Multiple bubbles: Collective modes and the origin of superresonances

Abstract

Acoustic resonances and scattering from systems of multiple air bubbles in water are described using a coupled differential equation method. By recombination, the problem may be analyzed by scattering from the individual normal modes of vibration of the ensemble. The modes are of two types: ‘‘Symmetric’’ modes, where the bubbles vibrate in phase with each other, typically show downward shifts in frequency and increased damping; ‘‘antisymmetric’’ modes, where some or all of the bubbles vibrate in antiphase, generally show upward frequency shifts and reduced damping and may become super-resonant. For two bubbles the method reproduces frequency shifts measured experimentally. Examination of the modal response functions shows that super-resonances may occur for specific bubble spacings if the individual bubbles are primarily radiation damped. For two and three bubble systems super-resonant scattering is strongly 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 should show the phenomenon strongly. By extending multiple bubbles in a line the damping rates predicted by Weston for an infinite line array may be approached. The method outlined can easily be applied, using matrix methods, to describe acoustic scattering from large ensembles. [Work supported by ONR (Element 602435N). Technical management provided by NRL-SSC.]