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Resonance in flows with vortex sheets and edges

Published online by Cambridge University Press:  20 April 2006

Paul A. Durbin
Paul A. Durbin
Affiliation:
NASA Lewis Research Center, Cleveland, Ohio 44135
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Abstract

It is shown that the vortex sheet in a slot between two semi-infinite plates does not admit incompressible resonant perturbations. The semi-infinite vortex sheet entering a duct does admit incompressible resonance. These results indicate that the vortex-sheet approximation is less useful for impinging shear flows than for non-impinging flows. They also suggest an important role of downstream vortical disturbances in resonant flows.

The general solution for perturbations to flow with a vortex sheet and edges is written in terms of a Cauchy integral. Requirements on the behaviour of this solution at edges and at downstream infinity fix the criteria for resonance.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 145 , August 1984 , pp. 275 - 285
Copyright
© 1984 Cambridge University Press

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