a href="/wiki/El_Ni%C3%B1o%E2%80%93Southern_Oscillation" title="El Niño–Southern Oscillation">El Niño–Southern Oscillation</a></li> <li><a href="/wiki/General_circulation_model" title="General circulation model">General circulation model</a></li> <li><a href="/wiki/Geochemical_Ocean_Sections_Study" title="Geochemical Ocean Sections Study">Geochemical Ocean Sections Study</a></li> <li><a href="/wiki/Geostrophic_current" title="Geostrophic current">Geostrophic current</a></li> <li><a href="/wiki/Global_Ocean_Data_Analysis_Project" title="Global Ocean Data Analysis Project">Global Ocean Data Analysis Project</a></li> <li><a href="/wiki/Gulf_Stream" title="Gulf Stream">Gulf Stream</a></li> <li><a href="/wiki/Humboldt_Current" title="Humboldt Current">Humboldt Current</a></li> <li><a href="/wiki/Hydrothermal_circulation" title="Hydrothermal circulation">Hydrothermal circulation</a></li> <li><a class="mw-selflink selflink">Langmuir circulation</a></li> <li><a href="/wiki/Longshore_drift" title="Longshore drift">Longshore drift</a></li> <li><a href="/wiki/Loop_Current" title="Loop Current">Loop Current</a></li> <li><a href="/wiki/Modular_Ocean_Model" title="Modular Ocean Model">Modular Ocean Model</a></li> <li><a href="/wiki/Ocean_current" title="Ocean current">Ocean current</a></li> <li><a href="/wiki/Ocean_dynamical_thermostat" title="Ocean dynamical thermostat">Ocean dynamical thermostat</a></li> <li><a href="/wiki/Ocean_dynamics" title="Ocean dynamics">Ocean dynamics</a></li> <li><a href="/wiki/Ocean_gyre" title="Ocean gyre">Ocean gyre</a></li> <li><a href="/wiki/Overflow_(oceanography)" title="Overflow (oceanography)">Overflow</a></li> <li><a href="/wiki/Princeton_Ocean_Model" title="Princeton Ocean Model">Princeton Ocean Model</a></li> <li><a href="/wiki/Rip_current" title="Rip current">Rip current</a></li> <li><a href="/wiki/Subsurface_ocean_current" title="Subsurface ocean current">Subsurface ocean current</a></li> <li><a href="/wiki/Sverdrup_balance" title="Sverdrup balance">Sverdrup balance</a></li> <li><a href="/wiki/Thermohaline_circulation" title="Thermohaline circulation">Thermohaline circulation</a> <ul><li><a href="/wiki/Shutdown_of_thermohaline_circulation" class="mw-redirect" title="Shutdown of thermohaline circulation">shutdown</a></li></ul></li> <li><a href="/wiki/Upwelling" title="Upwelling">Upwelling</a></li> <li><a href="/wiki/Whirlpool" title="Whirlpool">Whirlpool</a></li> <li><a href="/wiki/Wind_generated_current" title="Wind generated current">Wind generated current</a></li> <li><a href="/wiki/World_Ocean_Circulation_Experiment" title="World Ocean Circulation Experiment">World Ocean Circulation Experiment</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Tide" title="Tide">Tides</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/Amphidromic_point" title="Amphidromic point">Amphidromic point</a></li> <li><a href="/wiki/Earth_tide" title="Earth tide">Earth tide</a></li> <li><a href="/wiki/Head_of_tide" title="Head of tide">Head of tide</a></li> <li><a href="/wiki/Internal_tide" title="Internal tide">Internal tide</a></li> <li><a href="/wiki/Lunitidal_interval" title="Lunitidal interval">Lunitidal interval</a></li> <li><a href="/wiki/Perigean_spring_tide" title="Perigean spring tide">Perigean spring tide</a></li> <li><a href="/wiki/Rip_tide" title="Rip tide">Rip tide</a></li> <li><a href="/wiki/Rule_of_twelfths" title="Rule of twelfths">Rule of twelfths</a></li> <li><a href="/wiki/Slack_tide" title="Slack tide">Slack tide</a></li> <li><a href="/wiki/Theory_of_tides" title="Theory of tides">Theory of tides</a></li> <li><a href="/wiki/Tidal_bore" title="Tidal bore">Tidal bore</a></li> <li><a href="/wiki/Tidal_force" title="Tidal force">Tidal force</a></li> <li><a href="/wiki/Tidal_power" title="Tidal power">Tidal power</a></li> <li><a href="/wiki/Tidal_race" title="Tidal race">Tidal race</a></li> <li><a href="/wiki/Tidal_range" title="Tidal range">Tidal range</a></li> <li><a href="/wiki/Tidal_resonance" title="Tidal resonance">Tidal resonance</a></li> <li><a href="/wiki/Tide_gauge" title="Tide gauge">Tide gauge</a></li> <li><a href="/wiki/Tideline" title="Tideline">Tideline</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Landform" title="Landform">Landforms</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/Abyssal_fan" title="Abyssal fan">Abyssal fan</a></li> <li><a href="/wiki/Abyssal_plain" title="Abyssal plain">Abyssal plain</a></li> <li><a href="/wiki/Atoll" title="Atoll">Atoll</a></li> <li><a href="/wiki/Bathymetric_chart" title="Bathymetric chart">Bathymetric chart</a></li> <li><a href="/wiki/Carbonate_platform" title="Carbonate platform">Carbonate platform</a></li> <li><a href="/wiki/Coastal_geography" title="Coastal geography">Coastal geography</a></li> <li><a href="/wiki/Cold_seep" title="Cold seep">Cold seep</a></li> <li><a href="/wiki/Continental_margin" title="Continental margin">Continental margin</a></li> <li><a href="/wiki/Continental_rise" title="Continental rise">Continental rise</a></li> <li><a href="/wiki/Continental_shelf" title="Continental shelf">Continental shelf</a></li> <li><a href="/wiki/Contourite" title="Contourite">Contourite</a></li> <li><a href="/wiki/Guyot" title="Guyot">Guyot</a></li> <li><a href="/wiki/Hydrography" title="Hydrography">Hydrography</a></li> <li><a href="/wiki/Knoll_(oceanography)" title="Knoll (oceanography)">Knoll</a></li> <li><a href="/wiki/Ocean_bank" title="Ocean bank">Ocean bank</a></li> <li><a href="/wiki/Oceanic_basin" title="Oceanic basin">Oceanic basin</a></li> <li><a href="/wiki/Oceanic_plateau" title="Oceanic plateau">Oceanic plateau</a></li> <li><a href="/wiki/Oceanic_trench" title="Oceanic trench">Oceanic trench</a></li> <li><a href="/wiki/Passive_margin" title="Passive margin">Passive margin</a></li> <li><a href="/wiki/Seabed" title="Seabed">Seabed</a></li> <li><a href="/wiki/Seamount" title="Seamount">Seamount</a></li> <li><a href="/wiki/Submarine_canyon" title="Submarine canyon">Submarine canyon</a></li> <li><a href="/wiki/Submarine_volcano" title="Submarine volcano">Submarine volcano</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Plate_tectonics" title="Plate tectonics">Plate<br />tectonics</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/Convergent_boundary" title="Convergent boundary">Convergent boundary</a></li> <li><a href="/wiki/Divergent_boundary" title="Divergent boundary">Divergent boundary</a></li> <li><a href="/wiki/Fracture_zone" title="Fracture zone">Fracture zone</a></li> <li><a href="/wiki/Hydrothermal_vent" title="Hydrothermal vent">Hydrothermal vent</a></li> <li><a href="/wiki/Marine_geology" title="Marine geology">Marine geology</a></li> <li><a href="/wiki/Mid-ocean_ridge" title="Mid-ocean ridge">Mid-ocean ridge</a></li> <li><a href="/wiki/Mohorovi%C4%8Di%C4%87_discontinuity" title="Mohorovičić discontinuity">Mohorovičić discontinuity</a></li> <li><a href="/wiki/Oceanic_crust" title="Oceanic crust">Oceanic crust</a></li> <li><a href="/wiki/Outer_trench_swell" title="Outer trench swell">Outer trench swell</a></li> <li><a href="/wiki/Ridge_push" title="Ridge push">Ridge push</a></li> <li><a href="/wiki/Seafloor_spreading" title="Seafloor spreading">Seafloor spreading</a></li> <li><a href="/wiki/Slab_pull" title="Slab pull">Slab pull</a></li> <li><a href="/wiki/Slab_suction" title="Slab suction">Slab suction</a></li> <li><a href="/wiki/Slab_window" title="Slab window">Slab window</a></li> <li><a href="/wiki/Subduction" title="Subduction">Subduction</a></li> <li><a href="/wiki/Transform_fault" title="Transform fault">Transform fault</a></li> <li><a href="/wiki/Vine%E2%80%93Matthews%E2%80%93Morley_hypothesis" title="Vine–Matthews–Morley hypothesis">Vine–Matthews–Morley hypothesis</a></li> <li><a href="/wiki/Volcanic_arc" title="Volcanic arc">Volcanic arc</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Ocean zones</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/Benthic_zone" title="Benthic zone">Benthic</a></li> <li><a href="/wiki/Deep_ocean_water" title="Deep ocean water">Deep ocean water</a></li> <li><a href="/wiki/Deep_sea" title="Deep sea">Deep sea</a></li> <li><a href="/wiki/Littoral_zone" title="Littoral zone">Littoral</a></li> <li><a href="/wiki/Mesopelagic_zone" title="Mesopelagic zone">Mesopelagic</a></li> <li><a href="/wiki/Oceanic_zone" title="Oceanic zone">Oceanic</a></li> <li><a href="/wiki/Pelagic_zone" title="Pelagic zone">Pelagic</a></li> <li><a href="/wiki/Photic_zone" title="Photic zone">Photic</a></li> <li><a href="/wiki/Surf_zone" title="Surf zone">Surf</a></li> <li><a href="/wiki/Swash" title="Swash">Swash</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Sea_level" title="Sea level">Sea level</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/Deep-ocean_Assessment_and_Reporting_of_Tsunamis" title="Deep-ocean Assessment and Reporting of Tsunamis">Deep-ocean Assessment and Reporting of Tsunamis</a></li> <li><a href="/wiki/Global_Sea_Level_Observing_System" title="Global Sea Level Observing System">Global Sea Level Observing System</a></li> <li><a href="/wiki/North_West_Shelf_Operational_Oceanographic_System" title="North West Shelf Operational Oceanographic System">North West Shelf Operational Oceanographic System</a></li> <li><a href="/wiki/Sea-level_curve" title="Sea-level curve">Sea-level curve</a></li> <li><a href="/wiki/Sea_level_drop" title="Sea level drop">Sea level drop</a></li> <li><a href="/wiki/Sea_level_rise" title="Sea level rise">Sea level rise</a></li> <li><a href="/wiki/World_Geodetic_System" title="World Geodetic System">World Geodetic System</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Acoustical_oceanography" class="mw-redirect" title="Acoustical oceanography">Acoustics</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/Deep_scattering_layer" title="Deep scattering layer">Deep scattering layer</a></li> <li><a href="/wiki/Ocean_acoustic_tomography" title="Ocean acoustic tomography">Ocean acoustic tomography</a></li> <li><a href="/wiki/Sofar_bomb" title="Sofar bomb">Sofar bomb</a></li> <li><a href="/wiki/SOFAR_channel" title="SOFAR channel">SOFAR channel</a></li> <li><a href="/wiki/Underwater_acoustics" title="Underwater acoustics">Underwater acoustics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Satellites</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/Jason-1" title="Jason-1">Jason-1</a></li> <li><a href="/wiki/OSTM/Jason-2" title="OSTM/Jason-2">OSTM/Jason-2</a></li> <li><a href="/wiki/Jason-3" title="Jason-3">Jason-3</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/Ocean_acidification" title="Ocean acidification">Acidification</a></li> <li><a href="/wiki/Argo_(oceanography)" title="Argo (oceanography)">Argo</a></li> <li><a href="/wiki/Benthic_lander" title="Benthic lander">Benthic lander</a></li> <li><a href="/wiki/Color_of_water" title="Color of water">Color of water</a></li> <li><a href="/wiki/DSV_Alvin" title="DSV Alvin">DSV <i>Alvin</i></a></li> <li><a href="/wiki/Marginal_sea" class="mw-redirect" title="Marginal sea">Marginal sea</a></li> <li><a href="/wiki/Marine_energy" title="Marine energy">Marine energy</a></li> <li><a href="/wiki/Marine_pollution" title="Marine pollution">Marine pollution</a></li> <li><a href="/wiki/Mooring_(oceanography)" title="Mooring (oceanography)">Mooring</a></li> <li><a href="/wiki/National_Oceanographic_Data_Center" title="National Oceanographic Data Center">National Oceanographic Data Center</a></li> <li><a href="/wiki/Ocean" title="Ocean">Ocean</a></li> <li><a href="/wiki/Ocean_exploration" title="Ocean exploration">Explorations</a></li> <li><a href="/wiki/Ocean_observations" title="Ocean observations">Observations</a></li> <li><a href="/wiki/Ocean_reanalysis" title="Ocean reanalysis">Reanalysis</a></li> <li><a href="/wiki/Ocean_surface_topography" title="Ocean surface topography">Ocean surface topography</a></li> <li><a href="/wiki/Ocean_temperature" title="Ocean temperature">Ocean temperature</a></li> <li><a href="/wiki/Ocean_thermal_energy_conversion" title="Ocean thermal energy conversion">Ocean thermal energy conversion</a></li> <li><a href="/wiki/Oceanography" title="Oceanography">Oceanography</a> <ul><li><a href="/wiki/Outline_of_oceanography" title="Outline of oceanography">Outline of oceanography</a></li></ul></li> <li><a href="/wiki/Pelagic_sediment" title="Pelagic sediment">Pelagic sediment</a></li> <li><a href="/wiki/Sea_surface_microlayer" title="Sea surface microlayer">Sea surface microlayer</a></li> <li><a href="/wiki/Sea_surface_temperature" title="Sea surface temperature">Sea surface temperature</a></li> <li><a href="/wiki/Seawater" title="Seawater">Seawater</a></li> <li><a href="/wiki/Science_On_a_Sphere" title="Science On a Sphere">Science On a Sphere</a></li> <li><a href="/wiki/Ocean_stratification" title="Ocean stratification">Stratification</a></li> <li><a href="/wiki/Thermocline" title="Thermocline">Thermocline</a></li> <li><a href="/wiki/Underwater_glider" title="Underwater glider">Underwater glider</a></li> <li><a href="/wiki/Water_column" title="Water column">Water column</a></li> <li><a href="/wiki/World_Ocean_Atlas" title="World Ocean Atlas">World Ocean Atlas</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:Physical_oceanography" title="Category:Physical oceanography">Category</a></li> <li><span class="noviewer" typeof="mw:File"><span title="Commons page"><img alt="" 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