Interactions of two bubbles along a gaseous interface undergoing the Richtmyer-Meshkov instability in two dimensions
The vorticity-driven interactions involving bubbles and spikes along a shock-accelerated interface significantly affect the dynamics of the flow and likely contribute to an eventual turbulent transition. In this study, the interaction of two adjacent bubbles of different sizes undergoing the Richtmyer-Meshkov process is investigated numerically in two dimensions. In particular, we compare two-bubble configurations with different initial amplitude ratios and wavelength ratios. Simulations are performed using an in-house, high-order accurate Discontinuous Galerkin code solving the Euler equations for a shock-accelerated interface initially perturbed with a periodic array of alternating sinusoids of different sizes. Two types of departures from existing bubble-merging models are observed, caused by a vorticity imbalance on the sides of the bubbles leading to spikes that either diverge or converge beneath the larger bubble, thus resulting in the generation of vortex dipoles escaping the confines of the mixing region or in the reacceleration of the larger bubbles. A vorticity-based criterion for predicting the generation of vortex dipoles and the reacceleration of larger bubbles from the initial conditions is developed.