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The instability of a vortex sheet on a subsonic stream under acoustic radiation

Published online by Cambridge University Press:  24 October 2008

D. S. Jones  and
J. P. Morgan
D. S. Jones
Affiliation:
Department of Mathematics, The University, Dundee
J. P. Morgan
Affiliation:
Department of Mathematics, The University, Dundee
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Abstract

This paper is concerned with the linear theory of the transmission of sound through a vortex sheet separating two fluids in relative motion, but with the same density and sound speed. For harmonic excitation asolution is determined, with particular attention to transition regions where large effects might be expected, and it is found that Helmholtz instability plays no role in this solution. However, this harmonic field does not lead to a solution of the initial value problem which satisfies causality. When causality is complied with an additional field must be superimposed which gives waves growing exponentially in space in the harmonic case and a singularity, which is more severe than has been previously encountered, in the time-dependent problem. The consequent effects of this instability are discussed.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 3 , November 1972 , pp. 465 - 488
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

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