Explicit solutions of atmospheric Ekman flows for some eddy viscosities in ellipsoidal coordinates

In ellipsoidal coordinates, we study the motion of the wind in the steady atmospheric Ekman layer for the height-dependent eddy viscosities in the form of some quadratic, fourth and rational power functions. We construct the explicit solutions for these forms of the eddy viscosities by using suitable boundary conditions. Furthermore, we write down a formula of the angle between the wind vector and the geostrophic wind vector at any height.