Explicit solution and dynamical properties of atmospheric Ekman flows with boundary conditions

Abstract

In this paper, we study the classical problem of the wind in the steady atmospheric Ekman layer with the constant eddy viscosity. Different from the previous work, we modify the boundary conditions and derive the explicit solution by using the notation of matrix cosine and matrix sine. For the arbitrary height-dependent eddy viscosity, we get the solution of the classical problem with zero velocity and acceleration at the bottom of the layer. In addition, uniqueness is shown and dynamical properties of solution are characterized.

Keywords

• ekman layer
• variable eddy viscosity
• explicit solutions
• existence
• dynamical properties