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The extension of the Miles-Howard theorem to compressible fluids

Published online by Cambridge University Press:  29 March 2006

G. Chimonas
G. Chimonas
Affiliation:
Department of Physics, University of Toronto, Toronto 5, Canada
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Abstract

A statically stable, gravitationally stratified compressible fluid containing a parallel shear flow is examined for stability against infinitesimal adiabatic perturbations. It is found that the Miles–Howard theorem of incompressible fluids may be generalized to this system, so that n2 ≥ ¼U′2 throughout the flow is a sufficient condition for stability. Here n2 is the Brunt–Väissälä frequency and U’ is the vertical gradient of the flow speed. Howard's upper bound on the growth rate of an unstable mode also generalizes to this compressible system.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 43 , Issue 4 , 2 October 1970 , pp. 833 - 836
Copyright
© 1970 Cambridge University Press

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References

Eckart, C. 1963 Phys. Fluids, 6, 1042
Howard, L. N. 1961 J. Fluid Mech. 10, 50.
Miles, J. W. 1961 J. Fluid Mech. 10, 49.
Warren, F. W. G. 1968 Quart. J. Mech. Appl. Math. 21, 43.