The late-time dynamics of the single-mode Rayleigh-Taylor instability

Abstract

We report on numerical simulations of the detailed evolution of the single mode Rayleigh-Taylor [Lord Rayleigh, Scientific Papers II (Cambridge University Press, Cambridge, 1900), p. 200; G. I. Taylor, “The instability of liquid surfaces when accelerated in a direction perpendicular to their plane,” Proc. R. Soc. London, Ser. A 201, 192 (1950)10.1098/rspa.1950.0052; S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Oxford University Press, Oxford, 1961)] instability to late times and high aspect ratios. In contrast to established potential flow models that predict a terminal velocity and a constant Froude number at low Atwood numbers, we observe a complex sequence of events that can be summarized in four stages: I. Exponential growth of imposed perturbations, II. Saturation to terminal velocity, III. Reacceleration to a higher Froude number, and IV. Chaotic mixing. The observed reacceleration away from the Froude number predicted by potential flow theory is attributed to the appearance of second...