Acoustic scattering in bubbly water at frequencies below individual bubble resonances

We are interested in acoustic scattering by bubble clouds in water at frequencies and densities such that the acoustic wavelength is large relative to the average distance between bubbles and large relative to that corresponding to the bubble resonance frequency. At high frequency and moderate bubble density, bubble scattered intensity is proportional to N (the number density of the bubbles, m 4), which corresponds to incoherent scattering. Effective medium theory has been shown to predict predominantly incoherent scattering at high frequencies, but coherent scattering (scattered intensity proportional to N2) at lower frequencies. Applying incoherent scattering at low frequencies can substantially under predict the bubble scattered signal. Coherent (low frequency) scattering from bubble assemblages has also been explained in terms of collective shape, but this approach does not provide a means of predicting the temporal extent of the scattered signal in low frequency regimes. The literature apparently does not provide precise guidance as to when and how bubble scattering transitions from incoherent to coherent scattering in response to increasing wavelength, and the relationship between the acoustic wavelength and average bubble separation. Modeling and a tank experiment are underway that we hope will provide some answers to this question.