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On strongly nonlinear vortex/wave interactions in boundary-layer transition

Published online by Cambridge University Press:  26 April 2006

P. Hall  and
F. T. Smith
P. Hall
Affiliation:
Mathematics Department, The University, Exeter EX4 4QE, UK Current address: Mathematics Department, The University, Manchester, M13 9PL, UK.
F. T. Smith
Affiliation:
Mathematics Department, University College, Gower Street, London WC1E 6BT, UK
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Abstract

The interactions between longitudinal vortices and accompanying waves considered here are strongly nonlinear, in the sense that the mean-flow profile throughout the boundary layer is completely altered from its original undisturbed state. Nonlinear interactions between vortex flow and Tollmien-Schlichting waves are addressed first, and some analytical and computational properties are described. These include the possibility in the spatial-development case of a finite-distance break-up, inducing a singularity in the displacement thickness. Second, vortex/Rayleigh-wave nonlinear interactions are considered for the compressible boundary layer, along with certain special cases of interest and some possible solution properties. Both types, vortex/Tollmien-Schlichting and vortex/Rayleigh, are short-scale/long-scale interactions and they have potential applications to many flows at high Reynolds numbers. Their strongly nonlinear nature is believed to make them very relevant to fully fledged transition to turbulence.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 227 , June 1991 , pp. 641 - 666
Copyright
© 1991 Cambridge University Press

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