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Non-axisymmetric instability of a rotating layer of fluid

Published online by Cambridge University Press:  20 April 2006

Y. T. Fung
Y. T. Fung
Affiliation:
Fluid Dynamics Branch, Marine Technology Division, Naval Research Laboratory, Washington, D.C. 20375
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Abstract

A mechanism previously proposed for the possible interaction between a rotating sheet of fluid and a rotating environment is re-investigated using the normal-mode method. Only azimuthal modes are considered. Stability of such a flow, if any, will appear as the neutral condition, i.e. the stability domain will be present as a stability boundary. The stability boundary for the present flow exists only for one azimuthal mode with no density inhomogeneity. For general heterogeneous rotating flows subject to non-axisymmetric disturbances, a semi-ellipse theorem is derived with a restriction. In contrast with the semicircle theorem in two-dimensional stratified flows, the restriction suggests that the semicircle in the complex phase-velocity plane does not in general provide an upper bound on all unstable waves. For rigidly rotating flows all unstable waves lie on a semicircle in the complex phase-velocity plane regardless of the density distributions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 127 , February 1983 , pp. 83 - 90
Copyright
© 1983 Cambridge University Press

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References

Fung, Y. T. & Kurzweg, U. H. 1975 Stability of swirling flows with radius-dependent density J. Fluid Mech. 72, 243–255.Google Scholar
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