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Published February 10, 1994 | Published
Journal Article Open

The scattering of sound waves by a vortex: numerical simulations and analytical solutions


The scattering of plane sound waves by a vortex is investigated by solving the compressible Navier-Stokes equations numerically, and analytically with asymptotic expansions. Numerical errors associated with discretization and boundary conditions are made small by using high-order-accurate spatial differentiation and time marching schemes along with accurate non-reflecting boundary conditions. The accuracy of computations of flow fields with acoustic waves of amplitude five orders of magnitude smaller than the hydrodynamic fluctuations is directly verified. The properties of the scattered field are examined in detail. The results reveal inadequacies in previous vortex scattering theories when the circulation of the vortex is non-zero and refraction by the slowly decaying vortex flow field is important. Approximate analytical solutions that account for the refraction effect are developed and found to be in good agreement with the computations and experiments.

Additional Information

© 1994 Cambridge University Press.v Received 4 July 1992; in revised form 13 August 1993; published online 26 April 2006. The authors are indebted to Professor J. B. Keller for suggesting the high-frequency analysis and for his assistance in carrying it out. The authors would also like to thank Dr Cliff Horne for bringing his experiments to their attention and for his helpful discussions, and Dr M. E. Goldstein for his helpful remarks. This work was supported by the Office of Naval Research under contract numbers ONR-N00014-88-K-0592 and ONR-N00014-92-J-1626. The computer time was provided by NASA-Ames Research Center. Some of this work was presented in AIAA Paper-91-0494.

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August 20, 2023
August 20, 2023