Atmospheric Ekman-type solutions with some eddy viscosities in ellipsoidal coordinates

Abstract

In this paper, we investigate the motion of the wind in the steady atmospheric Ekman layer with suitable boundary conditions in ellipsoidal coordinates. Firstly, we consider the system with the piecewise eddy viscosity coefficients. When the eddy viscosity of the upper layer is constant and the eddy viscosity of the bottom layer is related to the height, we transform the system to a first-order Riccati equation with a suitable initial value. Then, we also construct the solution to the system with the piecewise-constant eddy viscosity. Secondly, we derive the explicit solution to the system with a small perturbation of a constant. Finally, by choosing an exponential variation of the eddy viscosity, we get the explicit solution to the system.