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On the initial stages of vortex wave interactions in highly curved boundary layer flows

Published online by Cambridge University Press:  26 February 2010

Philip Hall
Philip Hall
Affiliation:
Department of Mathematics, University of Manchester, Manchester, Ml 3 9PL
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Abstract

The nonlinear interaction equations describing vortex-Rayleigh wave interactions in highly curved boundary layers are derived. These equations describe a strongly nonlinear interaction between an inviscid wave system and a streamwise vortex. The coupling between the two structures is quite different from that found by Hall and Smith [13] in the absence of wall curvature. Here the vortex is forced over a finite region of the flow rather than in the critical layer associated with the wave system. When the interaction takes place the wave system remains locally neutral as it moves downstream and its self interaction drives a vortex field of the same magnitude as that driven by the wall curvature. This modification of the mean state then alters the wave properties and forces the wave amplitude to adjust itself in order that the wave frequency is constant. Solutions of the interaction equations are found for the initial stages of the interaction in the case when the wave amplitude is initially small. Our analysis suggests that finite amplitude disturbances can only exist when the vortex field is nonzero at the initial position where the interaction is stimulated.

Type
Research Article
Information
Mathematika , Volume 41 , Issue 1 , June 1994 , pp. 40 - 67
Copyright
Copyright © University College London 1994

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References

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