On validation of turbulent mixing simulations for Rayleigh-Taylor instability

The purpose of this paper is to analyze the validation achieved in recent simulations of Rayleigh-Taylor unstable mixing. The simulations are already in agreement with experiment; mesh refinement or insertion of a calibrated subgrid model for mass diffusion will serve to refine this validation and possibly shed light on the role of unobserved long wavelength perturbations in the initial data. In this paper we present evidence to suggest that a subgrid model will have a barely noticeable effect on the simulation. The analysis is of independent interest, as it connects a validated simulation to common studies of mixing properties. The average molecular mixing parameter θ for the ideal and immiscible simulations is zero at a grid block level, as is required by the exact microphysics of these simulations. Averaging of data over volumes of (4Δx)³ to (8Δx)³ yields a conventional value θ∼0.8, suggesting that fluid entrainment in front tracked simulations produces a result similar to numerical mass diffusion in untracked simulations. The miscible simulations yield a nonzero θ∼0.8 in agreement with experimental values. We find spectra in possible approximate agreement with the Kolmogorov theory. A characteristic upturn especially in the density fluctuation spectrum at high wave numbers suggests the need for a subgrid mass diffusion model, while the small size of the upturn and the analysis of θ suggest that the magnitude of the model will not be large. We study directly the appropriate settings for a subgrid diffusion coefficient, to be inserted into simulations modeling miscible experiments. This is our most definitive assessment of the role for a subgrid model. We find that a Smagorinsky-type subgrid mass diffusion model would have a diffusion coefficient at most about 0.15% of the value of the physical mass diffusion for the (mass diffusive) experiment studied.