Propagation of acoustic waves in disordered flows composed of many vortices. II. Examples

The theory of acoustic wave propagation through systems of many vortices ra ndomly distributed, developed in Part I, is applied to specific examples in two and three dimensions. Two classes of vortex blobs are considered; vort ices with an axisymmetric distribution of vorticity, such as disks or tubes , and vortices with a nonvanishing dipolar moment such as dipoles or rings. The index of refraction and attenuation length are numerically computed as a function of wavelength for various values of vortex parameters. The asym ptotic behavior of the dispersion relation for very short and very long wav elengths is also derived analytically. At short wavelengths lambda the atte nuation length scales as lambda(-2) in all examples studied. At long wavele ngths the scaling depends on the lowest nonvanishing multipole moment of th e vorticity distribution; say, for vortex rings, it is lambda(-4) as in Tho mson scattering. For an ideal gas, the phase velocity of the coherent acous tic wave is greater than in the undisturbed flow for long wavelengths and s maller than in the undisturbed flow for short wavelengths. This appears to be a robust feature. When properly normalized, the attenuation length does not depend very strongly on the ratio l/epsilon, where l is a vortex length scale and epsilon the thickness of the vorticity bearing region, both in t wo and three dimensions. The effective index of refraction, however, does d epend on this ratio. The conditions of applicability of the results, which rely on a Born approximation scheme, are also determined. The expressions o btained in this paper for the scattering cross sections are used to discuss the properties of sound localization in two dimensional disordered flows. (C) 1999 American Institute of Physics. [S1070-6631(99)02112-1].