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The Quarterly Journal of Mechanics and Applied Mathematics 1970 23(1):127-136; doi:10.1093/qjmam/23.1.127
© 1970 by Oxford University Press
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ON THE STABILITY OF OSCILLATING, PLANE COUETTE FLOW

R. E. KELLY and ALISON M. CHEERS

( Dept. of Engineering, University of California Los Angeles
Aerodynamics Div., National Physical Laboratory Teddington, Middlesex )

The analysis concerns the stability to small disturbances of plane Couette flow when the flow is composed of a periodic, unsteady velocity as well as a mean velocity. Attention is restricted mainly to the case of large values of the product of wave-number and Reynolds number. In this region, a resonant interaction is possible which diminishes the decay rate of small disturbances by a term proportional to the amplitude of the unsteady velocity. Numerical results indicate that the flow is quite unlikely to be destabilized by this mechanism.


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