Optimal subharmonic emission of stable bubble oscillations in a tube

The subharmonic acoustic emission of a stable oscillating bubble inside a rigid tube is investigated by direct numerical simulation. The mechanisms of bubble-tube interaction on the acoustic wave emitted by the bubble are clarified. When the bubble is small compared to the tube diameter, a critical threshold for the pressure amplitude appears beyond the point which nonspherical effects become important and bubble breaks. For a finite tube diameter, the scattered wave by the bubble is shown to generate a plane wave where the intensity of the subharmonic component becomes maximum for an optimal distance between the bubble and the tube wall. This effect seems to be directly related to the appearance of local resonance phenomena and a bubble resonance shift where liquid's compressibility plays a major role.