Thermal wind

(′thər·məl ′wind)

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

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5min Related Video: Thermal wind

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Sci-Tech Encyclopedia: Thermal wind

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The difference in the geostrophic wind between two heights in the atmosphere over a given position on Earth. It approximates the variation of the actual winds with height for large-scale and slowly changing motions of the atmosphere. Such structure in the wind field is of fundamental importance to the description of the atmosphere and to processes causing its day-to-day changes. The thermal wind embodies a basic relationship between vertical fluctuations of the horizontal wind and horizontal temperature gradients in the atmosphere. This relationship arises from the combination of the geostrophic wind law, the hydrostatic equation, and the gas law.

The geostrophic wind law applies directly to steady, straight, and unaccelerated horizontal motion and is a good approximation for large-scale and slowly changing motions in the atmosphere. The hydrostatic equation combined with the gas law relates the atmospheric pressure and temperature fields. The relationship is accurate for most atmospheric situations but not for small-scale and rapidly changing conditions such as in turbulence and thunderstorms. The equation gives the change of pressure in the vertical direction as a function of pressure and temperature. The key conclusion is that at a given level in the atmosphere the pressure change (decrease) with height is more rapid in cold air than in warm air. See also Atmosphere; Geostrophic wind; Hydrostatics; Troposphere.

Geography Dictionary: thermal wind

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Not a real wind, but an expression of wind shear for a given layer of atmosphere; the vector expressing the difference between the geostrophic winds at the bottom and top of the layer. It is proportional to the thickness of the layer, and is directed along the isotherms, with cold air to the left in the Northern Hemisphere, and to the right in the Southern.

However, the term is used to denote a wind developing as follows: the pressure gradients which produce surface winds may be due to the presence of cold and warm air masses. The fall in pressure with height is rapid in cold air, and much less rapid in warm air. Thus, at height, air pressure in the cold air will be less than that in the warm air. This creates a high-level pressure gradient and, therefore, a wind, often described as the ‘thermal wind’. The strength of this wind is a function of its height and the temperature difference between air masses; the greater the difference, the stronger the wind. Since there is a marked meridional temperature gradient in the troposphere, influenced at height by a powerful westerly factor, thermal winds are very strong at the point where the temperature gradient is greatest; at the polar front. The result is the polar front jet. The force of a thermal wind may be strengthened by any pressure gradient at ground level.

Wikipedia: Thermal wind

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The jet stream (shown here in pink) is a well-known example of the thermal wind. It arises from the horizontal temperature gradient from the warm tropics to the cold polar regions.

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.

1 Description
- 1.1 Physical Intuition
- 1.2 Mathematical Formalism
2 Examples
3 Further reading

Description

Physical Intuition

The vertical variation of geostrophic wind 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. The temperature difference is restricted to the boundary in (a) and extends through the region 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). This causes thermal wind to occur only in a baroclinic atmosphere.

The geostrophic wind is proportional to the slope of geopotential on a surface of constant pressure. In a barotropic atmosphere, one where density is a function only of pressure, the slope of isobaric surfaces is independent of temperature, 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 geopotential thickness of an atmospheric layer is described by the hypsometric equation:

$\ h = \Phi_2 - \Phi_1 = R \bar{T} \ln \left [ \frac{p_1}{p_2} \right ]$ ,

where $\, R \,$ is the specific gas constant for air, $\, \Phi_n \,$ is the geopotential at pressure level $\, p_n \,$ , and $\bar{T}$ is the vertically-averaged temperature of the layer. This formula shows that the layer 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, $\mathbf{v}_g = \frac{1}{f} \mathbf{k} \times \nabla_p \Phi$ (where $\; f \;$ is the Coriolis parameter, $\mathbf{k}$ is the vertical unit vector, and the subscript "p" on the gradient operator denotes gradient on a constant pressure surface) with respect to pressure, and integrate from pressure level $\, p_0 \,$ to $\, p_1 \,$ , we obtain the thermal wind equation:

$\mathbf{v}_T = \frac{1}{f} \mathbf{k} \times \nabla_p ( \Phi_1 - \Phi_0 )$ .

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

$\mathbf{v}_T = \frac{R}{f} \ln \left [ \frac{p_1}{p_2}\right ] \mathbf{k} \times \nabla_p \bar{T}$ .

Note that the thermal wind is at right angles to the horizontal temperature gradient, to the counter clockwise in the northern hemisphere. In the southern hemisphere, the change in sign of $\; f \;$ flips the direction.

Examples

Advection Turning

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.

If a component of the geostrophic wind is parallel to the temperature gradient, the thermal wind will cause the geostrophic wind to rotate with height. If the geostrophic wind blows from cold air to warm air (cold advection) the geostrophic wind will turn counterclockwise with height, a phenomenon known as wind backing. Otherwise, if the geostrophic wind blows from warm air to cold air (warm advection) the wind will turn clockwise 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.

		Sci-Tech Dictionary. McGraw-Hill Dictionary of Scientific and Technical Terms. Copyright © 2003, 1994, 1989, 1984, 1978, 1976, 1974 by McGraw-Hill Companies, Inc. All rights reserved. Read more
		Sci-Tech Encyclopedia. McGraw-Hill Encyclopedia of Science and Technology. Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. Read more
		Geography Dictionary. A Dictionary of Geography. Copyright © Susan Mayhew 1992, 1997, 2004. All rights reserved. Read more
		Wikipedia. This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article "Thermal wind". Read more

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