Geostrophic Wind - Governing Formula

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 F_r 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: