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Nonlinear evolution of subsonic and supersonic disturbances on a compressible free shear layer

Published online by Cambridge University Press:  26 April 2006

S. J. Leib
S. J. Leib
Affiliation:
Sverdrup Technology, Inc., Lewis Research Center Group, Cleveland, OH 44135, USA
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Abstract

We consider the effects of a nonlinear–non-equilibrium–viscous critical layer on the spatial evolution of subsonic and supersonic instability modes on a compressible free shear layer. It is shown that the instability wave amplitude is governed by an integro-differential equation with cubic-type nonlinearity. Numerical and asymptotic solutions to this equation show that the amplitude either ends in a singularity at a finite downstream distance or reaches an equilibrium value, depending on the Prandtl number, viscosity law, viscous parameter and a real parameter which is determined by the linear in viscid stability theory. A necessary condition for the existence of the equilibrium solution is derived, and whether or not this condition is met is determined numerically for a wide range of physical parameters including both subsonic and supersonic disturbances. It is found that no equilibrium solution exists for the subsonic modes unless the temperature ratio of the low-to high-speed streams exceeds a critical value, while equilibrium solutions for the most rapidly growing supersonic mode exist over most of the parameter range examined.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 224 , March 1991 , pp. 551 - 578
Copyright
© 1991 Cambridge University Press

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