Spatiotemporal evolution model for compression of mixing width in reshocked Richtmyer-Meshkov turbulence

Turbulent mixing induced by reshocked Richtmyer-Meshkov (RM) instability is a critical process in both natural phenomena and high-energy-density applications. Among the physical quantities describing RM turbulent mixing, the mixing width is of fundamental importance. Although its temporal evolution has been extensively studied in the past several decades, there is currently no quantitative model for the compression of the mixing width caused by second shock waves. This study presents a model to predict its spatiotemporal evolution in compression process. By combining the Whitham method with Rankine–Hugoniot relations, we quantify the spatiotemporal evolution of the associated physical quantities when shock waves traverse variable-density mixing zones. Furthermore, using these quantities, we derive a model for the spatiotemporal evolution of mixing width, as well as compression rate. Good agreement between the model predictions and numerical simulations across cases with varying density ratios, incident shock waves, and density profiles confirms the model's accuracy. These findings are crucial for developing a unified model for the entire multi-stage evolution of RM turbulent mixing width, with significant implications for high-energy-density physics and engineering applications.