Largescale oceanic currents as shallowwater asymptotic solutions of the NavierStokes equation in rotating spherical coordinates
Abstract
We show that a consistent shallowwater approximation of the incompressible NavierStokes equation written in a spherical, rotating coordinate system produces, at leading order in a suitable limiting process, a general linear theory for windinduced ocean currents which goes beyond the limitations of the classical Ekman spiral. In particular, we obtain Ekmantype 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).
 Publication:

Deep Sea Research Part II: Topical Studies in Oceanography
 Pub Date:
 February 2019
 DOI:
 10.1016/j.dsr2.2018.12.007
 Bibcode:
 2019DSRII.160...32C
 Keywords:

 Incompressible NavierStokes equation;
 Ekmantype solution;
 Rotating spherical coordinates