Abstract

This presentation first discusses the derivation of radiative transfer equations for acoustic waves propagating in a randomly fluctuating half-space in the weak-scattering regime, and the study of boundary effects through an asymptotic analysis of the Wigner transform of the wave solution. These radiative transfer equations allow to model the transport of wave energy density, taking into account the scattering by random heterogeneities. The approach builds on the method of images, where the half-space problem is extended to a full-space, with two symmetric sources and an even map of mechanical properties. Two contributions to the total energy density are then identified: one similar to the energy density propagation in a full-space, for which the resulting lack of statistical stationarity of the medium properties has no leading-order effect; and one supported within one wavelength of the boundary, which describes interference effects between the waves produced by the two symmetric sources. In the case of a homogeneous Neumann boundary conditions, this boundary effect yields a doubling of the intensity, and in the case of homogeneous Dirichlet boundary conditions, a canceling of that intensity. In a second part of the presentation, these results will be extended to the case of a randomly-fluctuating slab (layer of material bounded by two parallel planes) and of a randomly-fluctuating box. The extension of the method of images to slabs requires the consideration of models fluctuating periodically at the large scale, but this has no first-order influence on the results obtained for the half space. Radiative transfer simulations (using a Monte-Carlo approach) will be presented to illustrate the results. This is a joint work with Adel Messaoudi and Christophe Gomez. The first part of the presentation can be read at https://hal.science/hal-03878927/document.