Investigation of Rayleigh–Taylor turbulence and mixing using direct numerical simulation with experimentally measured initial conditions. I. Comparison to experimental data

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 Rayleigh–Taylor mixing experiment [Mueschke et al., J. Fluid Mech. 567, 27 (2006)] is presented. In particular, the Atwood number is 7.5×10−4, and temperature diffusion is modeled by mass diffusion with an equivalent Schmidt number of 7. The density and velocity fluctuations measured just off of the splitter plate in this buoyantly unstable water channel experiment were parametrized to provide physically realistic, anisotropic initial conditions for the DNS. The methodology for parametrizing the measured data and numerically implementing the resulting perturbation spectra in the simulation is discussed in detail. The DNS is then validated by comparing quantities from the simulation to experimental measurements. In particular, large-scale quantities (such as the bubble front penetration hb and the mixing layer growth parameter αb), higher-order statistics (such as velocity variances and the molecular mixing parameter θ on the center plane), and vertical velocity and density variance spectra from the DNS are shown to be in favorable agreement with the experimental data. The DNS slightly underestimates the growth of the bubble front hb but predicts αb≈0.07 at the latest time, in excellent agreement with the experimental measurement. While the molecular mixing parameter θ is also slightly underestimated by the DNS during the nonlinear and weakly turbulent growth phases, the late-time value θ≈0.55 compares favorably with the value θ≈0.6 measured in the experiment. The one-dimensional density and vertical velocity variance spectra are in excellent agreement between the DNS and experimental measurements. Differences between the quantities obtained from the DNS and from experimental measurements are related to limitations in the dynamic range of scales resolved in the DNS and other idealizations of the simulation. Specifically, the statistical convergence of the DNS results and confidence interval bounds are discussed. This work demonstrates that a parametrization of experimentally measured initial conditions can yield simulation data that quantitatively agrees well with experimentally measured low- and higher-order statistics in a Rayleigh–Taylor mixing layer. This study also provides resolution and initial conditions implementation requirements needed to simulate a physical Rayleigh–Taylor mixing experiment. In Paper II [Mueschke and Schilling, Phys. Fluids 21, 014107 (2009)], 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, other local and global mixing parameters, and the statistical composition of mixed fluid. These quantities are valuable for assessing the predictions of Reynolds-averaged Navier–Stokes and large-eddy simulation models of Rayleigh–Taylor turbulent mixing.