Multiple scattering through clouds of gas bubbles in liquids: Accounting for clustering in the higher-order moments.

Abstract

The presence of bubble clouds can change the sound speed and attenuation in liquids, both of which are often treated as first moment quantities that can be derived using a multiple scattering approach for an effective medium. The same multiple scattering framework can be used to examine higher-order statistical moments, accounting for the large variability that is often observed in acoustic signals in the presence of bubble clouds. When clustering of bubbles (preferred concentrations) is present, multiple scattering theory shows that the statistical moments should change. These cluster-induced, frequency dependent changes in sound speed, attenuation, and higher-order moments can be examined both from a theoretical standpoint and with the aid of numerical simulations. Simulations have shown that while point measurements of the acoustic field for non-clustered bubble clouds appear normally distributed, clustering introduces both a non-zero skewness and a higher than expected kurtosis, depending on the number density of the bubble clouds and the nature of the clustering. This type of behavior is expected to be present both for forward scattering and backscattering scenarios.