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.

In implicit large-eddy simulation (ILES), energy-containing large scales are resolved, and physics capturing numerics are used to spatially filter out unresolved scales and to implicitly model subgrid scale effects. From an applied perspective, it is highly desirable to estimate a characteristic Reynolds number (Re)-and therefore a relevant effective viscosity-so that the impact of resolution on predicted flow quantities and their macroscopic convergence can usefully be characterized. We argue in favor of obtaining robust Re estimates away from the smallest scales of the simulated flow-where numerically controlled dissipation takes place and propose a theoretical basis and framework to determine such measures. ILES examples include forced turbulence as a steady flow case, the Taylor-Green vortex to address transition and decaying turbulence, and simulations of a laser-driven reshock experiment illustrating a fairly complex turbulence problem of current practical interest.

Turbulent mixing of a passive scalar by forced isotropic turbulence with a prescribed mean scalar gradient is studied in the context of implicit large-eddy simulation. The simulation strategy uses a multi-dimensional compressible flux-corrected transport algorithm, with low wavenumber momentum forcing imposed separately for the solenoidal and dilatational velocity components. Effects of grid resolution on the flow and scalar mixing are investigated at turbulent Mach numbers 0.13 and 0.27. Turbulence metrics are used to show that an implicit large-eddy simulation can accurately capture the mixing transition and asymptotic self-similar behaviors predicted by previous theoretical, laboratory, and direct numerical simulation studies, including asymptotically constant scalar variance and increasing velocity-to-scalar Taylor micro-scales ratio as function of effective Reynolds number determined by grid resolution. The results demonstrate the feasibility of predictive under-resolved simulations of high Reynolds number turbulent scalar mixing using implicit large-eddy simulation.

An experiment that seeks to investigate buoyancy driven mixing of miscible fluids by microwave volumetric energy deposition is presented. The experiment involves the use of a light, non-polar fluid that initially rests on top of a heavier fluid which is more polar. Microwaves preferentially heat the polar fluid, and its density decreases due to thermal expansion. As the microwave heating continues, the density of the lower fluid eventually becomes less than that of the upper, and buoyancy driven Rayleigh-Taylor mixing ensues. The choice of fluids is crucial to the success of the experiment, and a description is given of numerous fluid combinations considered and characterized. After careful consideration, the miscible pair of toluene/tetrahydrofuran (THF) was determined as having the best potential for successful volumetric energy deposition buoyancy driven mixing. Various single fluid calibration experiments were performed to facilitate the development of a heating theory. Thereafter, results from two-fluid mixing experiments are presented that demonstrate the capability of this novel Rayleigh-Taylor driven experiment. Particular interest is paid to the onset of buoyancy driven mixing and unusual aspects of the experiment in the context of typical Rayleigh-Taylor driven mixing.