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We study the propagation of sound waves in a three-dimensional, infiniteambient flow with weak random fluctuations of the mean particle velocity andspeed of sound. We more particularly address the regime where the acousticwavelengths are comparable to the correlation lengths of the weakinhomogeneities--the so-called weak coupling limit. The analysis is carried onstarting from the linearized Euler equations and the convected wave equationwith variable density and speed of sound, which can be derived from thenonlinear Euler equations. We use a multi-scale expansion of the Wignerdistribution of a velocity potential associated to the waves to derive aradiative transfer equation describing the evolution of the angularly resolvedwave action in space/time phase space. The latter experiences convection,refraction and scattering when it propagates through the heterogeneous ambientflow, although the overall wave action is conserved. The convection andrefraction phenomena are accounted for by the convective part of the transportequation and depend on the smooth variations of the ambient quantities. Thescattering phenomenon is accounted for by the collisional part of the transportequation and depends on the cross-power spectral densities of the fluctuationsof the ambient quantities at the wavelength scales. The refraction, phaseshift, spectral broadening, and multiple scattering effects of thehigh-frequency regimes described in various previous publications are thusencompassed by the proposed model. The overall derivation is based on theinterpretation of spatial-temporal Wigner transforms in terms of semiclassicaloperators in their standard quantization.

Kinetic modeling of multiple scattering of acoustic waves in randomly heterogeneous flows