Geostrophic wind

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The geostrophic wind is the wind resulting from what is called the geostrophic balance between the Coriolis force and the pressure gradient force acting on a parcel of air, causing the wind to blow parallel to isobars of pressure in the earth's atmosphere. Such a wind is a zero-frequency inertial wave. However, this balance is rarely found exactly in nature, due to other forces acting on the wind, such as friction from the ground, or the centrifugal force from curved fluid flow. Thus, the isobars must be straight in pure geostrophic flow. Despite this, much of the atmosphere outside the tropics is close to geostrophic flow much of the time and it is a valuable first approximation.

Air naturally moves from areas of high pressure to areas of low pressure, due to the pressure gradient force. As soon as the air starts to move, however, the coriolis force deflects it due to the rotation of the earth. The 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).

Near the surface, 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.

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 altimeters are also used to measure sea surface height anomaly, which permits a calculation of the geostrophic current at the surface.

[edit] Modeling

Frictional effects are neglected, which is usually a very good approximation for the synoptic scale instantaneous flow in the midlatitude mid-troposphere. However, although ageostrophic terms are relatively small, they are important for the time evolution of the flow.

The geostrophic wind $(u g, v g)$ can be derived from the primitive equations, using the geostrophic approximation:

$u_g = - {g \over f} {\partial Z \over \partial y}$

$v_g = {g \over f} {\partial Z \over \partial x}$

- 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 height field. The validity of this approximation is dependent 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.