In this type of atmosphere, Euler equations reduces into the barotropic vorticity equation.
2.
As usual for the vorticity dynamics, the pressure drops out of the vorticity equation.
3.
The vorticity equation for a frictionless atmosphere may be written using pressure as the vertical coordinate:
4.
The derivation of the \ omega equation is based on the vorticity equation and the thermodynamic equation.
5.
The vorticity equation only gives a non-trivial component in the z-direction, where it becomes
6.
The barotropic vorticity equation is the simplest way for forecasting the movement of Rossby waves ( that is, the hPa geopotential height ) over a limited amount of time ( a few days ).
7.
Assuming, as did Sverdrup, that there is a level below which motion ceases, the vorticity equation can be integrated from this level to the base of the Ekman surface layer to obtain:
8.
The quasi-geostrophic vorticity equation can be obtained from the { x } and { y } components of the quasi-geostrophic momentum equation which can then be derived from the horizontal momentum equation
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