# Thermal wind

From AMS Glossary

## thermal wind

The mean wind-shear vector in geostrophic balance with the gradient of mean temperature of a layer bounded by two isobaric surfaces.

Its analogy to the geostrophic wind is best demonstrated by expressing the thermal wind where where

**v**_{T}in terms of the thickness*h*of the layer:*f*is the Coriolis parameter,**k**the vertical unit vector,*g*the acceleration of gravity, and**∇**_{p}the del operator in the isobaric surface. The thermal wind is directed along the isotherms with cold air to the left in the Northern Hemisphere and to the right in the Southern Hemisphere. Its magnitude*V*_{T}is given by the formula*n*is a coordinate normal to the thickness lines.*See*thermal wind equation.