In the large eddy simulation ͑LES͒ approach, large-scale energy-containing structures are resolved, smaller structures are filtered out, and unresolved subgrid effects are modeled. Extensive recent work has demonstrated that predictive under-resolved simulations of the velocity fields in turbulent flows are possible without resorting to explicit subgrid models when using a class of physics-capturing high-resolution finite-volume numerical algorithms. This strategy is denoted as implicit LES ͑ILES͒. Tests in fundamental applications ranging from canonical to complex flows indicate that ILES is competitive with conventional LES in the LES realm proper-flows driven by large-scale features. The performance of ILES in the substantially more difficult problem of under-resolved material mixing driven by under-resolved velocity fields and initial conditions is a focus of the present work. Progress in addressing relevant resolution issues in studies of mixing driven by Richtmyer-Meshkov instabilities in planar shock-tube laboratory experiments is reported. Our particular focus is devoted to the initial material interface characterization and modeling difficulties, and effects of initial condition specifics ͑resolved spectral content͒ on transitional and late-time turbulent mixing-which were not previously addressed.

A numerical study of the evolution of the multimode planar Richtmyer-Meshkov instability (RMI) in a light-heavy (air-SF6, Atwood number A = 0.67) configuration involving a Mach number Ma = 1.5 shock is carried out. Our results demonstrate that the initial material interface morphology controls the evolution characteristics of RMI (for fixed A, Ma), and provide a significant basis to develop metrics for transition to turbulence. Depending on initial rms slope of the interface, RMI evolves into linear or nonlinear regimes, with distinctly different flow features and growth rates, turbulence statistics, and material mixing rates. We have called this the bipolar behavior of RMI. Some of our findings are not consistent with heuristic notions of mixing in equilibrium turbulence: more turbulent flow—as measured by spectral bandwidth, can be associated with higher material mixing but, paradoxically, to lower integral measures of turbulent kinetic energy and mixing layer width.

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We report implicit large-eddy simulations of (Mach 1.2) shocked SF 6 gas curtain (GC) experiments addressing the impact of initial conditions (ICs) on material mixing and transition to turbulence. Initial GCs with realistic three-dimensional characteristics are generated with separate Navier-Stokes-Boussinesq simulations of a mixture of SF 6 and air falling through the shock-tube test section. SF 6 concentration fluctuations present in the laboratory experiments are emulated to address their potential effects. The predicted evolution of shocked GC widths is fairly robust and insensitive to ICs and grid resolution before reshock and in good agreement with laboratory experiments. After reshock, predicted results are sensitive to IC spectral content and its consequences on the morphology of the thicker more-complex mixing layers at reshock time. The presence of small-scale material-concentration fluctuations in ICs can promote late-time features traditionally associated with transition to turbulence, i.e., faster GC width growth, more isotropic features, and self-similar spectra. An effective data reduction procedure is found useful in improving comparisons with the laboratory data and characterizing the instability behaviors. As in our recent planar Richtmyer-Meshkov studies, we find that a single IC parameter can be usefully identified as relevant in determining whether the shockdriven flow is in linear ballistic or nonlinear mode-coupling regimes; we are thus able to demonstrate the recently reported bipolar behavior of the planar Richtmyer-Meshkov instability also in the case of the shocked GC configuration.