Direct Numerical Simulation of weakly nonlinear bubble oscillations*

Bubble dynamics have been studied extensively during the last century. Because of the highly nonlinear nature, the oscillations of gas bubbles in a liquid are of great practical interest and relevant in diverse technologies. Traditionally, to study stably oscillating micro-bubbles subjected to ultrasound or megasound, Rayleigh-Plesset (R-P) type equations assuming spherical symmetry are frequently chosen. However, although the bubble can oscillate without breaking in such weakly nonlinear oscillation regimes, non-spherical effects neglected in RP models will become increasingly important with the increasing of the amplitude of pressure pulse and the frequency of the incident wave. To investigate such non-spherical mechanisms, we present simulations of the interaction between a traveling acoustic wave and a single bubble using Direct Numerical Simulations (DNS) [Fuster and Popinet. (2018). J. Comput. Phys. 374, 752-768]. Depending on the pressure waves emitted by the moving non-spherical bubble, we characterize different weakly nonlinear oscillation regimes as a function of the Reynolds, Weber and the amplitude of incident pressure. The comparison between DNS and R-P type equations is also done to quantitatively estimate the range of applicability of simplified models.