An experimental and numerical investigation of the dependency on the initial conditions of the Richtmyer-Meshkov instability

Abstract

The nonlinear evolution of 2D single-mode Richtmyer-Meshkov instabilities is investigated through experiments in shock tube and numerical simulations. In our shock tube, the interface is materialized by a thin membrane attached to a stereo-lithographed grid. The purpose of this study is to compare experimental and numerical results, verify that using a higher Mach number for the incident shock wave (Misw) than in a previous study [C. Mariani, M. Vandenboomgaerde, G. Jourdan, D. Souffland, and L. Houas, “Investigation of the Richtmyer-Meshkov instability with stereolithographed interfaces,” Phys. Rev. Lett. 100, 254503 (2008)] drastically reduces the deleterious effects of the membrane remnants, explore the effect of a high initial amplitude at the interface on the growth of the perturbation, and understand the lack of roll-up structures in the nonlinear phase of the instability. Using grayscale gradient rather than gray level, a new processing of the raw pictures is developed. Numerical simulations run with the TRICLADE code show that adding short-wavelength (swl) perturbations to the single-mode interface is necessary to understand the morphology of the experimental pictures. Through these comparisons, a minimal description of the swl perturbations is proposed. The experimental growth rates are correctly predicted by the TRICLADE code. Positive agreements are also obtained by models only if they take into account the effect of a high initial amplitude. A first result is the agreement that we obtain between experiment, simulations, and models indicates that the membrane remnants no longer influence the global dynamics of the instability. This is due to the increase of Misw from 1.15 to 1.45. Another result of this investigation is that swl perturbations disrupt the spikes which grow at the interface and prevent the appearance of roll-up structures. Numerical simulations show the importance of a diffuse transition layer at the initial interface as a stabilizing process of the swl perturbations. In our case, only such a layer would allow the roll-up structures to grow. Finally, our analysis confirms that, when they are present at the same time, the swl perturbations distort the long wavelength perturbations, and that the latter decreases the growth of the former.