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On the linear stability of compressible plane Couette flow

Published online by Cambridge University Press:  26 April 2006

Peter W. Duck ,
Gordon Erlebacher  and
M. Yousuff Hussaini
Peter W. Duck
Affiliation:
Department of Mathematics, University of Manchester, Manchester, M13 9PL, UK
Gordon Erlebacher
Affiliation:
Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, Hampton, VA 23665, USA
M. Yousuff Hussaini
Affiliation:
Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, Hampton, VA 23665, USA
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Abstract

The linear stability of compressible plane Couette flow is investigated. The appropriate basic velocity and temperature distributions are perturbed by a small-amplitude normal-mode disturbance. The full small-amplitude disturbance equations are solved numerically at finite Reynolds numbers, and the inviscid limit of these equations is then investigated in some detail. It is found that instabilities can occur, although the corresponding growth rates are often quite small; the stability characteristics of the flow are quite different from unbounded flows. The effects of viscosity are also calculated, asymptotically, and shown to have a stabilizing role in all the cases investigated. Exceptional regimes to the problem occur when the wave speed of the disturbances approaches the velocity of either of the walls, and these regimes are also analysed in some detail. Finally, the effect of imposing radiation-type boundary conditions on the upper (moving) wall (in place of impermeability) is investigated, and shown to yield results common to both bounded and unbounded flows.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 258 , 10 January 1994 , pp. 131 - 165
Copyright
© 1994 Cambridge University Press

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