Radiative Transfer of Sound Waves in a Random Flow: Turbulent Scattering, Straining, and Mode-Coupling

Abstract

We study the sound wave propagation in a random flow, whose mean flow is large compared with its fluctuation, in the infinite three-dimensional space. We consider the intermediate regime, where the range of acoustic wave numbers overlaps with the range of turbulent wave numbers. We use the multiscale expansions for the Wigner distributions to derive the radiative transport equations that describe the evolution of acoustic correlation and the turbulent scattering, straining, and mode-coupling of sound waves. We show that, because of the flow-straining term, the flow-acoustic scattering becomes nonconservative and, depending on the propagation direction, a sound wave can gain or lose energy. We calculate the attenuation/amplification coefficients due to mode-coupling and/or turbulent scattering with flow-straining. These coefficients depict interesting dependence on the propagating direction and the wave length of sound wave. We demonstrate numerically that the attenuation/amplification coefficients are enhanced significantly when both the straining and the mode-coupling effects are present. We also obtain the diffusion equations on the physical space and, thus, further reduce the dimension of the flow-acoustic equations.