The dynamics of an oscillating non-spherical bubble

Recent analytical studies have demonstrated the importance of nonlinear coupling between changes in bubble volume and shape in determining both the acoustic response and breakup of oscillating bubbles. In an effort to better understand the interactions between volume and shape oscillations at finite amplitude, we conduct a numerical investigation of free oscillations in a quiescent fluid and oscillations resulting from an impulsive decrease in pressure. The numerical study demonstrates that interactions between volume and shape oscillations decrease the bubble's efficiency as a source of sound, providing an explanation for the over-prediction of the acoustic response by the Rayleigh-Plesset theory. We also observe a non-resonant finite amplitude effect where the amplitude of shape oscillations grow dramatically as a bubble collapses and further erodes the strength of the bubble as a monopole source of sound. In the course of this work, we identify mechanisms for bubble breakup in the absence of strong gradients in pressure or stress normally associated with breakup in time-dependent or turbulent flows. In addition to the numerical study, we conduct an analytical investigation of a periodically forced bubble under the conditions of 3:1 internal resonance. The objective of this work is to include in the analysis of resonant interactions between volume and shape oscillations the first nonlinear features of the individual modes which do not appear in the earlier work on 1:1 and 2:1 resonance. We find that the nonlinear nature of the individual modes dominates the dynamic response of the oscillating bubble and that there is little interaction between modes under the conditions of 3:1 resonance.