Acoustic localization in weakly compressible elastic media containing random air bubbles

Abstract

We study theoretically the propagation of longitudinal wave in weakly compressible elastic media containing random air bubbles by using a self-consistent method. By inspecting the scattering cross section of an individual bubble and estimating the mean free paths of the elastic wave propagating in the bubbly weakly compressible media, the mode conversion is numerically proved negligible as the longitudinal wave is scattered by the bubbles. On the basis of the bubble dynamic equation, the wave propagation is solved rigorously with the multiple scattering effects incorporated. In a range of frequency slightly above the bubble resonance frequency, the acoustic localization in such a class of media is theoretically identified with even a very small volume fraction of bubbles. We present a method by analyzing the spatial correlation of wave field to identify the phenomenon of localization, which turns out to be effective. The sensibility of the features of localization to the structure parameters is numerically investigated. The spatial distribution of acoustic energy is also studied and the results show that the waves are trapped within a spatial domain adjacent to the source when localization occurs.