Convergent Richtmyer–Meshkov instability of light gas layer with perturbed outer surface

Abstract

The convergent Richtmyer–Meshkov instability (RMI) of an layer with a uniform outer surface and a sinusoidal inner surface surrounded by air (generated by a novel soap film technique) is studied in a semiannular convergent shock tube using high-speed schlieren photography. The outer interface initially suffers only a slight deformation over a long period of time, but distorts quickly at late stages when the inner interface is close to it and produces strong coupling effects. The development of the inner interface can be divided into three stages. At stage I, the interface amplitude first drops suddenly to a lower value due to shock compression, then decreases gradually to zero (phase reversal) and later increases sustainedly in the negative direction. After the reshock (stage II), the perturbation amplitude exhibits long-term quasi-linear growth with time. The quasi-linear growth rate depends weakly on the pre-reshock amplitude and wavelength, but strongly on the pre-reshock growth rate. An empirical model for the growth of convergent RMI under reshock is proposed, which reasonably predicts the present results and those in the literature. At stage III, the perturbation growth is promoted by the Rayleigh–Taylor instability caused by a rarefaction wave reflected from the outer interface. It is found that both the Rayleigh–Taylor effect and the interface coupling depend heavily on the layer thickness. Therefore, controlling the layer thickness is an effective way to modulate the late-stage instability growth, which may be useful for the target design.