Effects of Surface Tension on the Richtmyer-Meshkov-Instability-Induced Perturbation Growth in Fully Compressible and Inviscid Fluids

We present novel numerical simulations investigating the Richtmyer-Meshkov instability (RMI) with surface tension. With a fully nonlinear, compressible numerical formulation which directly models surface tension on a volume-of-fluid interface, we validate and bridge existing theoretical models of surface tension's effects on the RMI in linear, transitional and nonlinear post-shock growth regimes. We propose a dimensional scheme, from which we first develop scaled models for the perturbation growth in the small-amplitude (linear) oscillatory regime, where good collapses of simulation data are found under the scalings. Next, we heuristically identify a criterion for transition into a nonlinear oscillation regime. Finally, we show good agreement with nonlinear theory for asymptotic interface growth in the limit of small surface tension. These results highlight the utility of our model for compressible problems featuring surface tension, and pave the way for a broader investigation into mixed compressible/incompressible problems.