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Energy stability of modulated circular Couette flow

Published online by Cambridge University Press:  11 April 2006

Peter J. Riley  and
Robert L. Laurence
Peter J. Riley
Affiliation:
Department of Chemical Engineering, University of Massachusetts, Amherst
Robert L. Laurence
Affiliation:
Department of Chemical Engineering, University of Massachusetts, Amherst
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Abstract

The stability of circular Couette flow when the outer cylinder is at rest and the inner is modulated both with and without a mean shear is examined in the narrow-gap limit. Disturbances are assumed to be axisymmetric. Two criteria are used to determine conditions for stability; the first requires that the motion be strongly stable, the second only that disturbances of arbitrary initial energy decay from cycle to cycle. The behaviour of critical parameters as a function of frequency is similar for the linear and the energy analysis. The range of Reynolds numbers bounded above by certain instability and below by conditional nonlinear stability is enlarged by modulation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 79 , Issue 3 , 9 March 1977 , pp. 535 - 552
Copyright
© 1977 Cambridge University Press

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