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On vortex/wave interactions. Part 1. Non-symmetrical input and cross-flow in boundary layers

Published online by Cambridge University Press:  26 April 2006

S. N. Brown  and
F. T. Smith
S. N. Brown
Affiliation:
Department of Mathematics, University College, Gower Street, London WC1E 6BT, UK
F. T. Smith
Affiliation:
Department of Mathematics, University College, Gower Street, London WC1E 6BT, UK
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Abstract

The paper studies certain effects of non-symmetry on vortex/wave interactions, for inviscid inflexional waves interacting nonlinearly with the vortex component of the mean flow in boundary-layer transition at large Reynolds number. Two types of non-symmetry are investigated, namely for unequal input wave amplitudes and for small cross-flows. These lead to coupled integro-differential equations for spatial development of the wave amplitudes, which are examined in an essentially equivalent differential form for various degrees of the non-symmetry present. Each type of non-symmetry can have a significant influence on the nonlinear interaction properties. Special emphasis is given to bounded solutions, and numerous interesting new flow responses are found analytically and computationally. The theory provides a basis for tackling enhanced non-symmetry in the input or stronger cross-flows.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 307 , 25 January 1996 , pp. 101 - 133
Copyright
© 1996 Cambridge University Press

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