Thermal wind

thermal wind balanceair currentbacking winds and CAAsoutherly low-level windsthermal wind equationwarm-air advection
The thermal wind is the vector difference between the geostrophic wind at upper altitudes minus that at lower altitudes in the atmosphere.wikipedia
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Wind shear

windshearvertical wind shearshear
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.
The thermal wind concept explains how differences in wind speed at different heights are dependent on horizontal temperature differences, and explains the existence of the jet stream.

Jet stream

jetstreampolar jet streamsubtropical jet stream
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.
Jet streams are fast flowing, narrow, meandering air currents in the atmospheres of some planets, including Earth.

Geostrophic wind

geostrophicgeostrophic balancegeostrophic flow
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. The thermal wind is the vector difference between the geostrophic wind at upper altitudes minus that at lower altitudes in the atmosphere. The thermal wind relation results from hydrostatic balance and geostrophic balance in the presence of a temperature gradient along constant pressure surfaces, or isobars.

Barotropic fluid

barotropicBarotropity
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 isobaric surfaces will also be isothermal surfaces, hence (from the thermal wind equation) the geostrophic wind will not vary with depth.

Frontogenesis

redevelopedfrontogenetic processesfrontogenetical
Thermal wind causes a deformation field and frontogenesis may occur.
During frontogenesis, the temperature gradient tightens and as a result, the thermal wind becomes imbalanced.

Balanced flow

The combination of these two force balances is called thermal wind balance, a term generalizable also to more complicated horizontal flow balances such as gradient wind balance.

Geopotential height

geopotentialgeopotential altitudeheight
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.

Virtual temperature

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.

Troposphere

troposphericdivergencemid-tropospheric
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.

Hydrostatic equilibrium

hydrostatic balanceequilibriumhydrostatic
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. The thermal wind relation results from hydrostatic balance and geostrophic balance in the presence of a temperature gradient along constant pressure surfaces, or isobars. In addition, when forces acting in the vertical dimension are dominated by the vertical pressure-gradient force and the gravitational force, hydrostatic balance occurs.

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

Contour line

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

Coriolis force

Coriolis effectCoriolisCoriolis acceleration
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.

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. In addition, when forces acting in the vertical dimension are dominated by the vertical pressure-gradient force and the gravitational force, hydrostatic balance occurs.

Gravity

gravitationgravitationalgravitational force
In addition, when forces acting in the vertical dimension are dominated by the vertical pressure-gradient force and the gravitational force, hydrostatic balance occurs.

Hypsometric equation

thicknesshypsometricallyThickness (meteorology)
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.

Gas constant

universal gas constantideal gas constantspecific gas constant
where \, R \, is the specific gas constant for air, is the geopotential at pressure level \, p_n \, and is the vertically-averaged temperature of the layer.

Geopotential

Geopotential functiongeopotential numbergeopotential numbers
where \, R \, is the specific gas constant for air, is the geopotential at pressure level \, p_n \, and is the vertically-averaged temperature of the layer.

Coriolis frequency

Coriolis parameterCoriolis coefficient
Differentiating the geostrophic wind, (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)

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.

Phenomenon

phenomenaphenomenalphysical phenomena
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.

Clockwise

counterclockwiseCCWCW
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.

Atmospheric sounding

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

Isothermal process

isothermalisothermallyisotherm
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.

North

NNordNorth Korea
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.