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Sound generation by hydrodynamic sources near a cavitated line vortex

Published online by Cambridge University Press:  29 March 2006

J. E. Ffowcs Williams  and
S. O'shea
J. E. Ffowcs Williams
Affiliation:
Mathematics Department, Imperial College, London
S. O'shea
Affiliation:
Mathematics Department, Imperial College, London
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Abstract

The paper examines the scattering properties of a cavitated line vortex when excited by line and point sources of sound. It is found that the vortex resonances discovered by Kelvin for incompressible flow are essentially unmodified by fluid compressibility, and that many of the resonant modes radiate energy to infinity. Those resonant modes dominate the vortex response, their amplitude growing algebraically with time in a driven instability of the model flow.

The off resonance response is dependent on the value of a normalized frequency parameter (ω/Ω)2|ln ka|. Ω denotes the angular velocity of the steady vortex flow, k the acoustic wave-number, and a the cavity radius. Even off resonance the cavity is an extremely efficient wave scatterer, the scattering efficiency increasing with source order. For example, the scattered energy of a point quadrupole is shown to exceed that of the direct field by a factor of 108 for the typical underwater flow Mach number of 10−2.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 43 , Issue 4 , 2 October 1970 , pp. 675 - 688
Copyright
© 1970 Cambridge University Press

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References

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