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In the context of forecasting temperature and pressure fields inhigh-intensity focussed ultrasound, the accuracy of predictive models iscritical for the safety and efficacy of treatment. In such fields inertialcavitation is often observed. Classically, estimations of cavitation thresholdshave been based on the assumption that the incident wave at the surface of abubble was the same as in the far-field, neglecting the effect of nonlinearwave propagation. By modelling the incident wave as a solution to Burgers'equation using weak shock theory, the effects of nonlinear wave propagation oninertial cavitation are investigated using both numerical and analyticaltechniques. From radius-time curves for a single bubble, it is observed thatthere is a reduction in the maximum size of a bubble undergoing inertialcavitation and that the inertial collapse occurs earlier in contrast with theclassical case. Corresponding stability thresholds for a bubble whose initialradius is slightly below the critical Blake radius are calculated. Bifurcationdiagrams and frequency-response curves are presented associated with the lossof stability. The consequences and physical implications of the results arediscussed with respect to the classical results.

The effects of nonlinear wave propagation on the stability of inertial cavitation