Transient wave propagation through bubbly layers via the Foldy–Twersky integral equation

This work considers transient linear acoustic wave propagation through a layer of small gas bubbles in a liquid. The analysis is based on multiple scattering theory and the Foldy–Twersky integral equation is used. The transmitted coherent wave for a distribution of uncorrelated scattering bubbles is studied. The case of a weak scattering density is investigated for the regimes of single scattering and Foldy–Twersky multiple scattering. A condition for the column density for the single scattering regime is derived and found to be more restrictive than earlier heuristically derived results. The influence of the low-frequency region of the monopole part of the scattering amplitude of a spherical gas bubble is analyzed. It is shown that a combination of the expression for the wave number for the transmitted coherent wave and the formula used for the low-frequency region of the monopole coefficient yield a well-posed initial-value problem. The effects due to single scattering are shown to be negligible so a pulse propagates essentially undisturbed. For the case of Foldy–Twersky scattering, however, the influence of the bubbles can be substantial. The main characteristics of linear transient wave propagation in bubbly liquids experimentally observed by Kuznetsov et al. are qualitatively predicted by the theory used in this paper.