Difference between revisions of "Omega equation"

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<div class="definition"><div class="short_definition">A [[diagnostic equation]] by which the [[vertical velocity]] in [[pressure coordinates]]  (&#x003c9; = ''Dp''/''Dt'') may be calculated according to [[quasigeostrophic theory]]:    <div class="display-formula"><blockquote>[[File:ams2001glos-Oe5.gif|link=|center|ams2001glos-Oe5]]</blockquote></div>    for which ''f'' is the [[Coriolis parameter]], &#x003c3; is the [[static stability]], '''v'''<sub>''g''</sub> is the [[geostrophic]] velocity  [[vector]], &#x003b6;<sub>''g''</sub> is the geostrophic [[relative vorticity]], &#x003c6; is the [[geopotential]], &nabla;<sub>H</sub><sup>2</sup> is the horizontal [[Laplacian  operator]], and '''&nabla;'''<sub>H</sub> is the horizontal [[del operator]].</div><br/> <div class="paragraph">The right-hand side of the omega equation can also be expressed in terms of the [[divergence]]  of the '''Q''' [[vector]].</div><br/> </div><div class="reference">Holton, J. R. 1992. An Introduction to Dynamic Meteorology. 3d edition, Academic Press, . 166&ndash;175. </div><br/>  
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<div class="definition"><div class="short_definition">A [[diagnostic equation]] by which the [[vertical velocity]] in [[pressure coordinates]]  (&#x003c9; = ''Dp''/''Dt'') may be calculated according to [[quasigeostrophic theory]]:    <div class="display-formula"><blockquote>[[File:ams2001glos-Oe5.gif|link=|center|ams2001glos-Oe5]]</blockquote></div>    for which ''f'' is the [[Coriolis parameter]], &#x003c3; is the [[static stability]], '''v'''<sub>''g''</sub> is the [[geostrophic]] velocity  [[vector]], &#x003b6;<sub>''g''</sub> is the geostrophic [[relative vorticity]], &#x003c6; is the [[geopotential]], &nabla;<sub>H</sub><sup>2</sup> is the horizontal [[Laplacian operator|Laplacian  operator]], and '''&nabla;'''<sub>H</sub> is the horizontal [[del operator]].</div><br/> <div class="paragraph">The right-hand side of the omega equation can also be expressed in terms of the [[divergence]]  of the '''Q''' [[vector]].</div><br/> </div><div class="reference">Holton, J. R. 1992. An Introduction to Dynamic Meteorology. 3d edition, Academic Press, . 166&ndash;175. </div><br/>  
 
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Latest revision as of 17:32, 25 April 2012



omega equation

A diagnostic equation by which the vertical velocity in pressure coordinates (ω = Dp/Dt) may be calculated according to quasigeostrophic theory:
ams2001glos-Oe5
for which f is the Coriolis parameter, σ is the static stability, vg is the geostrophic velocity vector, ζg is the geostrophic relative vorticity, φ is the geopotential, ∇H2 is the horizontal Laplacian operator, and H is the horizontal del operator.

The right-hand side of the omega equation can also be expressed in terms of the divergence of the Q vector.

Holton, J. R. 1992. An Introduction to Dynamic Meteorology. 3d edition, Academic Press, . 166–175.