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Interaction of oblique instability waves with weak streamwise vortices

Published online by Cambridge University Press:  26 April 2006

M. E. Goldstein  and
David W. Wundrow
M. E. Goldstein
Affiliation:
NASA, Lewis Research Center, Cleveland, OH 44135, USA
David W. Wundrow
Affiliation:
Nyma, Inc., Lewis Research Center Group, Cleveland, OH 44135, USA
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Abstract

This paper is concerned with the effect of a weak spanwise-variable mean-flow distortion on the growth of oblique instability waves in a Blasius boundary layer. The streamwise component of the distortion velocity initially grows linearly with increasing streamwise distance, reaches a maximum, and eventually decays through the action of viscosity. This decay occurs slowly and allows the distortion to destabilize the Blasius flow over a relatively large streamwise region. It is shown that even relatively weak distortions can cause certain oblique Rayleigh instability waves to grow much faster than the usual two-dimensional Tollmien–Schlichting waves that would be the dominant instability modes in the absence of the distortion. The oblique instability waves can then become large enough to interact nonlinearly within a common critical layer. It is shown that the common amplitude of the interacting oblique waves is governed by the amplitude evolution equation derived in Goldstein & Choi (1989). The implications of these results for Klebanoff-type transition are discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 284 , 10 February 1995 , pp. 377 - 407
Copyright
© 1995 Cambridge University Press

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