Numerical study of the oscillations of a non-spherical bubble in an inviscid, incompressible liquid. Part I: free oscillations from non-equilibrium initial conditions

Abstract

We consider the dynamics of a non-spherical gas bubble undergoing large amplitude oscillations of shape and volume in an inviscid, incompressible fluid. Solutions obtained via either a spectral or boundary-integral technique. The primary objective is to explore the coupling between oscillations of bubble volume and shape, starting from initial conditions where the bubble is either deformed in shape or at a non-equilibrium volume, and the fluid is stationary far from the bubble. For bubbles with a spherical mean shape, we consider conditions that are near 2:1 resonance (as predicted by small amplitude theory). We find that the small deformation theory provides a reasonable estimate of the conditions for shape instability, and of the time scales for resonant interactions between the purely radial and shape modes. However, other features such as the onset of higher order shape modes, or strong departures from Rayleigh–Plesset predictions, are not well approximated by the small amplitude theory. Bubbles which have a non-spherical mean shape exhibit two frequency ranges, corresponding to 2:1 and 1:1 resonance, where Rayleigh–Plesset theory is insufficient to describe the volume response of an oscillating bubble. We also show that purely radial initial conditions can lead to bubble breakup as energy is transferred from purely radial oscillations to shape oscillations.