Thermal wind

In atmospheric science, the thermal wind is the vector difference between the geostrophic wind at upper altitudes minus that at lower altitudes in the atmosphere.

It is the hypothetical vertical wind shear that would exist if the winds obey geostrophic balance in the horizontal, while pressure obeys hydrostatic balance in the vertical.

Since the geostrophic wind at a given pressure level flows along geopotential height contours on a map, and the geopotential thickness of a pressure layer is proportional to virtual temperature, it follows that the thermal wind flows along thickness or temperature contours.

For instance, the thermal wind associated with pole-to-equator temperature gradients is the primary physical explanation for the jet stream in the upper half of the troposphere, which is the atmospheric layer extending from the surface of the planet up to altitudes of about 12–15 km.

Also called baroclinic flow, the thermal wind varies with height in proportion to the horizontal temperature gradient.

The thermal wind relation results from hydrostatic balance and geostrophic balance in the presence of a temperature gradient along constant pressure surfaces, or isobars.

The term thermal wind was originally proposed by British meteorologist Ernest Gold.

Whenever the Earth's rotation plays a dominant role in fluid dynamics, as in the mid-latitudes, a balance between the Coriolis force and the pressure-gradient force develops.

However, the Coriolis force intervenes and nudges the air towards the right (in the northern hemisphere).

[2] In addition, when forces acting in the vertical dimension are dominated by the vertical pressure-gradient force and the gravitational force, hydrostatic balance occurs.In a barotropic atmosphere, where density is a function only of pressure, a horizontal pressure gradient will drive a geostrophic wind that is constant with height.

Such a coupling causes the slope of the isobars to increase with height, as illustrated in panel (b) of the figure to the left.

Because isobars are steeper at higher elevations, the associated pressure gradient force is stronger there.

[3] The geopotential thickness of an atmospheric layer defined by two different pressures is described by the hypsometric equation:

This formula shows that the layer thickness is proportional to the temperature.

Substituting the hypsometric equation, one gets a form based on temperature,

Note that thermal wind is at right angles to the horizontal temperature gradient, counter clockwise in the northern hemisphere.

If geostrophic wind blows from cold air to warm air (cold advection) the geostrophic wind will turn counterclockwise with height (for the northern hemisphere), a phenomenon known as wind backing.

Wind backing and veering allow an estimation of the horizontal temperature gradient with data from an atmospheric sounding.

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.

Thermal wind causes a deformation field and frontogenesis may occur.

A horizontal temperature gradient exists while moving North-South along a meridian because 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.

The Northern and Southern Hemispheres exhibit similar jet stream patterns in the mid-latitudes.

The strongest part of jet streams should be in proximity where temperature gradients are the largest.

Due to land masses in the northern hemisphere, largest temperature contrasts are observed on the east coast of North America (boundary between Canadian cold air mass and the Gulf Stream/warmer Atlantic) and Eurasia (boundary between the boreal winter monsoon/Siberian cold air mass and the warm Pacific).

Therefore, the strongest boreal winter jet streams are observed over east coast of North America and Eurasia.

Since stronger vertical shear promotes baroclinic instability, the most rapid development of extratropical cyclones (so called bombs) is also observed along the east coast of North America and Eurasia.

Jet streams (shown in pink) are well-known examples of thermal wind. They arise from the horizontal temperature gradients between the warm tropics and the colder polar regions .
The geostrophic wind on different isobaric levels in a barotropic atmosphere (a) and in a baroclinic atmosphere (b). The blue portion of the surface denotes a cold region while the orange portion denotes a warm region. This temperature structure is restricted to the surface in (a) but extends through the depth of the fluid in (b). The dotted lines enclose isobaric surfaces which remain at constant slope with increasing height in (a) and increase in slope with height in (b). Pink arrows illustrate the direction and amplitude of the horizontal wind. Only in the baroclinic atmosphere (b) do these vary with height. Such variation illustrates the thermal wind.
In (a), cold advection is occurring, so the thermal wind causes the geostrophic wind to rotate counterclockwise (for the northern hemisphere) with height. In (b), warm advection is occurring, so the geostrophic wind rotates clockwise with height.