# Difference between revisions of "Omega equation"

From Glossary of Meteorology

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− | <div class="definition"><div class="short_definition">A [[diagnostic equation]] by which the [[vertical velocity]] in [[pressure coordinates]] (ω = ''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]], σ is the [[static stability]], '''v'''<sub>''g''</sub> is the [[geostrophic]] velocity [[vector]], ζ<sub>''g''</sub> is the geostrophic [[relative vorticity]], φ is the [[geopotential]], ∇<sub>H</sub><sup>2</sup> is the horizontal [[Laplacian operator]], and '''∇'''<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, . 166–175. </div><br/> | + | <div class="definition"><div class="short_definition">A [[diagnostic equation]] by which the [[vertical velocity]] in [[pressure coordinates]] (ω = ''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]], σ is the [[static stability]], '''v'''<sub>''g''</sub> is the [[geostrophic]] velocity [[vector]], ζ<sub>''g''</sub> is the geostrophic [[relative vorticity]], φ is the [[geopotential]], ∇<sub>H</sub><sup>2</sup> is the horizontal [[Laplacian operator|Laplacian operator]], and '''∇'''<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, . 166–175. </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 = for which

*Dp*/*Dt*) may be calculated according to quasigeostrophic theory:*f*is the Coriolis parameter, σ is the static stability,**v**_{g}is the geostrophic velocity vector, ζ_{g}is the geostrophic relative vorticity, φ is the geopotential, ∇_{H}^{2}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.