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Generation of Tollmien–Schlichting waves on interactive marginally separated flows

Published online by Cambridge University Press:  21 April 2006

M. E. Goldstein ,
S. J. Leib  and
S. J. Cowley
M. E. Goldstein
Affiliation:
Lewis Research Center, Cleveland, OH 44135, USA
S. J. Leib
Affiliation:
Lewis Research Center, Cleveland, OH 44135, USA
S. J. Cowley
Affiliation:
Imperial College of Science and Technology, Department of Mathematics, London SW7 2BZ, UK
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Abstract

This paper is concerned with the interaction of very long-wavelength free-stream disturbances with the small but abrupt changes in the mean flow that occur near the minimum-skin-friction point in an interactive marginally separated boundary layer. We choose the source frequency so that the eigensolutions with that frequency have an ‘interactive’ structure in the region of marginal separation. The eigensolution wavelength scale must then differ from the lengthscale of the marginal separation and a composite expansion technique has to be used to obtain the solution.

The initial instability wave amplitude turns out to be exponentially small, but eventually dominates the original disturbance owing to its exponential growth. It then begins to decay but ultimately turns into a standard spatially growing Tollmien-Schlichting wave much further downstream.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 181 , August 1987 , pp. 485 - 517
Copyright
© 1987 Cambridge University Press

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