Initial perturbation dependence on Richtmyer–Meshkov instability with reshock

The Richtmyer–Meshkov instability at gas interfaces with controllable initial perturbation spectra under reshock conditions is investigated both experimentally and theoretically. A soap-film method is adopted to generate well-defined single-, dual- and triple-mode air/SF $_6$ interfaces. By inserting an acrylic block into the test section, a reflected shock with controllable reshock timing is created. The results reveal a complex relationship between the post-reshock perturbation growth rate and the pre-reshock interface morphology. For single-mode interfaces, the post-reshock growth rate exhibits a strong dependence on pre-reshock conditions. In contrast, for multi-mode interfaces, this dependence weakens significantly due to mode-coupling effects. It is found that, following reshock, each fundamental mode develops independently and later is significantly influenced by mode-coupling effects. Based on this finding, we propose an empirical model that matches the initial linear growth rate and the asymptotic growth rate, accurately predicting the evolution of fundamental modes from early to late stages across all three configurations. Furthermore, a theoretical formula is derived, linking the empirical coefficient in the model of Charakhch’An (2020 J. Appl. Mech. Tech. Phys. vol. 41, no. 1, pp. 23–31) to the initial perturbation. This provides a unified framework to explain the varying dependence of post-reshock growth rates on pre-reshock morphology observed in previous experiments.