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Properties of strongly nonlinear vortex/Tollmien–Schlichting-wave interactions

Published online by Cambridge University Press:  26 April 2006

A. G. Walton  and
F. T. Smith
A. G. Walton
Affiliation:
Department of Mathematics, Imperial College, London SW7 2BZ, UK
F. T. Smith
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK
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Abstract

An analytical and computational study is presented on solution properties of strongly nonlinear vortex/wave interactions involving Tollmien–Schlichting waves, in boundary-layer transition. The longitudinal vortex part, i.e. the total mean flow, is governed by a three-dimensional vortex system but coupled, through an effective spanwise slip condition at the surface, with the accompanying wave part, so that both the vortex and the wave parts are unknowns. Terminal forms of the space-marching or time-marching problem are proposed first, yielding either a lift-off separation singularity or a strong-attachment singularity. Second, a similarity version of the complete system is addressed numerically and analytically. This leads to a number of interesting solution features as the typical wave pressure is increased into the strongly nonlinear regime. In particular, lift-off separation and attachment forms seem to emerge which are analogous with those proposed above. The flow developments beyond the terminal forms are discussed, together with the links of the work with recent computational results and, tentatively, with experimental observations including the creation of lambda vortices (as a form of lift-off separation).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 244 , November 1992 , pp. 649 - 676
Copyright
© 1992 Cambridge University Press

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