Acoustic propagation through clustered bubble clouds

One of the underlying assumptions in the effective medium theory describing the propagation of acoustic waves through bubble clouds is that the probability of an individual bubble being located at some position in space is independent of the locations of other bubbles. However, bubbles within naturally occurring clouds may be influenced by the dynamics of the fluids in which they are entrained so that they become preferentially concentrated, or clustered, leading to statistical dependence in their positions. For bubble clouds in which the important scattering terms include those with interactions between at least two bubbles, statistical dependence between bubble positions leads to a reduction in the attenuation of the coherent acoustic pressure field from that which would be predicted for a nonclustered bubble cloud. Bubble clustering can be accommodated in effective medium theories using correlation functions describing the relationship between the positions of the bubbles. For double scattering, the two-bubble correlation (i.e., the pair correlation function) must be used, for triple scattering, the three bubble correlation must be used, and so on. In contrast to the attenuation of the coherent field, making the assumption of independent bubble positions leads to an underestimate of the incoherent field. Both the coherent and incoherent acoustic fields for bubble clouds exhibiting correlated bubble positions are explored in this paper with the use of numerical simulations.