Study of ultrahigh Atwood-number Rayleigh–Taylor mixing dynamics using the nonlinear large-eddy simulation method

Abstract

The Nonlinear Large-Eddy Simulation (nLES) method [G. C. Burton, “The nonlinear large-eddy simulation method (nLES) applied to Sc≈1 and Sc⪢1 passive-scalar mixing,” Phys. Fluids 20, 035103 (2008)] is employed in the first numerical study of multimode miscible Rayleigh–Taylor instability (RTI) in the ultrahigh Atwood-number regime above A≥0.90. The present work focuses on the dynamics of turbulent mixing at the large density ratios that may be encountered in certain astrophysical contexts and engineering applications. Using the initial condition from the landmark (N=30723) direct numerical study of Cabot and Cook [W. Cabot and A. W. Cook, “Reynolds number effects on Rayleigh-Taylor instability with possible implications for type-Ia supernovae,” Nat. Phys. 2, 562 (2006)], the nLES method is first validated in simulations of A=0.5 RTI mixing and is shown to recover important statistical measures of the mixing process, such as bubble and spike growth rates and mixing efficiency reported in that study, but at the significantly coarser resolutions typical of most large-eddy simulations. The first simulations of RTI at Atwood numbers A>0.90 are then used to explore the effects of varying the density ratio on mixing dynamics at very high Atwood numbers 0.75≤A≤0.96. Spike heights and mixing layer growth rates are shown to be strongly affected by the initial density ratio. An empirical power-law scaling relationship is shown to predict nearly exactly the variation in the ratio of spike to bubble heights as a function of Atwood number. Mixing efficiency is shown to be influenced by the initial density difference but the competition between increased molecular mixing and entrainment largely cancel, producing a relatively modest variation in these flow parameters when compared with the intermediate Atwood-number case. Late-time power spectra show the appearance of an inertial range, indicating that the mixing layer has transitioned to a fully turbulent state. The role of bubble and spike structures in the interscale transfer of kinetic energy is explored for the first time for high Atwood-number RTI flows. Bubble heads (stems) are shown to produce forward (reverse) transfer due to compressive (extensional) straining at intermediate Atwood number. At high Atwood number, however, spike stems are shown to produce forward transfer due to compressive straining generated from the larger spike penetration velocity and the differing spike morphology produced at the higher Atwood number. The study indicates that stable and accurate simulations of ultrahigh Atwood-number mixing may be conducted using the nLES method on grids significantly coarser than used previously to examine RTI flows.