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so as to keep it matched with the rotation of the earth underneath it. The left-hand side of the Sverdrup equation represents the motion required to maintain this match between the absolute vorticity of a water column and the planetary vorticity, whilethe right represents the applied force of the wind.

Derivation

The Sverdrup relation can be derived from the linearized barotropic vorticity equation for steady motion:

:.

Here is the geostrophic interior

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