Maximum initial growth-rate of strong-shock-driven Richtmyer-Meshkov instability

We focus on the classical problem of the dependence on the initial conditions of the initial growth-rate of strong shock driven Richtmyer-Meshkov instability (RMI) by developing a novel empirical model and by employing rigorous theories and Smoothed Particle Hydrodynamics simulations to describe the simulation data with statistical confidence in a broad parameter regime. For the given values of the shock strength, fluid density ratio, and wavelength of the initial perturbation of the fluid interface,
we find the maximum value of the RMI initial growth-rate, the corresponding amplitude scale of the initial perturbation, and the maximum fraction of interfacial energy. This amplitude scale is independent of the shock strength and density ratio and is characteristic quantity of RMI dynamics. We discover the exponential decay of the ratio of the initial and linear growth-rates of RMI with the
initial perturbation amplitude that excellently agrees with available data.