The coastal boundary layers of a lake when horizontal and vertical Ekman numbers are of different orders of magnitudes

We investigate the linear hydrostatic boundary layers which bring the horizontal motion to rest at the shore of a lake of horizontal extent L and depth H containing a homogeneous fluid with constant, though vastly differing, horizontal and vertical eddy viscosities, A_H and A_V. The lake rotates with angular speed f/2 about a vertical axis and the motion is induced by a steady, nonuniform wind stress. Our results are applicable when

(H/L)² ≤ (A_V/fH²)^1/2 (A_H/fL²) ≤ (A_V/fH²)³ < < 1.

It is found that under these conditions the flow near the shore is determined by the local wind stress and the local value of the interior velocity parallel to the coast. It is found that under certain wind stress conditions there is a region of flow, adjacent to the shore, in which the fluid is effectively confined to the coast.