The deflection angle between a wind-forced surface current and the overlying wind in an ocean with vertically varying eddy viscosity

The angle between the wind stress that overlies the ocean and the resulting current at the ocean surface is calculated for a two-layer ocean with uniform eddy viscosity in the lower layer and for several assumed eddy viscosity profiles in the upper layer. The calculation of the deflection angle is greatly simplified by transforming the linear, second-order, vertical structure equation to its associated nonlinear, first-order, Riccati equation. The transformation to a Riccati equation can be used as an alternate numerical scheme, but its main advantage is that it yields analytic expressions for several eddy viscosity profiles.