Effect of Atwood number on convergent Richtmyer–Meshkov instability

Abstract

Developments of two-dimensional single-mode light/heavy interfaces driven by convergent shock waves are numerically investigated, focusing on the effect of the Atwood number on the Rayleigh–Taylor stabilization, the compressibility and the nonlinearity. Five different test gases, including $$\hbox {CO}_2$$ , Kr, R22, R12 and $$\hbox {SF}_6$$ , are considered with air as the ambient gas. It is clarified for the first time that the unperturbed interface begins to decelerate when the shock focuses at the convergence center, and the acceleration during the deceleration phase is proportional to the Atwood number. During the first reshock, the interface moves outwards with a deceleration until it starts moving inwards. When the initial interface is weakly disturbed, a more obvious amplitude reduction is observed for the case with a larger Atwood number before the reshock, which means that the Rayleigh–Taylor stabilization is stronger. To assess the effect of the Atwood number on the compressibility and the nonlinearity, three models, including a linear incompressible model, a nonlinear incompressible model and a linear compressible model, are adopted to predict the amplitude growth before the reshock. The results show that the nonlinearity is weak, and is almost not influenced by the Atwood number before the reshock. The compressibility, however, greatly changes the amplitude growth. As the Atwood number increases, the compressibility plays a less significant role in the amplitude growth because a heavier gas is harder to be compressed. Although a gas with a larger specific heat ratio is also difficult to be compressed, the specific heat ratio plays a minor role to the compressibility relative to the Atwood number. During the reshock, the amplitude grows linearly until the nonlinearity in the cases with large Atwood numbers is strong enough to reduce the amplitude growth rate.