Investigation of Rayleigh–Taylor turbulence and mixing using direct numerical simulation with experimentally measured initial conditions. II. Dynamics of transitional flow and mixing statistics

Abstract

A 1152×760×1280 direct numerical simulation (DNS) using initial conditions, geometry, and physical parameters chosen to approximate those of a transitional, small Atwood number, nonreacting Rayleigh–Taylor mixing experiment was presented in Paper I [Mueschke and Schilling, Phys. Fluids 21, 014106 (2009)]. In addition, the DNS model of the experiment was validated by comparing quantities from the simulation to experimental measurements, including large-scale quantities, higher-order statistics, and vertical velocity and density variance spectra. In Paper II of this study, other quantities not measured in the experiment are obtained from the DNS and discussed, such as the integral- and Taylor-scale Reynolds numbers, Reynolds stress and dissipation anisotropy, two-dimensional density and velocity variance spectra, hypothetical chemical product formation measures (similar to those used in reacting shear flow experiments), other local and global mixing parameters, and the statistical composition of mixed fluid. The integral- and Taylor-scale Reynolds numbers, together with visualizations of vertical and center plane slices of the density and vorticity fields, are used to elucidate the various evolutionary stages of the flow. It is shown that the early-time evolution retains a primarily two-dimensional character until the flow begins to transition to a more three-dimensional state at later times, as also observed in the experiment. The evolution of the three diagonal components of the anisotropy tensors showed that anisotropy persists to the latest times in the simulation. Compensated spectra at the latest time in the DNS suggest very short k−5/3 and k−5/4 inertial subrange scalings of the vertical velocity and density variance spectra, respectively. By interpreting the mixing between the two fluids as a hypothetical, infinitely fast, reversible chemical reaction between the species, the local formation of chemical product, equivalent product thickness, and other standard measures of mixing used in shear-driven turbulence are obtained from the DNS and discussed. Other measures of molecular mixing are shown to be qualitatively similar to the molecular mixing parameter θ on the center plane. Finally, the statistical composition of the mixed fluid is examined using the probability distribution function of the heavy-fluid volume fraction and the averaged composition of mixed fluid. Thus, DNS modeled closely after a physical Rayleigh–Taylor instability and mixing experiment can provide additional insights into the flow physics complementary to the experiment.