Ablative Rayleigh–Taylor instability driven by time-varying acceleration

Abstract

In this article, the asymptotic nonlinear behavior of the Rayleigh–Taylor hydrodynamic instability driven by time dependent variable accelerations of the form $g(1-e^{-\frac{t}{T}})$ and $g(1-e^{-\frac{t}{T}})(1+\cos \mu t)$ has been reported simultaneously. The nonlinear model based on potential flow theory has been extended to describe the effect of afore mentioned accelerations with vorticity generation inside the bubble. It is seen that the asymptotic growth rate and curvature of the tip of the bubble like interface tends to a finite saturation value and depends on the parameters T and $\mu$. Also, an oscillatory behavior is observed for the acceleration $g(1-e^{-\frac{t}{T}})(1+\cos \mu t)$. Such time-dependent accelerations are a representative of the flow conditions in several applications including Inertial Confinement Fusion, type la supernova and several Rayleigh–Taylor experiments.