Difference between revisions of "Vorticity"

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<div class="definition"><div class="short_definition">A [[vector]] measure of local rotation in a fluid flow, defined mathematically as the [[curl]] of  the [[velocity]] vector,  <div class="display-formula"><blockquote>[[File:ams2001glos-Ve19.gif|link=|center|ams2001glos-Ve19]]</blockquote></div> where &#x003b6; is the vorticity, '''u''' the velocity, and '''&nabla;''' the [[del operator]].</div><br/> <div class="paragraph">The vorticity component normal to a small plane element is the limit of the [[circulation]] per  unit area as the area of the element approaches zero (<br/>''see'' [[Stokes's theorem]]). The vorticity of a  [[solid rotation]] is twice the [[angular velocity]] vector. In meteorology, "the vorticity" usually refers  to the vertical component of the vorticity. <br/>''See also'' [[relative vorticity]], [[absolute vorticity]], [[geostrophic  vorticity]], [[thermal vorticity]], [[vorticity equation]], [[curl]]; <br/>''compare'' [[deformation]], [[divergence]].</div><br/></div>
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<div class="definition"><div class="short_definition">A [[vector]] measure of local rotation in a fluid flow, defined mathematically as the [[curl]] of  the [[velocity]] vector,  <div class="display-formula"><blockquote>[[File:ams2001glos-Ve19.gif|link=|center|ams2001glos-Ve19]]</blockquote></div> where &#x003b6; is the vorticity, '''u''' the velocity, and '''&nabla;''' the [[del operator]].</div><br/> <div class="paragraph">The vorticity component normal to a small plane element is the limit of the [[circulation]] per  unit area as the area of the element approaches zero (<br/>''see'' [[Stokes's theorem]]). The vorticity of a  [[solid rotation]] is twice the [[angular velocity]] vector. In meteorology, "the vorticity" usually refers  to the vertical component of the vorticity. <br/>''See also'' [[relative vorticity]], [[absolute vorticity]], [[geostrophic vorticity|geostrophic  vorticity]], [[thermal vorticity]], [[vorticity equation]], [[curl]]; <br/>''compare'' [[deformation]], [[divergence]].</div><br/></div>
 
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Revision as of 17:13, 25 April 2012



vorticity

A vector measure of local rotation in a fluid flow, defined mathematically as the curl of the velocity vector,
ams2001glos-Ve19
where ζ is the vorticity, u the velocity, and the del operator.

The vorticity component normal to a small plane element is the limit of the circulation per unit area as the area of the element approaches zero (
see Stokes's theorem). The vorticity of a solid rotation is twice the angular velocity vector. In meteorology, "the vorticity" usually refers to the vertical component of the vorticity.
See also relative vorticity, absolute vorticity, geostrophic vorticity, thermal vorticity, vorticity equation, curl;
compare deformation, divergence.


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