Atmospheric Ekman flows with uniform density in ellipsoidal coordinates: Explicit solution and dynamical properties

In this paper, we present a new general system of equations describing the steady motion of atmosphere with uniform density in ellipsoidal coordinates, which is derived from the general governing equations for viscous fluids. We first show that this new system can be reduced to the classic Ekman equations. Secondly, we obtain the explicit solution of the Ekman equations in ellipsoidal coordinates. Thirdly, for the viscosity related to the height, we obtain the solution of the classical problem with zero acceleration at the bottom of Ekman layer. Finally, the uniqueness and dynamical properties of solution are demonstrated.