Governing Formula
Newton's Second law can be written as follows if only the pressure gradient, gravity, and friction act on an air parcel, where the bold symbolizes a vector.
Where Fr is the friction and g is the acceleration due to gravity (9.81 m.s−2).
Locally this can be expanded in cartesian coordinates, with a positive u representing an eastward direction and a positive v representing a northward direction. Neglecting friction and vertical motion, we have:
With the Coriolis parameter (approximately 10−4 s−1, varying with latitude).
Assuming geostrophic balance, the system is stationary and the first two equations become:
By substituting using the third equation above, we have:
with Z the height of the constant pressure surface (satisfying ).
This leads us to the following result for the geostrophic wind components :
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 height Φ on a surface of constant pressure:
Read more about this topic: Geostrophic Wind
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