THE RESONANT SUPERCOMPRESSION AND SONOLUMINESCENCE OF A GAS BUBBLE INA LIQUID-FILLED FLASK

The spherically-symmetric problem of the oscillations of a small gas b ubble in the center of a spherical flask filled with a compressible li quid that is excited by small radial displacement of the flask's wall is considered. Two asymptotic solutions have been found for the low Ma ch number stage. The first one is an asymptotic solution for the field far from the bubble, and it corresponds to linear wave theory. The se cond one is an asymptotic solution for the boundary layer near the bub ble and it corresponds to an incompressible fluid. In the analytical s olution of the low Mach number stage matching of these asymptotic solu tions is done. A generalization of the Rayleigh-Plesset equation for a compressible liquid is given in the form of two ordinary difference-d ifferential equations that take into account the pressure waves which are reflecting from the bubble and those that are incident on the bubb le from the flask wall. The initial value problem for the initiation o f the bubble oscillations due to flask wall excitation and for the evo lution of these oscillations was considered. Linear and non-linear per iodic bubble oscillations were analyzed analytically, and resonant fre quencies were identified. Non-linear resonant and near-resonant soluti ons for the bubble's non-harmonic oscillations, which are excited by h armonic pressure or velocity oscillations on the flask wall, are obtai ned.