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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.
Davis, S. H. 1969 Proc. Roy. Soc. A 310, 341.
Joseph, D. D. 1965 Arch. Rat. Mech. Anal. 20, 59.
Joseph, D. D. & Shir, C. C. 1966 J. Fluid Mech. 26, 753.
Nield, D. A. 1964 J. Fluid Mech. 19, 341.
Pearson, J. R. A. 1958 J. Fluid Mech. 4, 489.
Scanlon, J. W. & Segel, L. A. 1967 J. Fluid Mech. 30, 149.
Scriven, L. E. & Sternling, C. V. 1964 J. Fluid Mech. 19, 321.
Smith, K. A. 1966 J. Fluid Mech. 24, 401.