Ekman-type solutions of surface ocean currents with vertically varying eddy viscosity

In this paper, a linear system with variable eddy viscous terms is studied by using the governing equation of viscous fluid in a rotating spherical coordinate system, combined with the mass conservation equation and appropriate boundary conditions, in the context of an asymptotic model derived by letting the aspect ratio go to zero. The exact solution of Ekman flow is obtained when the eddy viscosity profile is either a constant, or a quadratic function, or a power function; moreover, the exact expression of the corresponding pressure is given. At the same time, the angle between the motion of the upper ocean and the wind stress is also discussed.