A decoupled mechanism of interface growth in single-mode hydrodynamic instabilities

Abstract

One of the most significant issues in hydrodynamic interfacial instabilities is the growth rate of the interfacial perturbations, which plays an important role in both scientific research (e.g. supernova explosion) and engineering applications (e.g. inertial confinement fusion). Yet the underlying mechanisms of such flow phenomena remain unclear or controversial. In this paper the decoupled mechanisms of two effects are found to dominate the interface growth of the single-mode Rayleigh–Taylor instability (RTI) and Richtmyer–Meshkov instability (RMI) via Layzer's potential-flow model. One is the inertial effect induced by the interfacial density gradient and the acceleration, and the other is the frontal distortion effect stemming from interface shape evolution. The former determines the dominant features of interface evolution, while the latter influences the local concavity and convexity of growth rate such as the overshoot phenomenon. These two effects can be approximated as a linearly decoupled analytical solution if their nonlinear interaction term is neglected. With the decoupled solution, the theoretical growth rates agree well with high-fidelity numerical simulation results. The present result indicates that the long-time evolution of fluid interface in both RTI and RMI at all density ratios can be accurately predicted if both inertia and frontal distortion effects are taken into account. Furthermore, the strong dependence of instability evolution on initial amplitude is quantified based on the effects of decoupling, which sheds light on the physical origin of the overshoot phenomenon.