Boundary layers on characteristic surfaces for time-dependent rotating flows

It is shown that boundary layers (and free shear layers) have scales of variation of E to the 1/3 and E to the 1/4 when the surface is a characteristic surface for the associated inviscid problem. Whereas the formulation given here can be adapted to specific problems, an adaptation may not be practical in cases where an inviscid solution is not available. It is pointed out that in the usual Ekman layer problem, the balance is between the viscous force and a combination of the leading terms of the Coriolis force and the inertial force. For the characteristic layers, the primary balance is between the Coriolis and inertial forces, which leaves the viscous force unbalanced. In such a case, the viscous force is balanced by a combination of horizontal pressure gradients and the weak Coriolis force associated with local normal velocities. When cos theta = 0, this weak Coriolis force vanishes, and the horizontal pressure gradient is also weakened in consequence. This explains why the E to the 1/3 layer disappears in that case.