Influence of key initial parameters on reshocked Richtmyer-Meshkov instability

Abstract

This paper presents an experimental and theoretical study on Richtmyer-Meshkov instability at a light/heavy single-mode gaseous interface under reflected shock wave (reshock) conditions. Particular emphasis is placed on the influence of initial conditions (including shock strength, interface density ratio, and amplitude-to-wavelength ratio) on the perturbation growth following reshock. The results reveal that, for all cases, the interface amplitude exhibits a long-term linear growth with time after reshock, followed by a rapid decay in growth rate, highly similar to the perturbation growth behavior after single shock. Higher Mach numbers intensify transverse wave interactions with the interface, significantly affecting the interface morphology. Additionally, the interface is driven closer to the end wall, increasing the frequency of interactions between reverberating waves and the interface. This results in significantly enhanced mixing, as evidenced by the notably larger interface thickness, making the prediction of post-reshock growth rates across varying shock strengths particularly challenging. Interfaces with different density ratios demonstrate similar growth patterns, with the normalized perturbation growth showing near independence from the density ratio. As the amplitude-to-wavelength ratio increases, distinct transverse shock waves are generated after reshock, which produce high-pressure regions near the interface, causing the bubble head to present a cavity structure. For all cases, the early-stage post-reshock perturbation growth, when appropriately normalized, collapses well at the early stage but diverges at the late stage, especially for cases with varying Mach numbers. The linear superposition model, incorporating a reduction factor, effectively predicts the post-reshock growth rate for cases with different density ratios and initial amplitudes but loses precision for cases with varying shock strengths. Among existing models, the Sadot model (Sadot et al. 1998) offers the most reliable predictions for late-stage post-reshock perturbation growth.