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A mixing transition has been observed in a high-resolution large-eddy simulation of Rayleigh-Taylor instability. During the transition, an inertial range forms in the velocity spectrum and the rate of growth of the mixing zone is reduced. By measuring growth of the layer in units of dominant initial wavelength, criteria are established for reaching the hypothetical self-similar state of the mixing layer. A model including mixing effects is derived for the growth rate. The rate of growth of the mixing layer is determined by the net mass flux through the plane associated with the initial location of the interface. All of the information necessary for predicting the growth rate is contained in this plane. The model incorporates an effective Atwood number and provides a good match to the simulation data. The model suggests reduced growth for miscible fluids, compared to the immiscible case.

A method is presented whereby the fast chemistry reaction, Fuel+(r)Oxidizer →(1+r) Product, may be modeled in the context of a large eddy simulation (LES). The model is based on a presumed form for the subgrid-scale probability density function (PDF) of a conserved scalar. The nature of the subgrid-scale statistics is discussed and it is shown that a beta function representation of the subgrid-scale PDF is appropriate. Data from both laboratory experiments and direct numerical simulations (DNS) are used to show that the predictions of the model are very accurate, given the exact values for the filtered scalar and its variance. A possible model for this variance is presented based on scale similarity.

Direct numerical simulations (DNS) are presented of three-dimensional, RayleighTaylor instability (RTI) between two incompressible, miscible fluids, with a 3 : 1 density ratio. Periodic boundary conditions are imposed in the horizontal directions of a rectangular domain, with no-slip top and bottom walls. Solutions are obtained for the Navier-Stokes equations, augmented by a species transport-diffusion equation, with various initial perturbations. The DNS achieved outer-scale Reynolds numbers, based on mixing-zone height and its rate of growth, in excess of 3000. Initial growth is diffusive and independent of the initial perturbations. The onset of nonlinear growth is not predicted by available linear-stability theory. Following the diffusive-growth stage, growth rates are found to depend on the initial perturbations, up to the end of the simulations. Mixing is found to be even more sensitive to initial conditions than growth rates. Taylor microscales and Reynolds numbers are anisotropic throughout the simulations. Improved collapse of many statistics is achieved if the height of the mixing zone, rather than time, is used as the scaling or progress variable. Mixing has dynamical consequences for this flow, since it is driven by the action of the imposed acceleration field on local density differences.

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