A comparative study of the turbulent Rayleigh–Taylor instability using high-resolution three-dimensional numerical simulations: The Alpha-Group collaboration

Abstract

The turbulent Rayleigh–Taylor instability is investigated in the limit of strong mode-coupling using a variety of high-resolution, multimode, three dimensional numerical simulations (NS). The perturbations are initialized with only short wavelength modes so that the self-similar evolution (i.e., bubble diameter Db∝amplitude hb) occurs solely by the nonlinear coupling (merger) of saturated modes. After an initial transient, it is found that hb∼αbAgt2, where A=Atwood number, g=acceleration, and t=time. The NS yield Db∼hb/3 in agreement with experiment but the simulation value αb∼0.025±0.003 is smaller than the experimental value αb∼0.057±0.008. By analyzing the dominant bubbles, it is found that the small value of αb can be attributed to a density dilution due to fine-scale mixing in our NS without interface reconstruction (IR) or an equivalent entrainment in our NS with IR. This may be characteristic of the mode coupling limit studied here and the associated αb may represent a lower bound that is insensitive to the initial amplitude. Larger values of αb can be obtained in the presence of additional long wavelength perturbations and this may be more characteristic of experiments. Here, the simulation data are also analyzed in terms of bubble dynamics, energy balance and the density fluctuation spectra.