Effective medium theory applied to bubble scattering well below resonant frequency

Abstract

When ensonifying bubble assemblages using acoustic frequencies well below the resonant frequencies of the individual bubbles, resonant scattering theory for individual bubbles would suggest very low backscatter, whereas an “effective medium theory” predicts a result for backscattering that is orders of magnitude higher. For this case, a number of authors have suggested resonant scattering associated with the size of the bubble clusters, and backscatter measurements from bubble clouds have supported this hypothesis. Scattering can also be considered from a much larger bubble structure: a ship wake. At the stern, ship wakes contain a wide range of bubble sizes. Buoyancy quickly drives the largest bubbles to the surface, but small bubbles can persist for large distances. Ensonification at mid frequencies (1kHz–10 kHz) therefore cannot rely on resonant bubble scattering. Using a generic wake model developed from the literature, acoustic backscatter can be modeled at frequencies below those of the resonant bubbles. The approach discretizes the spatial bubble distribution and sums the backscatter coherently, following the work of Commander and Prosperetti [JASA (1989)]. Ongoing work includes a lab-scale comparison of the backscattering approach applied to the ship wake model. Work sponsored by the Office of Naval Research, Code 321US.