The attenuation and dispersion of sound in water containing multiply interacting air bubbles

The classic theory of linear acoustic propagation in bubbly water inaccurately represents the physical behavior of dense populations of resonating bubbles. It assumes the bubbles always oscillate independently, while they may actually be strongly coupled by acoustic radiation, especially when uniformly sized. Sound propagation can be properly understood only in terms of the collective action of the medium, which is dominated by the ''symmetric'' normal mode. In this work, the propagational characteristics of bubbly water are determined by averaging the ensemble behavior of the symmetric mode over distributions of bubble radii and locations. The method includes all orders of multiple scattering, and incorporates ''shielding'' effects in the medium. New theoretical expressions for the phase speed and attenuation are obtained, and compared to experimental data by integrating multiple scattering effects over a ''region of collective interaction'' around each bubble. For uniform bubbles and volume fractions beta greater than or equal to 0.22%, multiple scattering strongly influences propagation. When beta < 0.22%, the effects apparently diminish sharply. For nonuniform bubbles and beta approximate to 0.02%, multiple scattering effects are not indicated. These results imply that the classic theory should provide an adequate description of the acoustic properties of bubble plums and clouds typically encountered in the ocean.