Energy stability of the Ekman boundary layer

Abstract

The critical value R_E of the Reynolds number R is predicted by the application of the energy theory. When R < R_E, the Ekman layer is the unique steady solution of the Navier-Stokes equations and the same boundary conditions, and is, further, stable in a slightly weaker sense than asymptotically stable in the mean. The critical value R_E is determined by numerically integrating the relevant Euler-Lagrange equations. An analytic lower bound to R_E is obtained. Comparisons are made between R_E and R_L, the critical value of R according to linear theory, in order to demark the region of parameter space, R_E < R < R_L, in which subcritical instabilities are allowable.