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%.

中文翻译：

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夹带水的气泡在声反射边界附近的邻近共振

通过用两个入射场对整个空间中的两个气泡表示气泡及其图像，可以研究反​​射边界附近水中的辐射衰减气泡的声共振。将使用解析单极理论获得的结果与耦合球谐技术和边界元方法的结果进行比较。在刚性边界附近，共振频率降低，响应特性由单个气泡运动的主要单极特性确定，峰值幅度和Q的变化很小。在软边界附近，观察到较高频率的接近共振。单极场被抵消，并且响应由高阶散射模式确定，从而给出非常高的Q值。虽然单个气泡的散射程度显着增加，但总散射小于两个未耦合气泡的散射。对于8–28半径的气泡分离，所有这三种方法都预测两种边界类型的结果基本相同。对于小于一个半径的气泡间距，不包括高阶散射模式的单极子理论与边界元和耦合球谐法不同，后者的共振频率和振幅的高精度测定值均在0.1％以内。