# Difference between revisions of "Thermal wind equation"

From Glossary of Meteorology

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− | <div class="definition"><div class="short_definition">An equation for the vertical [[variation]] of the [[geostrophic wind]] in [[hydrostatic equilibrium]], which may be written in the form <div class="display-formula"><blockquote>[[File:ams2001glos-Te27.gif|link=|center|ams2001glos-Te27]]</blockquote></div> where '''v'''<sub>''g''</sub> is the [[vector]] geostrophic wind, ''p'' the [[pressure]] (used here as the vertical coordinate), ''R'' the [[gas constant]] for air, ''f'' the [[Coriolis parameter]], '''k''' a vertically directed unit vector, and '''∇'''<sub>''p''</sub> the isobaric [[del operator]].</div><br/> <div class="paragraph">This equation shows that the geostrophic wind shear -∂'''v'''<sub>''g''</sub>/∂''p'' is a vector parallel to the isotherms in such a sense that the cold air is on the left of the [[shear]] (in the Northern Hemisphere). The geostrophic wind at the top of an [[atmospheric layer]] may be considered the sum of the [[wind]] at the bottom of the layer and the [[thermal wind]] determined by the mean [[isotherms]] within the layer, that is, by the [[thickness pattern]] of the layer.</div><br/> </div> | + | <div class="definition"><div class="short_definition">An equation for the vertical [[variation]] of the [[geostrophic wind]] in [[hydrostatic equilibrium|hydrostatic equilibrium]], which may be written in the form <div class="display-formula"><blockquote>[[File:ams2001glos-Te27.gif|link=|center|ams2001glos-Te27]]</blockquote></div> where '''v'''<sub>''g''</sub> is the [[vector]] geostrophic wind, ''p'' the [[pressure]] (used here as the vertical coordinate), ''R'' the [[gas constant]] for air, ''f'' the [[Coriolis parameter]], '''k''' a vertically directed unit vector, and '''∇'''<sub>''p''</sub> the isobaric [[del operator]].</div><br/> <div class="paragraph">This equation shows that the geostrophic wind shear -∂'''v'''<sub>''g''</sub>/∂''p'' is a vector parallel to the isotherms in such a sense that the cold air is on the left of the [[shear]] (in the Northern Hemisphere). The geostrophic wind at the top of an [[atmospheric layer]] may be considered the sum of the [[wind]] at the bottom of the layer and the [[thermal wind]] determined by the mean [[isotherms]] within the layer, that is, by the [[thickness pattern]] of the layer.</div><br/> </div> |

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## Latest revision as of 17:05, 25 April 2012

## thermal wind equation

An equation for the vertical variation of the geostrophic wind in hydrostatic equilibrium, which may be written in the form where

**v**_{g}is the vector geostrophic wind,*p*the pressure (used here as the vertical coordinate),*R*the gas constant for air,*f*the Coriolis parameter,**k**a vertically directed unit vector, and**∇**_{p}the isobaric del operator.This equation shows that the geostrophic wind shear -∂

**v**_{g}/∂*p*is a vector parallel to the isotherms in such a sense that the cold air is on the left of the shear (in the Northern Hemisphere). The geostrophic wind at the top of an atmospheric layer may be considered the sum of the wind at the bottom of the layer and the thermal wind determined by the mean isotherms within the layer, that is, by the thickness pattern of the layer.

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