Turbulent Richtmyer-Meshkov instability (RMI) is investigated through a series of high resolution three dimensional smulations of two initial conditions with eight independent codes. The simulations are initialised with a narrowband perturbation such that instability growth is due to non-linear coupling/backscatter from the energetic modes, thus generating the lowest expected growth rate from a pure RMI. By independently assessing the results from each algorithm, and computing ensemble averages of multiple algorithms, the results allow a quantification of key flow properties as well as the uncertainty due to differing numerical approaches. A new analytical model predicting the initial layer growth for a multimode narrowband perturbation is presented, along with two models for the linear and non-linear regime combined. Overall, the growth rate exponent is determined as θ = 0.292 ± 0.009, in good agreement with prior studies; however, the exponent is decaying slowly in time. Also, θ is shown to be relatively insensitive to the choice of mixing layer width measurement. The asymptotic integral molecular mixing measures Θ = 0.792 ± 0.014, Ξ = 0.800±0.014 and Ψ = 0.782±0.013 which are lower than some experimental measurements but within the range of prior numerical studies. The flow field is shown to be persistently anisotropic for all algorithms, at the latest time having between 49% and 66% higher kinetic energy in the shock parallel direction compared to perpendicular and does not show any return to isotropy. The plane averaged volume fraction profiles at different time instants collapse reasonably well when scaled by the integral width, implying that the layer can be described by a single length scale and thus a single θ. Quantitative data given for both ensemble averages and individual algorithms provide useful benchmark results for future research.

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The dynamics of the reshocked multi-mode Richtmyer-Meshkov instability is investigated using 513 × 257 2 three-dimensional ninth-order weighted essentially nonoscillatory shock-capturing simulations. A two-mode initial perturbation with superposed random noise is used to model the Mach 1.5 air/SF 6 Vetter-Sturtevant shock tube experiment. The mass fraction and enstrophy isosurfaces, and density cross-sections are utilized to show the detailed flow structure before, during, and after reshock. It is shown that the mixing layer growth agrees well with the experimentally measured growth rate before and after reshock. The post-reshock growth rate is also in good agreement with the prediction of the Mikaelian model. A parametric study of the sensitivity of the layer growth to the choice of amplitudes of the short and long wavelength initial interfacial perturbation is also presented. Finally, the amplification effects of reshock are quantified using the evolution of the turbulent kinetic energy and turbulent enstrophy spectra, as well as the evolution of the baroclinic enstrophy production, buoyancy production, and shear production terms in the enstrophy and turbulent kinetic transport equations.

The reshocked single-mode Richtmyer-Meshkov instability is simulated in two spatial dimensions using the fifth-and ninth-order weighted essentially nonoscillatory shock-capturing method with uniform spatial resolution of 256 points per initial perturbation wavelength. The initial conditions and computational domain are modeled after the single-mode, Mach 1.21 air͑acetone͒/SF 6 shock tube experiment of Collins and Jacobs ͓J. Fluid Mech. 464, 113 ͑2002͔͒. The simulation densities are shown to be in very good agreement with the corrected experimental planar laser-induced fluorescence images at selected times before reshock of the evolving interface. Analytical, semianalytical, and phenomenological linear and nonlinear, impulsive, perturbation, and potential flow models for single-mode Richtmyer-Meshkov unstable perturbation growth are summarized. The simulation amplitudes are shown to be in very good agreement with the experimental data and with the predictions of linear amplitude growth models for small times, and with those of nonlinear amplitude growth models at later times up to the time at which the driver-based expansion in the experiment ͑but not present in the simulations or models͒ expands the layer before reshock. The qualitative and quantitative differences between the fifth-and ninth-order simulation results are discussed. Using a local and global quantitative metric, the prediction of the Zhang and Sohn ͓Phys. Fluids 9, 1106 ͑1997͔͒ nonlinear Padé model is shown to be in best overall agreement with the simulation amplitudes before reshock. The sensitivity of the amplitude growth model predictions to the initial growth rate from linear instability theory, the post-shock Atwood number and amplitude, and the velocity jump due to the passage of the shock through the interface is also investigated numerically.

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.