Interactive resonant scattering by a cluster of air bubbles in water

An exact, analytical solution is developed for the problem of acoustic-wave scattering from a cluster of ideal, gaseous, spherical bubbles in an unbounded, homogeneous, host fluid. This solution takes into account all modes of oscillation of the bubbles as well as all interactions between them; it is applicable to a wide range of bubble sizes and excitation frequencies. In the low frequency regime, the theory of this paper is shown to reduce to the "monopole" approximation, the effect of higher-order modes being non-negligible only for very small bubble-to-bubble separations. A numerical study of interactive backscattering from small clusters, comprising up to three ideal bubbles, is presented. Interactions between the bubbles are shown to produce downward shifts in the resonance frequency of the cluster, when the scattering configuration is symmetric. Furthermore, asymmetries of the scattering configuration are shown to generate sharp resonances at frequencies above the resonance of the symmetric mode. The results of this paper agree with previous theoretical and experimental work.