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Buoyancy-surface tension instability by the method of energy

Published online by Cambridge University Press:  29 March 2006

Stephen H. Davis
Stephen H. Davis
Affiliation:
Department of Mechanics, Johns Hopkins University
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Abstract

The energy theory, giving a sufficient condition for stability, is developed for the motions in a horizontal, heated layer subject to buoyancy and surface tension effects. The free surface is assumed to be non-deformable (Pearson's 1958 model).

It is shown that the equations governing the energy theory are the symmetric part of the time-independent linear theory problem, and that the surface tension terms behave like a bounded perturbation to the Bénard problem. The qualitative behaviour of the optimal stability boundary as a function of its parameters is given. The optimal stability boundary is computed, and compared with previous linear and non-linear stability theories in terms of allowable subcritical instabilities.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 39 , Issue 2 , 10 November 1969 , pp. 347 - 359
Copyright
© 1969 Cambridge University Press

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References

Courant, R. & Hilbert, D. 1937 Methods of Mathematical Physics vol. 1. New York: Interscience.
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