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Energy stability of the buoyancy boundary layer

Published online by Cambridge University Press:  29 March 2006

Joseph J. Dudis  and
Stephen H. Davis
Joseph J. Dudis
Affiliation:
The Johns Hopkins University, Baltimore, Maryland
Stephen H. Davis
Affiliation:
The Johns Hopkins University, Baltimore, Maryland
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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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 47 , Issue 2 , 31 May 1971 , pp. 381 - 403
Copyright
© 1971 Cambridge University Press

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