Thermal wind

From Glossary of Meteorology

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 vT in terms of the thickness h of the layer:
where 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 VT is given by the formula
where n is a coordinate normal to the thickness lines.
See thermal wind equation.