# Thermal wind

Thermal wind

The thermal wind is a vertical shear in the geostrophic wind caused by a horizontal temperature gradient. Its name is a misnomer, because the thermal wind is not actually a wind, but rather a wind gradient.

Description

Physical Intuition

, so geostrophic wind does not increase with height.

This does not hold true in a baroclinic atmosphere, one where density is a function of both pressure and temperature. Horizontal temperature gradients cause the thickness of gas layers between isobaric surfaces to increase with higher temperatures. When multiple atmospheric layers are stacked upon each other, the slope of isobaric surfaces increases with height. This also causes the magnitude of the geostrophic wind to increase with height.

Mathematical Formalism

The thickness of an atmospheric layer is described by the hypsometric equation:

$h = z_2 - z_1 = frac\left\{R cdot T\right\}\left\{g\right\} cdot ln left \left[ frac\left\{P_1\right\}\left\{P_2\right\} ight \right]$

which shows the thickness is proportional to the temperature. When there is a horizontal temperature gradient, the thickness of the layer would be greatest where the temperature is greatest.

If we differentiate the geostrophic wind,dwith respect to pressure, and integrate from pressure level "p0" to "p1", we obtain the thermal wind equation:

$f mathbf\left\{v\right\}_T = mathbf\left\{k\right\} imes abla \left( phi_1 - phi_0 \right)$.

Examples

with height, also known as wind veering.

Wind backing and veering allow us to estimate the horizontal temperature gradient with data from an atmospheric sounding.

Frontogenesis

As in the case of advection turning, when there is a cross-isothermal component of the geostrophic wind, a sharpening of the temperature gradient results. The thermal wind causes a deformation field and frontogenesis may occur.

Jet Stream

A horizontal temperature gradient exists while moving North-South along a meridian because the curvature of the Earth allows for more solar heating at the equator than at the poles. This creates a westerly geostrophic wind pattern to form in the mid-latitudes. Because thermal wind causes an increase in wind velocity with height, the westerly pattern increases in intensity up until the tropopause, creating a strong wind current known as the jet stream. The Northern and Southern Hemispheres exhibit similar jet stream patterns in the mid-latitudes.

*Holton, James R.: "An Introduction to Dynamic Meteorology", 2004. ISBN 0-12-354015-1
*Vasquez, Tim: "Weather Forecasting Handbook", 2002. ISBN 0-9706840-2-9
*Vallis, Geoffrey K.: "Atmospheric and Oceanic Fluid Dynamics", 2006. ISBN 0-521-84969-1
*Wallace, John M. and Peter V. Hobbs: "Atmospheric Science", 2006. ISBN 0-12-732951-X

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