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Inviscid spatial stability of a compressible mixing layer

Published online by Cambridge University Press:  26 April 2006

T. L. Jackson  and
C. E. Grosch
T. L. Jackson
Affiliation:
Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529, USA
C. E. Grosch
Affiliation:
Department of Oceanography and Department of Computer Science, Old Dominion University, Norfolk, VA 23529, USA
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Abstract

We present the results of the inviscid spatial stability of a parallel compressible mixing layer. The parameters of this study are the Mach number of the moving stream, the ratio of the temperature of the stationary stream to that of the moving stream, the frequency, and the direction of propagation of the disturbance wave. Stability characteristics of the flow as a function of these parameters are given. It is shown that if the Mach number exceeds a critical value there are always two groups of unstable waves. One of these groups is fast with phase speeds greater than ½ and is supersonic with respect to the stationary stream. The other is slow with phase speeds less than ½ and supersonic with respect to the moving stream. Phase speeds for the neutral and unstable modes are given, as well as growth rates for the unstable modes. Finally, we show that three-dimensional modes have the same general behaviour as the two-dimensional modes but with higher growth rates over some range of propagation direction.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 208 , November 1989 , pp. 609 - 637
Copyright
© 1989 Cambridge University Press

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