The generation of period-2 oscillation of a single bubble in the transitional region

The bubble oscillations in the transitional region driven by ultrasound are numerically calculated and analyzed. The oscillations in the transitional region in the process reaching the stationary oscillations contain important information to elucidate the nonlinear phenomena of a bubble. In particular, the bubble oscillations are treated on the condition that some kinds of tone burst waves with short cycles are applied as the driving sound of a bubble. As a result, it is revealed that the interactive frequency component between bubble resonance and driving sound plays an important role in the generation of period-2 oscillations. Precisely speaking, the period-2 oscillation grows under sufficiently high pressure amplitude, due to the self-positive feedback between the interactive component and the bubble resonance. To aid these analyses, a new mean dealing with the forced oscillation in the transitional region is introduced.