A discussion of the low‐frequency resonance scattering of a bubble cloud

A comparison of four different formulas to compute the lowest mode resonance frequency of a bubble cloud is provided in this presentation. Based on the comparison, it is concluded that only one of the four equations represents the generalized solution, which includes air bubbles as its asymptotic condition, of void traction equals unity. Also shown is the numerical calculation of the scattering of a spherical bubble cloud using the classical solution of acoustic scattering of elastic spheres. With the elastic properties of the bubble cloud approximated by Wood’s formulation, it is found that isothermal conditions exist only at a very low void fraction level (less than 0.0001). Within the range of void fraction from 0.001 to 0.1, the polytropic coefficient of the bubble cloud is approximately 1.2, which is halfway between adiabatic and isothermal conditions. Finally, two simple scaling laws for the resonance characteristics of a spherical bubble cloud are presented: (1) the dimensionless resonance wave number is uniquely determined by the void fraction; and (2) the backscatter cross section at resonance is uniquely determined by the resonance frequency. [Work supported by ARPA.]