Large-scale oceanic currents as shallow-water asymptotic solutions of the Navier-Stokes equation in rotating spherical coordinates

We show that a consistent shallow-water approximation of the incompressible Navier-Stokes equation written in a spherical, rotating coordinate system produces, at leading order in a suitable limiting process, a general linear theory for wind-induced ocean currents which goes beyond the limitations of the classical Ekman spiral. In particular, we obtain Ekman-type solutions which extend over large regions in both latitude and longitude; we present examples for constant and for variable eddy viscosities. We also show how an additional restriction on our solution recovers the classical Ekman solution (which is valid only locally).