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Vortex/inflectional-wave interactions with weakly three-dimensional input

Published online by Cambridge University Press:  10 October 1997

S. N. TIMOSHIN
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK
F. T. SMITH
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK

Abstract

The subtle impact of the spanwise scaling in nonlinear interactions between oblique instability waves and the induced longitudinal vortex field is considered theoretically for the case of a Rayleigh-unstable boundary-layer flow, at large Reynolds numbers. A classification is given of various flow regimes on the basis of Reynolds-stress mechanisms of mean vorticity generation, and a connection between low-amplitude non-parallel vortex/wave interactions and less-low-amplitude non-equilibrium critical-layer flows is discussed in more detail than in previous studies. Two new regimes of vortex/wave interaction for increased spanwise lengthscales are identified and studied. In the first, with the cross-scale just slightly larger than the boundary-layer thickness, the wave modulation is governed by an amplitude equation with a convolution and an ordinary integral term present due to nonlinear contributions from all three Reynolds-stress components in the cross-momentum balance. In the second regime the cross-scale is larger, and the wave modulation is found to be governed by an integral/partial differential equation. In both cases the main-flow non-parallelism contributes significantly to the coupled wave/vortex development.

Type
Research Article
Copyright
© 1997 Cambridge University Press

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