Proximity resonances of water-entrained air bubbles near acoustically reflecting boundaries

The acoustic resonances of radiatively damped air bubbles in water near reflecting boundaries are investigated by representing the bubble and its image by two bubbles in a full space, ensonified by two incident fields. Results obtained using an analytic monopole theory are compared with those of a coupled spherical harmonic technique and a boundary element method. Near a rigid boundary, the resonance frequency is reduced, and the response characteristics are determined by the predominant monopolar character of the individual bubble motion, with small changes in peak amplitude and Q. Near a sound-soft boundary, a higher frequency proximity resonance is observed. The monopole field is cancelled out, and the response is determined by higher-order scattering modes, giving very high values of Q. While the individual bubble scattering level increases significantly, the overall scattering is less than for two uncoupled bubbles. For bubble separations of 8-28 radii, all three approaches predict essentially identical results for both boundary types. For bubble separations less than one radius, the monopole theory, which does not include higher-order scattering modes, diverges from the boundary element and coupled spherical harmonic methods, whose high-accuracy determinations of resonance frequencies and amplitudes agree to within 0.1%.