Scattering from collective modes of air bubbles in water and the physical mechanism of superresonances

Abstract

A coupled oscillator method is used to describe collective acoustic resonances and scattering from multiple air bubbles in water. By recombining equations, the problem is decomposed into that of scattering from individual normal modes of the ensemble. Each mode has specific resonant properties. ‘‘Symmetric’’ modes, where the bubbles oscillate in phase with each other, typically show downward frequency shifts and increased damping. ‘‘Antisymmetric’’ modes, where some or all of the bubbles oscillate in antiphase, generally show upward frequency shifts and reduced damping. For two bubbles the method predicts frequency shifts which agree with experimental results. The resonance response functions predict that a two bubble system may become superresonant provided (a) the mode is antisymmetric, (b) the individual bubbles are primarily radiation damped, and (c) the bubbles are spaced such that the modal damping is small. Superresonant scattering is dipolar and propagates little energy in the far field, making the phenomenon difficult to observe experimentally. Scattering from a bubble reflected in a pressure release surface may show the phenomenon strongly. The antisymmetric modes of a triangular arrangement of three bubbles are degenerate and may also become superresonant. The damping of line ensembles of bubbles varies strongly with the bubble spacing.