1/2 order subharmonic waves of two cavitation bubbles

In the work, the 1/2 order subharmonic wave of two coupling cavitation bubbles is investigated numerically via Fourier spectrum analysis. By analyzing the dynamics of bubble, we find that the mutual interaction between bubbles can affect the appearance of $1/2$ order subharmonic. The results of parameter dependence show that the intensity of $1/2$ order subharmonic would be promoted or inhibited with the increase of mutual interaction. The higher the driving amplitude or the smaller the distance between bubbles, the stronger the mutual interaction is, and also the greater the promotion or suppression of the $1/2$ order subharmonic is. Moreover, while the 1/2 order subharmonic occurs, the energy of bubble would alternate between two different peaks, and the temperature inside bubble has a similar fluctuation while the bubble collapses. This qualitative analysis suggests that the bubble′s dynamics for multi-bubble case is complex. Understanding the generation of subharmonic of bubble′s dynamics is of great significance for helpful applying of cavitation bubble.