for western as opposed to eastern boundary currents, it gives us deep physical insights into the mechanism underlying the wind-driven circulation.
10.3.1. Rationalization of position, sense of circulation, and volume transport of ocean gyres
The Sverdrup relation, Eq. 10-17, is one of the cornerstones of dynamical oceanography. We can use it to derive a simple expression for the transport of ocean gyres as follows. The depth integrated flow must be horizontally nondivergent, and so we can introduce a streamfunction, Y, to map it out, [just as a streamfunction was used to represent the geostrophic flow in Section 7.1] where
Combining Eqs. 10-17 and 10-19 and integrating westward from the eastern boundary, where we set Y = 0 (no transport through the eastern boundary7) we obtain:
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