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

摘要

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 previouswork, we modify the boundary conditions and derive the explicit solution by using thenotation 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 accelerationat the bottom of the layer. In addition, uniqueness is shown and dynamical propertiesof solution are characterized.