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Nonlinear evolution of interacting oblique waves on two-dimensional shear layers

Published online by Cambridge University Press:  26 April 2006

M. E. Goldstein  and
S.-W. Choi
M. E. Goldstein
Affiliation:
National Aeronautics and Space Administration, Lewis Research Center, Cleveland, OH 44135, USA
S.-W. Choi
Affiliation:
National Aeronautics and Space Administration, 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 nominally two-dimensional shear layers between parallel streams. The analysis shows that three-dimensional effects cause nonlinearity to occur at much smaller amplitudes than it does in two-dimensional flows. The nonlinear instability wave amplitude is determined by an integro-differential equation with cubic-type nonlinearity. The numerical solutions to this equation are worked out and discussed in some detail. We show that they always end in a singularity at a finite downstream distance.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 207 , October 1989 , pp. 97 - 120
Copyright
© 1989 Cambridge University Press

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