Resonance in flows with vortex sheets and edges
- 1 August 1984
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 145 (-1) , 275-285
- https://doi.org/10.1017/s0022112084002925
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.Keywords
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