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class="vector-toc-numb">2</span> <span>Mathematical formulation</span> </div> </a> <button aria-controls="toc-Mathematical_formulation-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 Mathematical formulation subsection</span> </button> <ul id="toc-Mathematical_formulation-sublist" class="vector-toc-list"> <li id="toc-Ekman_layer_at_the_ocean_(or_free)_surface" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ekman_layer_at_the_ocean_(or_free)_surface"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Ekman layer at the ocean (or free) surface</span> </div> </a> <ul id="toc-Ekman_layer_at_the_ocean_(or_free)_surface-sublist" class="vector-toc-list"> <li id="toc-Solution" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Solution"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.1</span> <span>Solution</span> </div> </a> <ul id="toc-Solution-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Ekman_layer_at_the_bottom_of_the_ocean_and_atmosphere" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ekman_layer_at_the_bottom_of_the_ocean_and_atmosphere"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Ekman layer at the bottom of the ocean and atmosphere</span> </div> </a> <ul id="toc-Ekman_layer_at_the_bottom_of_the_ocean_and_atmosphere-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Experimental_observations_of_the_Ekman_layer" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Experimental_observations_of_the_Ekman_layer"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Experimental observations of the Ekman layer</span> </div> </a> <button aria-controls="toc-Experimental_observations_of_the_Ekman_layer-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 Experimental observations of the Ekman layer subsection</span> </button> <ul id="toc-Experimental_observations_of_the_Ekman_layer-sublist" class="vector-toc-list"> <li id="toc-Laboratory_demonstrations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Laboratory_demonstrations"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Laboratory demonstrations</span> </div> </a> <ul id="toc-Laboratory_demonstrations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-In_the_atmosphere" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#In_the_atmosphere"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>In the atmosphere</span> </div> </a> <ul id="toc-In_the_atmosphere-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-In_the_ocean" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#In_the_ocean"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>In the ocean</span> </div> </a> <ul id="toc-In_the_ocean-sublist" class="vector-toc-list"> <li id="toc-Instrumentation" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Instrumentation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3.1</span> <span>Instrumentation</span> </div> </a> <ul id="toc-Instrumentation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Observations" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Observations"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3.2</span> <span>Observations</span> </div> </a> <ul id="toc-Observations-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> 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href="https://de.wikipedia.org/wiki/Ekman-Schicht" title="Ekman-Schicht – German" lang="de" hreflang="de" data-title="Ekman-Schicht" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Capa_de_Ekman" title="Capa de Ekman – Spanish" lang="es" hreflang="es" data-title="Capa de Ekman" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%84%D8%A7%DB%8C%D9%87_%D8%A7%DA%A9%D9%85%D9%86" title="لایه اکمن – Persian" lang="fa" hreflang="fa" data-title="لایه اکمن" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Spirale_d%27Ekman#Couche_d'Ekman" title="Spirale d'Ekman – French" lang="fr" hreflang="fr" data-title="Spirale d'Ekman" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Strato_di_Ekman" title="Strato di Ekman – Italian" lang="it" hreflang="it" data-title="Strato di Ekman" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A9%D7%9B%D7%91%D7%AA_%D7%92%D7%91%D7%95%D7%9C_%D7%90%D7%A7%D7%9E%D7%9F" title="שכבת גבול אקמן – Hebrew" lang="he" hreflang="he" data-title="שכבת גבול אקמן" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%A8%E3%82%AF%E3%83%9E%E3%83%B3%E5%A2%83%E7%95%8C%E5%B1%A4" title="エクマン境界層 – Japanese" lang="ja" hreflang="ja" data-title="エクマン境界層" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Ekmanlag" title="Ekmanlag – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Ekmanlag" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Camada_de_Ekman" title="Camada de Ekman – Portuguese" lang="pt" hreflang="pt" data-title="Camada de Ekman" data-language-autonym="Português" 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<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"><style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Merge plainlinks metadata ambox ambox-move" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Merge-arrows.svg/50px-Merge-arrows.svg.png" decoding="async" width="50" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Merge-arrows.svg/75px-Merge-arrows.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/52/Merge-arrows.svg/100px-Merge-arrows.svg.png 2x" data-file-width="50" data-file-height="20" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">It has been suggested that this article be <a href="/wiki/Wikipedia:Merging" title="Wikipedia:Merging">merged</a> with <i><a href="/wiki/Ekman_spiral" title="Ekman spiral">Ekman spiral</a></i> to <i><a href="/wiki/Ekman_transport" title="Ekman transport">Ekman transport</a></i>. (<a href="/wiki/Talk:Ekman_layer" title="Talk:Ekman layer">Discuss</a>)<small><i> Proposed since November 2024.</i></small></div></td></tr></tbody></table> <div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Force equilibrium layer in a liquid</div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Ekman_layer.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Ekman_layer.jpg/350px-Ekman_layer.jpg" decoding="async" width="350" height="349" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Ekman_layer.jpg/525px-Ekman_layer.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Ekman_layer.jpg/700px-Ekman_layer.jpg 2x" data-file-width="769" data-file-height="766" /></a><figcaption>The Ekman layer is the layer in a fluid where the flow is the result of a balance between pressure gradient, Coriolis and turbulent drag forces. In the picture above, the wind blowing North creates a surface stress and a resulting <a href="/wiki/Ekman_spiral" title="Ekman spiral">Ekman spiral</a> is found below it in the column of water.</figcaption></figure> <p>The <b>Ekman layer</b> is the layer in a <a href="/wiki/Fluid" title="Fluid">fluid</a> where there is a <a href="/wiki/Force" title="Force">force</a> balance between <a href="/wiki/Pressure_gradient_force" class="mw-redirect" title="Pressure gradient force">pressure gradient force</a>, <a href="/wiki/Coriolis_force" title="Coriolis force">Coriolis force</a> and <a href="/wiki/Drag_(physics)" title="Drag (physics)">turbulent drag</a>. It was first described by <a href="/wiki/Vagn_Walfrid_Ekman" title="Vagn Walfrid Ekman">Vagn Walfrid Ekman</a>. Ekman layers occur both in the atmosphere and in the ocean. </p><p>There are two types of Ekman layers. The first type occurs at the surface of the ocean and is forced by surface winds, which act as a drag on the surface of the ocean. The second type occurs at the <a href="/wiki/Planetary_boundary_layer" title="Planetary boundary layer">bottom of the atmosphere</a> and ocean, where frictional forces are associated with flow over rough surfaces. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ekman_layer&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ekman developed the theory of the Ekman layer after <a href="/wiki/Fridtjof_Nansen" title="Fridtjof Nansen">Fridtjof Nansen</a> observed that <a href="/wiki/Iceberg" title="Iceberg">ice</a> drifts at an angle of 20°–40° to the right of the <a href="/wiki/Wind" title="Wind">prevailing wind</a> direction while on an <a href="/wiki/Arctic" title="Arctic">Arctic</a> expedition aboard the <a href="/wiki/Fram_(ship)" title="Fram (ship)">Fram</a>. Nansen asked his colleague, <a href="/wiki/Vilhelm_Bjerknes" title="Vilhelm Bjerknes">Vilhelm Bjerknes</a> to set one of his students upon study of the problem. Bjerknes tapped Ekman, who presented his results in 1902 as his <a href="/wiki/Doctoral_thesis" class="mw-redirect" title="Doctoral thesis">doctoral thesis</a>.<sup id="cite_ref-Cushman_1-0" class="reference"><a href="#cite_note-Cushman-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Mathematical_formulation">Mathematical formulation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ekman_layer&action=edit&section=2" title="Edit section: Mathematical formulation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The mathematical formulation of the Ekman layer begins by assuming a neutrally stratified fluid, a balance between the forces of pressure gradient, Coriolis and turbulent drag. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}-fv&=-{\frac {1}{\rho _{o}}}{\frac {\partial p}{\partial x}}+K_{m}{\frac {\partial ^{2}u}{\partial z^{2}}},\\[5pt]fu&=-{\frac {1}{\rho _{o}}}{\frac {\partial p}{\partial y}}+K_{m}{\frac {\partial ^{2}v}{\partial z^{2}}},\\[5pt]0&=-{\frac {1}{\rho _{o}}}{\frac {\partial p}{\partial z}},\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="0.8em 0.8em 0.3em" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mo>−</mo> <mi>f</mi> <mi>v</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> </msub> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>p</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>u</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>f</mi> <mi>u</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> </msub> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>p</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>v</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi></mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> </msub> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>p</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>z</mi> </mrow> </mfrac> </mrow> <mo>,</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}-fv&=-{\frac {1}{\rho _{o}}}{\frac {\partial p}{\partial x}}+K_{m}{\frac {\partial ^{2}u}{\partial z^{2}}},\\[5pt]fu&=-{\frac {1}{\rho _{o}}}{\frac {\partial p}{\partial y}}+K_{m}{\frac {\partial ^{2}v}{\partial z^{2}}},\\[5pt]0&=-{\frac {1}{\rho _{o}}}{\frac {\partial p}{\partial z}},\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b414923e6bbccd402f4da50e38b19f783ef876e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -9.838ex; width:28.123ex; height:20.843ex;" alt="{\displaystyle {\begin{aligned}-fv&=-{\frac {1}{\rho _{o}}}{\frac {\partial p}{\partial x}}+K_{m}{\frac {\partial ^{2}u}{\partial z^{2}}},\\[5pt]fu&=-{\frac {1}{\rho _{o}}}{\frac {\partial p}{\partial y}}+K_{m}{\frac {\partial ^{2}v}{\partial z^{2}}},\\[5pt]0&=-{\frac {1}{\rho _{o}}}{\frac {\partial p}{\partial z}},\end{aligned}}}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ u}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>u</mi> </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/80af8f51c503a32959adf851b071da60d09abe39" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.91ex; height:1.676ex;" alt="{\displaystyle \ u}"></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 \ v}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ v}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b13986081794fa359dd8f21458428d16289e97b3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.708ex; height:1.676ex;" alt="{\displaystyle \ v}"></span> are the velocities in the <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9923068b5684340554217dfc8b2b968523527d9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.91ex; height:1.676ex;" alt="{\displaystyle \ x}"></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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e64598c4f945fe21fbf547a5d349969c7e6d852d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.736ex; height:2.009ex;" alt="{\displaystyle \ y}"></span> directions, respectively, <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"> <mtext> </mtext> <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/4d5ff7312a01506eee6ecea7dca662763a101c9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.859ex; height:2.509ex;" alt="{\displaystyle \ f}"></span> is the local <a href="/wiki/Coriolis_parameter" class="mw-redirect" title="Coriolis parameter">Coriolis parameter</a>, 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 \ K_{m}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ K_{m}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ec0cc1d92c5e1fba5c3e9dfc2458c8794f60ff9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.229ex; height:2.509ex;" alt="{\displaystyle \ K_{m}}"></span> is the diffusive eddy viscosity, which can be derived using <a href="/wiki/Mixing_length_theory" class="mw-redirect" title="Mixing length theory">mixing length theory</a>. Note that <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 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/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> is a <a href="/wiki/Modified_pressure" title="Modified pressure">modified pressure</a>: we have incorporated the <a href="/wiki/Hydrostatic_pressure" class="mw-redirect" title="Hydrostatic pressure">hydrostatic</a> of the pressure, to take account of gravity. </p><p>There are many regions where an Ekman layer is theoretically plausible; they include the bottom of the atmosphere, near the surface of the earth and ocean, the bottom of the ocean, near the <a href="/wiki/Sea_floor" class="mw-redirect" title="Sea floor">sea floor</a> and at the top of the ocean, near the air-water interface. Different <a href="/wiki/Boundary_conditions" class="mw-redirect" title="Boundary conditions">boundary conditions</a> are appropriate for each of these different situations. Each of these situations can be accounted for through the boundary conditions applied to the resulting system of ordinary differential equations. The separate cases of top and bottom boundary layers are shown below. </p> <div class="mw-heading mw-heading3"><h3 id="Ekman_layer_at_the_ocean_(or_free)_surface"><span id="Ekman_layer_at_the_ocean_.28or_free.29_surface"></span>Ekman layer at the ocean (or free) surface</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ekman_layer&action=edit&section=3" title="Edit section: Ekman layer at the ocean (or free) surface"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>We will consider boundary conditions of the Ekman layer in the upper ocean:<sup id="cite_ref-Vallis_2-0" class="reference"><a href="#cite_note-Vallis-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{at }}z=0:\quad A{\frac {\partial u}{\partial z}}=\tau ^{x}\quad {\text{and}}\quad A{\frac {\partial v}{\partial z}}=\tau ^{y},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>at </mtext> </mrow> <mi>z</mi> <mo>=</mo> <mn>0</mn> <mo>:</mo> <mspace width="1em" /> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>u</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>z</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <msup> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msup> <mspace width="1em" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>and</mtext> </mrow> <mspace width="1em" /> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>v</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>z</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <msup> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{at }}z=0:\quad A{\frac {\partial u}{\partial z}}=\tau ^{x}\quad {\text{and}}\quad A{\frac {\partial v}{\partial z}}=\tau ^{y},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2166a34785f1490f5ac648e0ba33af0cf7a985ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:42.482ex; height:5.509ex;" alt="{\displaystyle {\text{at }}z=0:\quad A{\frac {\partial u}{\partial z}}=\tau ^{x}\quad {\text{and}}\quad A{\frac {\partial v}{\partial z}}=\tau ^{y},}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \tau ^{x}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msup> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \tau ^{x}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/26abe087b7e8601090f851e8fc327ac263c5496c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.011ex; height:2.343ex;" alt="{\displaystyle \ \tau ^{x}}"></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 \ \tau ^{y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msup> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \tau ^{y}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/afd599e41168c9f244624f15800e72f706111c76" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.888ex; height:2.343ex;" alt="{\displaystyle \ \tau ^{y}}"></span> are the components of the surface stress, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \tau }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <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/c3b59092e4fcb4395fe734d91fe5c22eccff7bd1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.783ex; height:1.676ex;" alt="{\displaystyle \ \tau }"></span>, of the wind field or ice layer at the top of the ocean, 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 \ A\equiv \rho K_{m}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>A</mi> <mo>≡</mo> <mi>ρ</mi> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ A\equiv \rho K_{m}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/353341aed7a2b55c18b9439e3f44dc66ea319942" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.272ex; height:2.676ex;" alt="{\displaystyle \ A\equiv \rho K_{m}}"></span> is the dynamic viscosity. </p><p>For the boundary condition on the other side, as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ z\to -\infty :u\to u_{g},v\to v_{g}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>z</mi> <mo stretchy="false">→</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mo>:</mo> <mi>u</mi> <mo stretchy="false">→</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msub> <mo>,</mo> <mi>v</mi> <mo stretchy="false">→</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ z\to -\infty :u\to u_{g},v\to v_{g}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72f36a7490f93a6aa9b509691904eb4900064dbe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:26.571ex; height:2.676ex;" alt="{\displaystyle \ z\to -\infty :u\to u_{g},v\to v_{g}}"></span>, where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ u_{g}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ u_{g}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9dac669f96aaf59ef014bb68dd0b5b4ed4c9e4db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.932ex; height:2.343ex;" alt="{\displaystyle \ u_{g}}"></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 \ v_{g}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ v_{g}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6862260a5b46859e1ed3bd9f0e73f82b3c1a2d68" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.73ex; height:2.343ex;" alt="{\displaystyle \ v_{g}}"></span> are the <a href="/wiki/Geostrophic" class="mw-redirect" title="Geostrophic">geostrophic</a> flows in the <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9923068b5684340554217dfc8b2b968523527d9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.91ex; height:1.676ex;" alt="{\displaystyle \ x}"></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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e64598c4f945fe21fbf547a5d349969c7e6d852d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.736ex; height:2.009ex;" alt="{\displaystyle \ y}"></span> directions. </p> <div class="mw-heading mw-heading4"><h4 id="Solution">Solution</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ekman_layer&action=edit&section=4" title="Edit section: Solution"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:EkmanSpiral.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/EkmanSpiral.svg/220px-EkmanSpiral.svg.png" decoding="async" width="220" height="285" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/EkmanSpiral.svg/330px-EkmanSpiral.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ee/EkmanSpiral.svg/440px-EkmanSpiral.svg.png 2x" data-file-width="765" data-file-height="990" /></a><figcaption>Three views of the wind-driven Ekman layer at the surface of the ocean in the Northern Hemisphere. The geostrophic velocity is zero in this example.</figcaption></figure> <p>These differential equations can be solved to find: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}u&=u_{g}+{\frac {\sqrt {2}}{\rho _{o}fd}}e^{z/d}\left[\tau ^{x}\cos(z/d-\pi /4)-\tau ^{y}\sin(z/d-\pi /4)\right],\\[5pt]v&=v_{g}+{\frac {\sqrt {2}}{\rho _{o}fd}}e^{z/d}\left[\tau ^{x}\sin(z/d-\pi /4)+\tau ^{y}\cos(z/d-\pi /4)\right],\\[5pt]d&={\sqrt {2K_{m}/|f|}}.\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="0.8em 0.8em 0.3em" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>u</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mn>2</mn> </msqrt> <mrow> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> </msub> <mi>f</mi> <mi>d</mi> </mrow> </mfrac> </mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> </mrow> </msup> <mrow> <mo>[</mo> <mrow> <msup> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msup> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> <mo>−</mo> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>4</mn> <mo stretchy="false">)</mo> <mo>−</mo> <msup> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msup> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> <mo>−</mo> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>4</mn> <mo stretchy="false">)</mo> </mrow> <mo>]</mo> </mrow> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>v</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mn>2</mn> </msqrt> <mrow> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> </msub> <mi>f</mi> <mi>d</mi> </mrow> </mfrac> </mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> </mrow> </msup> <mrow> <mo>[</mo> <mrow> <msup> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msup> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> <mo>−</mo> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>4</mn> <mo stretchy="false">)</mo> <mo>+</mo> <msup> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msup> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> <mo>−</mo> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>4</mn> <mo stretchy="false">)</mo> </mrow> <mo>]</mo> </mrow> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>d</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </msqrt> </mrow> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}u&=u_{g}+{\frac {\sqrt {2}}{\rho _{o}fd}}e^{z/d}\left[\tau ^{x}\cos(z/d-\pi /4)-\tau ^{y}\sin(z/d-\pi /4)\right],\\[5pt]v&=v_{g}+{\frac {\sqrt {2}}{\rho _{o}fd}}e^{z/d}\left[\tau ^{x}\sin(z/d-\pi /4)+\tau ^{y}\cos(z/d-\pi /4)\right],\\[5pt]d&={\sqrt {2K_{m}/|f|}}.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd8c7721137c50a08bef42bcd4c0b55ce89263e9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -9.505ex; width:60.28ex; height:20.176ex;" alt="{\displaystyle {\begin{aligned}u&=u_{g}+{\frac {\sqrt {2}}{\rho _{o}fd}}e^{z/d}\left[\tau ^{x}\cos(z/d-\pi /4)-\tau ^{y}\sin(z/d-\pi /4)\right],\\[5pt]v&=v_{g}+{\frac {\sqrt {2}}{\rho _{o}fd}}e^{z/d}\left[\tau ^{x}\sin(z/d-\pi /4)+\tau ^{y}\cos(z/d-\pi /4)\right],\\[5pt]d&={\sqrt {2K_{m}/|f|}}.\end{aligned}}}"></span></dd></dl> <p>The value <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.216ex; height:2.176ex;" alt="{\displaystyle d}"></span> is called the Ekman layer depth, and gives an indication of the penetration depth of wind-induced turbulent mixing in the ocean. Note that it varies on two parameters: the turbulent diffusivity <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{m}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{m}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d4b81165d9cdc72a3cc30acf9bc34e81292268a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.648ex; height:2.509ex;" alt="{\displaystyle K_{m}}"></span>, and the latitude, as encapsulated by <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 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>. For a typical <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{m}=0.1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mn>0.1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{m}=0.1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/07d5b4a95d64b4f80bf51dfc15177bd0992bef6b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.718ex; height:2.509ex;" alt="{\displaystyle K_{m}=0.1}"></span> m<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 ^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3abccdd2a8344117c797bb9b8cb39fe082fdf14b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.054ex; height:2.509ex;" alt="{\displaystyle ^{2}}"></span>/s, and at 45° latitude (<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=10^{-4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>4</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f=10^{-4}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8268be0050fc73c79c7dc9e29944c6e485fc69b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.035ex; height:3.009ex;" alt="{\displaystyle f=10^{-4}}"></span> s<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 ^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ^{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d21ba9ae71e157827da571c142bb49c24b78e1a0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:2.333ex; height:2.509ex;" alt="{\displaystyle ^{-1}}"></span>), then <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.216ex; height:2.176ex;" alt="{\displaystyle d}"></span> is approximately 45 meters. This Ekman depth prediction does not always agree precisely with observations. </p><p>This variation of horizontal velocity with 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 -z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78c4571a4a3ceb7e7e55712372835ebe65d20f3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:2.896ex; height:2.176ex;" alt="{\displaystyle -z}"></span>) is referred to as the <a href="/wiki/Ekman_spiral" title="Ekman spiral">Ekman spiral</a>, diagrammed above and at right. </p><p>By applying the continuity equation we can have the vertical velocity as following </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w={\frac {1}{f\rho _{o}}}\left[-\left({\frac {\partial \tau ^{x}}{\partial x}}+{\frac {\partial \tau ^{y}}{\partial y}}\right)e^{z/d}\sin(z/d)+\left({\frac {\partial \tau ^{y}}{\partial x}}-{\frac {\partial \tau ^{x}}{\partial y}}\right)(1-e^{z/d}\cos(z/d))\right].}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>f</mi> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow> <mo>[</mo> <mrow> <mo>−</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msup> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msup> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> </mrow> </msup> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msup> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msup> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> </mrow> </msup> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mrow> <mo>]</mo> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w={\frac {1}{f\rho _{o}}}\left[-\left({\frac {\partial \tau ^{x}}{\partial x}}+{\frac {\partial \tau ^{y}}{\partial y}}\right)e^{z/d}\sin(z/d)+\left({\frac {\partial \tau ^{y}}{\partial x}}-{\frac {\partial \tau ^{x}}{\partial y}}\right)(1-e^{z/d}\cos(z/d))\right].}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7300fc583368544b2d93fa68b4c97d6430129a17" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:80.048ex; height:6.176ex;" alt="{\displaystyle w={\frac {1}{f\rho _{o}}}\left[-\left({\frac {\partial \tau ^{x}}{\partial x}}+{\frac {\partial \tau ^{y}}{\partial y}}\right)e^{z/d}\sin(z/d)+\left({\frac {\partial \tau ^{y}}{\partial x}}-{\frac {\partial \tau ^{x}}{\partial y}}\right)(1-e^{z/d}\cos(z/d))\right].}"></span></dd></dl> <p>Note that when vertically-integrated, the volume transport associated with the Ekman spiral is to the right of the wind direction in the Northern Hemisphere. </p> <div class="mw-heading mw-heading3"><h3 id="Ekman_layer_at_the_bottom_of_the_ocean_and_atmosphere">Ekman layer at the bottom of the ocean and atmosphere</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ekman_layer&action=edit&section=5" title="Edit section: Ekman layer at the bottom of the ocean and atmosphere"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The traditional development of Ekman layers bounded below by a surface utilizes two boundary conditions: </p> <ul><li>A <a href="/wiki/No-slip_condition" title="No-slip condition">no-slip condition</a> at the surface;</li> <li>The Ekman velocities approaching the geostrophic velocities as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf368e72c009decd9b6686ee84a375632e11de98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.088ex; height:1.676ex;" alt="{\displaystyle z}"></span> goes to infinity.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Experimental_observations_of_the_Ekman_layer">Experimental observations of the Ekman layer</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ekman_layer&action=edit&section=6" title="Edit section: Experimental observations of the Ekman layer"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There is much difficulty associated with observing the Ekman layer for two main reasons: the theory is too simplistic as it assumes a constant eddy viscosity, which Ekman himself anticipated,<sup id="cite_ref-Ekman_3-0" class="reference"><a href="#cite_note-Ekman-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> saying </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>It is obvious that <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \left[\nu \right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow> <mo>[</mo> <mi>ν</mi> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \left[\nu \right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f42e24bd3af001fe2dd599781fc7cef71f07e14" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.494ex; height:2.843ex;" alt="{\displaystyle \ \left[\nu \right]}"></span> cannot generally be regarded as a constant when the density of water is not uniform within the region considered</p></blockquote> <p>and because it is difficult to design instruments with great enough sensitivity to observe the velocity profile in the ocean. </p> <div class="mw-heading mw-heading3"><h3 id="Laboratory_demonstrations">Laboratory demonstrations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ekman_layer&action=edit&section=7" title="Edit section: Laboratory demonstrations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The bottom Ekman layer can readily be observed in a rotating cylindrical tank of water by dropping in dye and changing the rotation rate slightly.<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> Surface Ekman layers can also be observed in rotating tanks.<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> </p> <div class="mw-heading mw-heading3"><h3 id="In_the_atmosphere">In the atmosphere</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ekman_layer&action=edit&section=8" title="Edit section: In the atmosphere"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the atmosphere, the Ekman solution generally overstates the magnitude of the horizontal wind field because it does not account for the velocity shear in the <a href="/wiki/Surface_layer" title="Surface layer">surface layer</a>. Splitting the <a href="/wiki/Planetary_boundary_layer" title="Planetary boundary layer">planetary boundary layer</a> into the surface layer and the Ekman layer generally yields more accurate results.<sup id="cite_ref-Holton_6-0" class="reference"><a href="#cite_note-Holton-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="In_the_ocean">In the ocean</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ekman_layer&action=edit&section=9" title="Edit section: In the ocean"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Ekman layer, with its distinguishing feature the Ekman spiral, is rarely observed in the ocean. The Ekman layer near the surface of the ocean extends only about 10 – 20 meters deep,<sup id="cite_ref-Holton_6-1" class="reference"><a href="#cite_note-Holton-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> and instrumentation sensitive enough to observe a velocity profile in such a shallow depth has only been available since around 1980.<sup id="cite_ref-Vallis_2-1" class="reference"><a href="#cite_note-Vallis-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Also, <a href="/wiki/Wind_waves" class="mw-redirect" title="Wind waves">wind waves</a> modify the flow near the surface, and make observations close to the surface rather difficult.<sup id="cite_ref-Santala_7-0" class="reference"><a href="#cite_note-Santala-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Instrumentation">Instrumentation</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ekman_layer&action=edit&section=10" title="Edit section: Instrumentation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Observations of the Ekman layer have only been possible since the development of robust surface moorings and sensitive current meters. Ekman himself developed a current meter to observe the spiral that bears his name, but was not successful.<sup id="cite_ref-Rudnick_8-0" class="reference"><a href="#cite_note-Rudnick-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> The Vector Measuring Current Meter <sup id="cite_ref-Weller_9-0" class="reference"><a href="#cite_note-Weller-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> and the <a href="/wiki/Acoustic_Doppler_Current_Profiler" class="mw-redirect" title="Acoustic Doppler Current Profiler">Acoustic Doppler Current Profiler</a> are both used to measure current. </p> <div class="mw-heading mw-heading4"><h4 id="Observations">Observations</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ekman_layer&action=edit&section=11" title="Edit section: Observations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The first documented observations of an Ekman-like spiral in the ocean were made in the Arctic Ocean from a drifting ice floe in 1958.<sup id="cite_ref-Hunkins_10-0" class="reference"><a href="#cite_note-Hunkins-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> More recent observations include (not an exhaustive list): </p> <ul><li>The 1980 <a href="/w/index.php?title=Mixed_layer_experiment&action=edit&redlink=1" class="new" title="Mixed layer experiment (page does not exist)">mixed layer experiment</a><sup id="cite_ref-Davis_11-0" class="reference"><a href="#cite_note-Davis-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup></li> <li>Within the Sargasso Sea during the 1982 Long Term Upper Ocean Study <sup id="cite_ref-Price_12-0" class="reference"><a href="#cite_note-Price-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup></li> <li>Within the California Current during the 1993 Eastern Boundary Current experiment <sup id="cite_ref-Chereskin_13-0" class="reference"><a href="#cite_note-Chereskin-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup></li> <li>Within the Drake Passage region of the Southern Ocean <sup id="cite_ref-Lenn_14-0" class="reference"><a href="#cite_note-Lenn-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup></li> <li>In the eastern tropical Pacific, at 2°N, 140°W, using 5 current meters between 5 and 25 meters depth.<sup id="cite_ref-cronin_15-0" class="reference"><a href="#cite_note-cronin-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> This study noted that the geostrophic shear associated with tropical stability waves modified the Ekman spiral relative to what is expected with horizontally uniform density.</li> <li>North of the Kerguelen Plateau during the 2008 SOFINE experiment <sup id="cite_ref-Roach_16-0" class="reference"><a href="#cite_note-Roach-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup></li></ul> <p>Common to several of these observations spirals were found to be "compressed", displaying larger estimates of eddy viscosity when considering the rate of rotation with depth than the eddy viscosity derived from considering the rate of decay of speed.<sup id="cite_ref-Price_12-1" class="reference"><a href="#cite_note-Price-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Chereskin_13-1" class="reference"><a href="#cite_note-Chereskin-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Lenn_14-1" class="reference"><a href="#cite_note-Lenn-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Roach_16-1" class="reference"><a href="#cite_note-Roach-16"><span class="cite-bracket">[</span>16<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=Ekman_layer&action=edit&section=12" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1259569809">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{clear:left;float:left;margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><span class="portalbox-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Waves_in_pacifica_1.jpg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/45/Waves_in_pacifica_1.jpg/32px-Waves_in_pacifica_1.jpg" decoding="async" width="32" height="22" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/45/Waves_in_pacifica_1.jpg/48px-Waves_in_pacifica_1.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/45/Waves_in_pacifica_1.jpg/64px-Waves_in_pacifica_1.jpg 2x" data-file-width="2000" data-file-height="1358" /></a></span></span><span class="portalbox-link"><a href="/wiki/Portal:Oceans" title="Portal:Oceans">Oceans portal</a></span></li></ul> <ul><li><a href="/wiki/Ekman_number" title="Ekman number">Ekman number</a> – Dimensionless ratio of viscous to Coriolis forces</li> <li><a href="/wiki/Ekman_spiral" title="Ekman spiral">Ekman spiral</a> – Velocity profile of wind driven current with depth</li> <li><a href="/wiki/Ekman_transport" title="Ekman transport">Ekman transport</a> – Net transport of surface water perpendicular to wind direction</li> <li><a href="/wiki/Ekman_velocity" title="Ekman velocity">Ekman velocity</a> – Formula for wind induced water current velocity</li> <li><a href="/wiki/Tea_leaf_paradox" title="Tea leaf paradox">Tea leaf paradox</a> – Fluid dynamics phenomenon</li> <li><a href="/wiki/Stewartson_layer" title="Stewartson layer">Stewartson layer</a> – Shear layer connecting differentially rotating regions</li> <li><a href="/wiki/Vagn_Walfrid_Ekman" title="Vagn Walfrid Ekman">Vagn Walfrid Ekman</a> – Swedish oceanographer (1874–1954)</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=Ekman_layer&action=edit&section=13" 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-Cushman-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-Cushman_1-0">^</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="CITEREFCushman-Roisin1994" class="citation book cs1">Cushman-Roisin, Benoit (1994). "Chapter 5 – The Ekman Layer". <i>Introduction to Geophysical Fluid Dynamics</i> (1st ed.). Prentice Hall. pp. 76–77. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-13-353301-9" title="Special:BookSources/978-0-13-353301-9"><bdi>978-0-13-353301-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Chapter+5+%E2%80%93+The+Ekman+Layer&rft.btitle=Introduction+to+Geophysical+Fluid+Dynamics&rft.pages=76-77&rft.edition=1st&rft.pub=Prentice+Hall&rft.date=1994&rft.isbn=978-0-13-353301-9&rft.aulast=Cushman-Roisin&rft.aufirst=Benoit&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEkman+layer" class="Z3988"></span></span> </li> <li id="cite_note-Vallis-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-Vallis_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Vallis_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVallis2006" class="citation book cs1">Vallis, Geoffrey K. (2006). "Chapter 2 – Effects of Rotation and Stratification". <i>Atmospheric and Oceanic Fluid Dynamics</i> (1st ed.). Cambridge, UK: Cambridge University Press. pp. 112–113. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-84969-2" title="Special:BookSources/978-0-521-84969-2"><bdi>978-0-521-84969-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Chapter+2+%E2%80%93+Effects+of+Rotation+and+Stratification&rft.btitle=Atmospheric+and+Oceanic+Fluid+Dynamics&rft.place=Cambridge%2C+UK&rft.pages=112-113&rft.edition=1st&rft.pub=Cambridge+University+Press&rft.date=2006&rft.isbn=978-0-521-84969-2&rft.aulast=Vallis&rft.aufirst=Geoffrey+K.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEkman+layer" class="Z3988"></span></span> </li> <li id="cite_note-Ekman-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-Ekman_3-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEkman1905" class="citation journal cs1">Ekman, V.W. (1905). "On the influence of the earth's rotation on ocean currents". <i>Ark. Mat. Astron. Fys</i>. <b>2</b> (11): 1–52.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Ark.+Mat.+Astron.+Fys.&rft.atitle=On+the+influence+of+the+earth%27s+rotation+on+ocean+currents&rft.volume=2&rft.issue=11&rft.pages=1-52&rft.date=1905&rft.aulast=Ekman&rft.aufirst=V.W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEkman+layer" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external autonumber" href="http://paoc.mit.edu/labguide/ekman.html">[1]</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20131022034132/http://paoc.mit.edu/labguide/ekman.html">Archived</a> 2013-10-22 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external autonumber" href="http://dennou-k.gaia.h.kyoto-u.ac.jp/library/gfd_exp/exp_e/exp/ek/1/app.htm">[2]</a></span> </li> <li id="cite_note-Holton-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-Holton_6-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Holton_6-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHolton2004" class="citation book cs1">Holton, James R. (2004). "Chapter 5 – The Planetary Boundary Layer". <i>Dynamic Meteorology</i>. International Geophysics Series. Vol. 88 (4th ed.). Burlington, MA: Elsevier Academic Press. pp. 129–130. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-354015-7" title="Special:BookSources/978-0-12-354015-7"><bdi>978-0-12-354015-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Chapter+5+%E2%80%93+The+Planetary+Boundary+Layer&rft.btitle=Dynamic+Meteorology&rft.place=Burlington%2C+MA&rft.series=International+Geophysics+Series&rft.pages=129-130&rft.edition=4th&rft.pub=Elsevier+Academic+Press&rft.date=2004&rft.isbn=978-0-12-354015-7&rft.aulast=Holton&rft.aufirst=James+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEkman+layer" class="Z3988"></span></span> </li> <li id="cite_note-Santala-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-Santala_7-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSantalaTerray1992" class="citation journal cs1">Santala, M. J.; Terray, E. A. (1992). "A technique for making unbiased estimates of current shear from a wave-follower". <i>Deep-Sea Research</i>. <b>39</b> (3–4): 607–622. <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/1992DSRA...39..607S">1992DSRA...39..607S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0198-0149%2892%2990091-7">10.1016/0198-0149(92)90091-7</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Deep-Sea+Research&rft.atitle=A+technique+for+making+unbiased+estimates+of+current+shear+from+a+wave-follower&rft.volume=39&rft.issue=3%E2%80%934&rft.pages=607-622&rft.date=1992&rft_id=info%3Adoi%2F10.1016%2F0198-0149%2892%2990091-7&rft_id=info%3Abibcode%2F1992DSRA...39..607S&rft.aulast=Santala&rft.aufirst=M.+J.&rft.au=Terray%2C+E.+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEkman+layer" class="Z3988"></span></span> </li> <li id="cite_note-Rudnick-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-Rudnick_8-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRudnick2003" class="citation journal cs1">Rudnick, Daniel (2003). "Observations of Momentum Transfer in the Upper Ocean: Did Ekman Get It Right?". <i>Near-Boundary Processes and Their Parameterization</i>. Manoa, Hawaii: School of Ocean and Earth Science and Technology.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Near-Boundary+Processes+and+Their+Parameterization&rft.atitle=Observations+of+Momentum+Transfer+in+the+Upper+Ocean%3A+Did+Ekman+Get+It+Right%3F&rft.date=2003&rft.aulast=Rudnick&rft.aufirst=Daniel&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEkman+layer" class="Z3988"></span></span> </li> <li id="cite_note-Weller-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-Weller_9-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWellerDavis1980" class="citation journal cs1">Weller, R.A.; Davis, R.E. (1980). "A vector-measuring current meter". <i>Deep-Sea Research</i>. <b>27</b> (7): 565–582. <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/1980DSRA...27..565W">1980DSRA...27..565W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0198-0149%2880%2990041-2">10.1016/0198-0149(80)90041-2</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Deep-Sea+Research&rft.atitle=A+vector-measuring+current+meter&rft.volume=27&rft.issue=7&rft.pages=565-582&rft.date=1980&rft_id=info%3Adoi%2F10.1016%2F0198-0149%2880%2990041-2&rft_id=info%3Abibcode%2F1980DSRA...27..565W&rft.aulast=Weller&rft.aufirst=R.A.&rft.au=Davis%2C+R.E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEkman+layer" class="Z3988"></span></span> </li> <li id="cite_note-Hunkins-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hunkins_10-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHunkins1966" class="citation journal cs1">Hunkins, K. (1966). "Ekman drift currents in the Arctic Ocean". <i>Deep-Sea Research</i>. <b>13</b> (4): 607–620. <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/1966DSRA...13..607H">1966DSRA...13..607H</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0011-7471%2866%2990592-4">10.1016/0011-7471(66)90592-4</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Deep-Sea+Research&rft.atitle=Ekman+drift+currents+in+the+Arctic+Ocean&rft.volume=13&rft.issue=4&rft.pages=607-620&rft.date=1966&rft_id=info%3Adoi%2F10.1016%2F0011-7471%2866%2990592-4&rft_id=info%3Abibcode%2F1966DSRA...13..607H&rft.aulast=Hunkins&rft.aufirst=K.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEkman+layer" class="Z3988"></span></span> </li> <li id="cite_note-Davis-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-Davis_11-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDavisde_SzoekeNiiler.1981" class="citation journal cs1">Davis, R.E.; de Szoeke, R.; Niiler., P. (1981). 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(2015). <a rel="nofollow" class="external text" href="http://ecite.utas.edu.au/99058">"Detecting and Characterizing Ekman Currents in the Southern Ocean"</a>. <i>Journal of Physical Oceanography</i>. <b>45</b> (5): 1205–1223. <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/2015JPO....45.1205R">2015JPO....45.1205R</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/10.1175%2FJPO-D-14-0115.1">10.1175/JPO-D-14-0115.1</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Physical+Oceanography&rft.atitle=Detecting+and+Characterizing+Ekman+Currents+in+the+Southern+Ocean&rft.volume=45&rft.issue=5&rft.pages=1205-1223&rft.date=2015&rft_id=info%3Adoi%2F10.1175%2FJPO-D-14-0115.1&rft_id=info%3Abibcode%2F2015JPO....45.1205R&rft.aulast=Roach&rft.aufirst=C.J.&rft.au=Phillips%2C+H.E.&rft.au=Bindoff%2C+N.L.&rft.au=Rintoul%2C+S.R.&rft_id=http%3A%2F%2Fecite.utas.edu.au%2F99058&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEkman+layer" 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=Ekman_layer&action=edit&section=14" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://paoc.mit.edu/labguide/ekman.html">Bottom Ekman layer lab demonstration</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20131022034132/http://paoc.mit.edu/labguide/ekman.html">Archived</a> 2013-10-22 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a rel="nofollow" class="external text" href="http://dennou-k.gaia.h.kyoto-u.ac.jp/library/gfd_exp/exp_e/exp/ek/1/app.htm">Surface Ekman layer lab demonstration</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output 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href="/wiki/Iribarren_number" title="Iribarren number">Iribarren number</a></li> <li><a href="/wiki/Kelvin_wave" title="Kelvin wave">Kelvin wave</a></li> <li><a href="/wiki/Kinematic_wave" title="Kinematic wave">Kinematic wave</a></li> <li><a href="/wiki/Longshore_drift" title="Longshore drift">Longshore drift</a></li> <li><a href="/wiki/Luke%27s_variational_principle" title="Luke's variational principle">Luke's variational principle</a></li> <li><a href="/wiki/Mild-slope_equation" title="Mild-slope equation">Mild-slope equation</a></li> <li><a href="/wiki/Radiation_stress" title="Radiation stress">Radiation stress</a></li> <li><a href="/wiki/Rogue_wave" title="Rogue wave">Rogue wave</a></li> <li><a href="/wiki/Rossby_wave" title="Rossby wave">Rossby wave</a></li> <li><a href="/wiki/Rossby-gravity_waves" title="Rossby-gravity waves">Rossby-gravity waves</a></li> <li><a href="/wiki/Sea_state" title="Sea state">Sea state</a></li> <li><a href="/wiki/Seiche" title="Seiche">Seiche</a></li> <li><a href="/wiki/Significant_wave_height" title="Significant wave height">Significant wave height</a></li> <li><a href="/wiki/Soliton" title="Soliton">Soliton</a></li> <li><a href="/wiki/Stokes_drift" title="Stokes drift">Stokes drift</a></li> <li><a href="/wiki/Stokes_problem" title="Stokes problem">Stokes problem</a></li> <li><a href="/wiki/Stokes_wave" title="Stokes wave">Stokes wave</a></li> <li><a href="/wiki/Swell_(ocean)" title="Swell (ocean)">Swell</a></li> <li><a href="/wiki/Trochoidal_wave" title="Trochoidal wave">Trochoidal wave</a></li> <li><a href="/wiki/Tsunami" title="Tsunami">Tsunami</a> <ul><li><a href="/wiki/Megatsunami" title="Megatsunami">megatsunami</a></li></ul></li> <li><a href="/wiki/Undertow_(water_waves)" title="Undertow (water waves)">Undertow</a></li> <li><a href="/wiki/Ursell_number" title="Ursell number">Ursell number</a></li> <li><a href="/wiki/Wave_action_(continuum_mechanics)" title="Wave action (continuum mechanics)">Wave action</a></li> <li><a href="/wiki/Wave_base" title="Wave base">Wave base</a></li> <li><a href="/wiki/Wave_height" title="Wave height">Wave height</a></li> <li><a href="/wiki/Wave_nonlinearity" title="Wave nonlinearity">Wave nonlinearity</a></li> <li><a href="/wiki/Wave_power" title="Wave power">Wave power</a></li> <li><a href="/wiki/Wave_radar" title="Wave radar">Wave radar</a></li> <li><a href="/wiki/Wave_setup" title="Wave setup">Wave setup</a></li> <li><a href="/wiki/Wave_shoaling" title="Wave shoaling">Wave shoaling</a></li> <li><a href="/wiki/Wave_turbulence" title="Wave turbulence">Wave turbulence</a></li> <li><a href="/wiki/Wave%E2%80%93current_interaction" title="Wave–current interaction">Wave–current interaction</a></li> <li><a href="/wiki/Waves_and_shallow_water" title="Waves and shallow water">Waves and shallow water</a> <ul><li><a href="/wiki/One-dimensional_Saint-Venant_equations" class="mw-redirect" title="One-dimensional Saint-Venant equations">one-dimensional Saint-Venant equations</a></li> <li><a href="/wiki/Shallow_water_equations" title="Shallow water equations">shallow water equations</a></li></ul></li> <li><a href="/wiki/Wind_fetch" title="Wind fetch">Wind fetch</a></li> <li><a href="/wiki/Wind_setup" title="Wind setup">Wind setup</a></li> <li><a href="/wiki/Wind_wave" title="Wind wave">Wind wave</a> <ul><li><a href="/wiki/Wind_wave_model" title="Wind wave 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 class="mw-selflink selflink">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 href="/wiki/Langmuir_circulation" title="Langmuir circulation">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" 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