| 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. For bubble clouds in which the important scattering terms include those with interactions between at least two bubbles, statistical dependence between bubble positions lead to an overestimate of the acoustic attenuation. Corrections to the effective medium theory can be made 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 acoustic field, assuming independent bubble positions when correlation is present leads to an underestimate of the incoherent acoustic field. The coherent and incoherent acoustic fields for bubble clouds exhibiting correlated bubble positions are explored in this thesis with the use of theory, numerical simulation, and laboratory experiments. Two methods are developed for identifying the presence correlated bubble positions: the consistency between the first and second moments describing acoustic propagation (i.e., the average acoustic field and the variance), and a direct measurement of the pair correlation function using a multibeam echosounder. |
