Abstract

We study the coherent propagation of an acoustic wave through a disordered flow with zero mean velocity. The flow is modeled as an assembly of vortices randomly distributed. The source term of the linear wave equation satisfied by the acoustic pressure must be expanded up to terms of order Mach number of the background flow squared. The complex wave number of the coherent wave is calculated analytically and related to average properties of the flow using multiple scattering theory in a Bourret approximation. The perturbations induced by the fluid motion on the index of refraction and on the attenuation length of the wave are of order Mach number squared. The role of the finite compressibility of the fluid is considered in detail, as well as the need, or lack thereof, to consider widely different time scales for acoustic propagation and flow evolution. For a gas and for long wavelengths, the phase velocity of the coherent wave may become higher than in the fluid at rest.