Numerical simulations of the dynamics and the acoustics of an axisymmetric bubble rising in an inviscid liquid

The dynamics and the acoustics of a bubble rising under the action of a uniform force field in an isochoric, inviscid liquid are numerically investigated. The bubble shape is assumed axisymmetric and the symmetry axis parallel to the external force. The numerical approach is based on a boundary integral formulation for the interface velocities. The weak singularities in the integrals of the Green function and of its normal derivative are carefully handled. The accuracy of the integration is checked through a step-by-step computation of the kinetic energy balance. The acoustic signal due to the bubble motion is also evaluated on a large neighborhood of the bubble itself (up to one hundred bubble radii). Dynamics and acoustics of the axisymmetric bubble are then compared with those of an equivalent 1D one (that is a spherical bubble with the same volume), in order to highlight the effects of the non-spherical bubble shape on motion and acoustic signal. The role played by the formation of the jet in the acoustic emission of the bubble is also investigated.