**MSC:**- 35J20 Variational methods for second-order, elliptic equations
- 35J25 Boundary value problems for second-order, elliptic equations

turbulent mass flow in shallow and small sized surface water is

discussed. The Dirichlet problem for the Ekman equation is shown to be

well posed in a weighted Sobolev space. Conditions for the existence

of classical solutions are given. The dependence of regularity and

asymptotics of the solution on the properties of the depth profile

are studied.