Large-scale oceanic currents as shallow-water asymptotic solutions of the Navier-Stokes equation in rotating spherical coordinates
Abstract
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).
- 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 Navier-Stokes equation;
- Ekman-type solution;
- Rotating spherical coordinates