Energy stability of the buoyancy boundary layer

Abstract

The critical value RE of the Reynolds number R is predicted by the application of the energy theory. When R < RE, the buoyancy boundary layer is the unique steady solution of the Boussinesq equations and the same boundary conditions, and is, further, stable in a slightly weaker sense than asymptotically stable in the mean. The critical value RE is determined by numerically integrating the relevant Euler–Lagrange equations. Analytic lower bounds to RE are obtained. Comparisons are made between RE and RL, the critical value of R according to linear theory, in order to demark the region of parameter space, RE < R < RL, in which subcritical instabilities are allowable.