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Three-dimensional acoustic scattering by vortical flows. II. Axisymmetric scattering by Hill's spherical vortex
The general theory of Part I is applied to the the specific case of scattering of a wave incident along the axis of Hill's spherical vortex. The full asymptotic solution to the initial-value problem i...

Three-dimensional acoustic scattering by vortical flows. I. General theory

Phys. Fluids 13, 2876 (2001); doi:10.1063/1.1401814

Issue Date: October 2001

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Stefan G. Llewellyn Smith
Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093-0411

Rupert Ford
Department of Mathematics, Imperial College of Science, Technology and Medicine, 180 Queen's Gate, London SW7 2BZ, United Kingdom
When an acoustic wave is incident on a three-dimensional vortical structure, with length scale small compared with the acoustic wavelength, what is the scattered sound field that results? A frequently used approach is to solve a forced wave equation for the acoustic pressure, with nonlinear terms on the right-hand side approximated by the bilinear product of the incident wave and the undisturbed vortex: we refer to this as the "acoustic analogy" approximation. In this paper, we show using matched asymptotic expansions that the acoustic analogy approximation always predicts the leading-order scattered sound field correctly, provided the Mach number of the vortex is small, and the acoustic wavelength is a factor of order M–1 larger than the scale of the vortex. The leading-order scattered field depends only on the vortex dipole moment. Our analysis is valid for acoustic frequencies of the same order or smaller than the vorticity of the vortex. Over long times, the vortex may become significantly disturbed by the incident acoustic wave. Additional conditions are derived to maintain validity of the acoustic analogy approximation over times of order M–1, long enough for motion of the vortex to be significant on the length scale of the acoustic waves. ©2001 American Institute of Physics.
History: Received 19 September 2000; accepted 5 June 2001
Permalink: http://link.aip.org/link/?PHFLE6/13/2876/1
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EDITORIALLY RELATED

  1. Three-dimensional acoustic scattering by vortical flows. II. Axisymmetric scattering by Hill's spherical vortex
    Stefan G. Llewellyn Smith et al.
    Phys. Fluids 13, 2890 (2001)

KEYWORDS and PACS

Keywords
PACS
  • 43.20.Fn
    Acoustics General linear acoustics Scattering of acoustic waves
  • 47.32.Cc
    Fluid dynamics Rotational flow and vorticity Vortex dynamics
  • 43.28.-g
    Acoustics Aeroacoustics and atmospheric sound
  • 43.30.Ft
    Acoustics Underwater sound Volume scattering
  • 62.60.+v
    Mechanical and acoustical properties of condensed matter Acoustical properties of liquids (see also 43.35 in acoustics)
  • YEAR: 2001

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PUBLICATION DATA

ISSN:
1070-6631 (print)   1089-7666 (online)
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