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Spatial evolution of nonlinear acoustic mode instabilities on hypersonic boundary layers

Published online by Cambridge University Press:  26 April 2006

M. E. Goldstein  and
D. W. Wundrow
M. E. Goldstein
Affiliation:
Lewis Research Center, Cleveland, OH 44135, USA
D. W. Wundrow
Affiliation:
Sverdrup Technology, Inc., Lewis Research Center, Cleveland, OH 44135, USA
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Abstract

We consider the effects of strong critical-layer nonlinearity on the spatial evolution of an initially linear ‘acoustic mode’ instability wave on a hypersonic flat-plate boundary layer. Our analysis shows that nonlinearity, which is initially confined to a thin critical layer, first becomes important when the amplitude of the pressure fluctuations becomes O(1/M4InM2), where M is the free-stream Mach number. The flow outside the critical layer is still determined by linear dynamics and therefore takes the form of a linear instability wave — but with its amplitude completely determined by the flow within the critical layer. The latter flow is determined by a coupled set of nonlinear equations, which we had to solve numerically.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 219 , October 1990 , pp. 585 - 607
Copyright
© 1990 Cambridge University Press

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