The Ekman spiral for piecewise-constant eddy viscosity

Abstract

We investigate the classical problem of wind-stress-induced non-equatorial steady ocean currents, considering a three-valued piecewise-constant eddy viscosity. This extends and generalizes recent results on piecewise-uniform eddy viscosity with only two layers. The aim is to determine how variations in the relative values of the eddy viscosity at different depths may account for the deviations from the surface current deflection of 45 • , predicted in the classical constant eddy viscosity case. Such variations are observed in field data, and we investigate analytically the effect the presence of a third region makes compared to the two-layer case.

Perturbation Analysis for the Surface Deflection Angle of Ekman-Type Flows with Variable Eddy Viscosity

“…In his classical work [10], the eddy viscosity (a quantity introduced as a measure of the frictional effects in the boundary layer-see the next section) is set as a constant, yielding a solution that, at the surface, is directed at an angle of 45 • to the right (left) of the wind direction in the Northern (Southern) Hemisphere. The source of the inaccuracy of the predicted surface deflection angle has been identified in the simplified assumption of constant eddy viscosity, and over the last few decades many attempts have been made at finding solutions for more general depth-dependent eddy viscosity profiles; many of the known explicit solutions for particular cases can be found for instance in [5,7,8,11,14,16]. Nevertheless, finding explicit solutions can be a very hard task even for rather simple eddy viscosity profiles, so alternative ways to tackle the problem have been sought.…”