Exact Solutions of the Ekman Problem with Periodic Forcing

Exact analytical solutions of the unsteady Ekman boundary layer equations are presented. An approach to finding analytical solutions, that is different from the commonly used, is employed. The solutions correspond to the unsteady (periodic) forcing. Two variants of forcing are considered: (1) The magnitude of the stress at the top of the layer oscillates with some frequency ω; (2) The magnitude of the stress is constant but the stress vector rotates with a constant angular velocity ω The lower boundary condition is specified in three ways. Firstly, the currents are taken to vanish deep in the ocean (at the infinite depth). Secondly, the currents vanish at some prescribed depth. And thirdly, the condition that the stress vanishes at some depth is applied. Resonant (ω =f) and non-resonant (ω≠f) cases are considered.