A Posteriori Tests of an A Priori Optimized Turbulence Model for Small and Large Schmidt Number Rayleigh-Taylor Mixing

Data from a $1152 \times 720 \times 1280$ direct numerical simulation (DNS) of a buoyancy-driven hot/cold water channel experiment is used to construct an optimized four-equation turbulence model for Rayleigh--Taylor mixing. The transport equations for the turbulent kinetic energy and its dissipation rate and of mass fraction variance and its dissipation rate are closed a priori by minimizing the $L_2$-norm between the exact unclosed terms and their gradient-diffusion or scale-similarity closures. The model is tested a posteriori by applying the model to both the $Sc = 7$ hot/cold water experiment and to a $Sc \sim 10^{3}$ salt/fresh water experiment. It is shown that the mixing layer growth and molecular mixing parameters measured from both experiments are well-predicted by the model. The dependence of the predictions on different initialization times of the model, as well on choosing constant late-time values of the parameters (rather than Reynolds number-dependent parameters), are discussed.