Analytical Atmospheric Ekman-Type Solutions with Height-Dependent Eddy Viscosities

We study the geophysical fluid dynamics problem in the steady atmospheric Ekman layer for height-dependent eddy viscosities in the form of some quadratic and rational power functions. We use the appropriate boundary conditions to obtain the wind velocity profiles analytically. For these Ekman-type solutions, the angle between the wind vector at the bottom and the geostrophic wind vector can be smaller or bigger than the traditional value of $$\frac{\pi }{4}$$ .