The geostrophic wind is the
theoretical windthat would result from an exact balance between the Coriolis forceand the pressure gradientforce. This condition is called "geostrophic balance." The geostrophic wind is directed parallelto isobars (lines of constant pressure at a given height). This balance seldom holds exactly in nature. The true wind almost always differs from the geostrophic wind due to other forces such as frictionfrom the ground or the centrifugal forcefrom curved fluid flow. Thus, the actual wind would equal the geostrophic wind only if there were no friction and the isobars were perfectly straight. Despite this, much of the atmosphere outside the tropicsis close to geostrophic flow much of the time and it is a valuable first approximation.
Airnaturally moves from areas of high pressure to areas of low pressure, due to the pressure gradientforce. As soon as the air starts to move, however, the Coriolis force deflects it due to the rotation of the earth. The wict|deflection is to the right in the northern hemisphere, and to the left in the southern hemisphere. As the air moves from the high pressure area, its speed increases, and so does the deflection from the Coriolis force. The deflection increases until the Coriolis and pressure gradient forces are in geostrophic balance, at which point the air is no longer moving from high to low pressure, but instead moves along an isobar, a line of equal pressure (note that this explanation assumes that the atmosphere starts in a geostrophically unbalanced state and describes how such a state would evolve into a balanced flow. In practice, the flow is nearly always balanced. The geostrophic approximation has no predictive value since it does not contain any expression for change: it is purely diagnostic). The geostrophic balance helps to explain why low pressure systems spin counterclockwise and high pressure systems spin clockwise in the northern hemisphere (and the opposite in the southern hemisphere).
Flow of ocean water is also largely geostrophic. Just as multiple weather balloons that measure pressure as a function of height in the atmosphere are used to map the atmospheric pressure field and infer the geostrophic wind, measurements of density as a function of depth in the ocean are used to infer geostrophic currents.
Satellite altimetersare also used to measure sea surface height anomaly, which permits a calculation of the geostrophic current at the surface. Geostrophic flow in air or water is a zero-frequency inertial wave.
Limitations of the Geostrophic approximation
The effect of friction, between the air and the land, breaks the geostrophic balance. Friction slows the flow, lessening the effect of the Coriolis force. As a result, the pressure gradient force has a greater effect and the air still moves from high pressure to low pressure, though with great deflection. This explains why high pressure system winds radiate out from the center of the system, while low pressure systems have winds that spiral inwards.
The geostrophic wind neglects
frictional effects, which is usually a good approximationFact|date=June 2008 for the synoptic scale instantaneous flow in the midlatitude mid- troposphere. Although ageostrophicterms are relatively small, they are essential for the time evolution of the flow and in particular are necessary for the growth and decay of storms.
Assuming geostrophic balance, the geostrophic wind components on a constant-pressure surface can be derived as:
where "g" is the acceleration due to gravity (9.81 m.s-2), "f" is the Coriolis parameter (approximately 10−4 s−1, varying with latitude) and "Z" is the
geopotential heightof the constant pressure surface. The validity of this approximation depends on the local Rossby number. It is invalid at the equator, because "f" is equal to zero there, and therefore generally not used in the tropics.
Other variants of the equation are possible; for example, the geostrophic wind vector can be expressed in terms of the gradient of the
geopotential heightΦ on a surface of constant pressure:
* [http://atmos.nmsu.edu/education_and_outreach/encyclopedia/geostrophic.htm Geostrophic approximation]
* [http://nsidc.org/arcticmet/glossary/geostrophic_winds.html Definition of geostrophic wind]
* [http://www.met.tamu.edu/class/ATMO151/tut/windpres/wind8.html Geostrophic wind description]
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