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Finite amplitude instability of plane Couette flow

Published online by Cambridge University Press:  12 April 2006

Terence Coffee
Terence Coffee
Affiliation:
Department of Mathematical Sciences, New Mexico State University, Las Cruces
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Abstract

The Orr–Sommerfeld equation is solved numerically using expansions in Chebyshev polynomials and the generalized Rayleigh quotient iteration. Accurate results for large values of the parameters are obtained, and these further verify the belief that plane Couette flow is stable to infinitesimal disturbances. For finite disturbances, a formal expansion based on the method of Stuart and Watson as modified by Reynolds & Potter is used. This method shows a transition to instability for a large enough amplitude.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 83 , Issue 3 , 5 December 1977 , pp. 401 - 413
Copyright
© 1977 Cambridge University Press

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