Propagation through nonlinear time-dependent bubble clouds and the estimation of bubble populations from measured acoustic characteristics

For several decades the propagation characteristics of acoustic pulses (attenuation and sound speed) have been inverted in attempts to measure the size distributions of gas bubbles in liquids. While this has biomedical and industrial applications, most notably it has been attempted in the ocean for defence and environmental purposes, where the bubbles are predominantly generated by breaking waves. Such inversions have required assumptions, and the state–of–the–art technique still assumes that the bubbles undergo linear, steady–state monochromatic pulsations in the free field, without interacting. The measurements always violate, to a greater or lesser extent, these assumptions. The errors incurred by the use of such assumptions have been difficult to quantify, but are expected to be most severe underneath breakers in the surf zone, where the void fraction is greatest. Very few measurements have been made in this important region of the ocean. This paper provides a method by which attenuation can be predicted through clouds of bubbles which need not be homogeneous, nor restricted to linear steady–state monochromatic pulsations. To allow inversion of measured surf zone attenuations to estimate bubble populations with current computational facilities, this model is simplified such that the bubble cloud is assumed to be homogeneous and the bubbles oscillating in steady state (although still nonlinearly). The uses of the new methods for assessing the errors introduced in using state–of–the–art inversions are discussed, as are their implications for oceanographic and industrial nonlinear bubble counters, for biomedical contrast agents, and for sonar target detection in the surf zone.