Nonlinear transient bubble oscillations

The investigation considers issues associated with transient regime of nonlinear bubble oscillations. The nonlinear response of a gas bubble to a low frequency pumping wave results in parametrically-generated shape oscillations above a well-defined threshold. This may be detected through insonification of the bubble by a high-frequency imaging wave, leading to the subharmonic and fundamental combinations frequency signals. The duration of the transient regimes of these two signals are very different. In this study the complete theory of the transient processes near the threshold of excitation of distortion modes has been derived. The detection of the subharmonic component is a general characteristic of cavitation and other nonlinear phenomena in liquids containing phase inclusions. As first observed by Neppiras, a small subharmonic component is also observed below threshold, so that the growth of this spectral component is not, strictly speaking, of a threshold character. The explanation proposed involves the analysis of transient processes near a subharmonic resonance. In this domain the ring up times of fundamental frequency signal can be greater than the duration of the pump pulse, and the corresponding component in the radiation spectrum can be interpreted as the appearance of subharmonic component below threshold