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Scattering of sound waves by a cylindrical vortex: a semi-analytical theory

Published online by Cambridge University Press:  25 February 1997

J. REINSCHKE ,
W. MÖHRING  and
F. OBERMEIER
J. REINSCHKE
Affiliation:
MPI für Strömungsforschung, Bunsenstraße 10, D–37073 Göttingen, Germany
W. MÖHRING
Affiliation:
MPI für Strömungsforschung, Bunsenstraße 10, D–37073 Göttingen, Germany
F. OBERMEIER
Affiliation:
MPI für Strömungsforschung, Bunsenstraße 10, D–37073 Göttingen, Germany
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Abstract

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A semi-analytical theory for the scattering of plane sound waves by a compressible, non-homentropic, circular-cylindrical, single vortex is presented in this paper. As a special case, the scattering of sound by a cylindrical inhomogeneity (hot spot) is investigated. Contrary to the otherwise analogous quantum-mechanical scattering problem, there are singularities in the modified acoustic wave equation for radii xs ∈ (0, ∞) when the scattering by a vortex is considered. It will be shown how these singularities can be treated.

This sound-scattering theory is applied to the problem of the interaction of weak plane shock waves with a strong cylindrical vortex. The calculated scattered sound signal has a rather complicated structure in which a cylindrical wave with an essentially quadrupolar directivity pattern is discernible. In the case of shock–hot-spot interaction a scattered sound signal with dipole-like amplitude is obtained. Both results qualitatively agree with experimental findings.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 333 , 25 February 1997 , pp. 273 - 299
Copyright
© 1997 Cambridge University Press