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Nonlinear evolution of oblique waves on compressible shear layers

Published online by Cambridge University Press:  26 April 2006

M. E. Goldstein  and
S. J. Leib
M. E. Goldstein
Affiliation:
National Aeronautics and Space Administration, Lewis Research Center, Cleveland, OH 44135, USA
S. J. Leib
Affiliation:
Sverdrup Technology, Inc. Lewis Research Center Group, NASA Lewis Research Center, Cleveland, OH 44135, USA
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Abstract

We consider the effects of critical-layer nonlinearity on spatially growing oblique instability waves on compressible shear layers between two parallel streams. The analysis shows that mean temperature non-uniformities cause nonlinearity to occur at much smaller amplitudes than it does when the flow is isothermal. The nonlinear instability wave growth rate effects are described by an integro-differential equation which bears some resemblance, to the Landau equation in that it involves a cubic-type nonlinearity. The numerical solutions to this equation are worked out and discussed in some detail. We show that inviscid solutions always end in a singularity at a finite downstream distance but that viscosity can eliminate this singularity for certain parameter ranges.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 207 , October 1989 , pp. 73 - 96
Copyright
© 1989 Cambridge University Press

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