Abstract
The scattering of a sound wave in a medium undergoing shear flow confined to a finite region is investigated under the assumption that the total velocity field is everywhere small compared to the velocity of sound. Formulas are obtained for the angular distribution and frequency distribution of the scattered wave in terms of the four-dimensional Fourier transform of the shear velocity field. Under typical conditions, the cross sections for the scattering of a plane wave of frequency ω by a shear flow of given scale and spatial structure are approximately of the form ω4M2, where M is a characteristic Mach number of the flow. The coupling between the shear and longitudinal velocity fields has a tensor character such the the scattering vanishes at 180 degrees and at 90 degrees. The spectrum of the scattered sound wave is very sharp in the forward direction and becomes broader at larger scattering angles. Explicit expressions for the cross sections are obtained for the case of scattering from a region of isotropic turbulence. When the frequencies of importance in the turbulence are small compared to the frequency of the incident sound wave, the average differential scattering cross section can be expressed directly in terms of the energy spectrum of the turbulence.
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