Frictional effects in wind-driven ocean currents

Surface ocean currents have a significant influence on the climate and their dynamics depend to a large extent on the behaviour of the vertical eddy viscosity. We present an analytic study of wind-driven surface currents for general depth-dependent vertical eddy viscosities. A novel formulation for Ekman-type flows, that relies of a transformation to polar coordinates, enables us to show that in the Northern Hemisphere the horizontal current profile decays in magnitude and turns clockwise with increasing depth, irrespective of the vertical variations in diffusivity. Using a perturbation approach, we also derive a formula for the deflection angle of the current at the surface from the wind direction and discuss its implications.