The motion of a single bubble or spike in Rayleigh-Taylor unstable interfaces

Abstract

The Rayleigh-Taylor instability in single-bubble systems has been studied by applying the front tracking method to the full two-dimensional Euler equations. The development of the instability is characterized by the penetration of the light (heavy) fluid into the heavy (light) fluid. A dynamic equation is proposed to model such penetrations. Extensive numerical simulations show good aggeement between the analytic results of the dynamical model and the numerical solutions of the full Euler equations. The dependence of the characteristic physical parameters at each development stage of the instability on the density and compressibility of fluids are established for the parameter range studied. The distribution of fluid density has a significant influence on the dynamic behavior of the systems. An exponentially stratified density distribution produces a dramatic effect on the penetration of light fluid into heavy fluid at late times. The proposed dynamic model plays an important rule in the study of chaotic flow in multibubble systems.