Investigation of Turbulence Dynamics in a Very Large Reynolds Number Rayleigh-Taylor Mixing Layer Using Direct Numerical Simulation Data

Classical gradient-diffusion models of turbulent transport in Rayleigh-Taylor instability-induced mixing are assessed using data from the Cabot and Cook [Nat. Phys. \textbf{2}, 562] $3072^3$ direct numerical simulation (DNS) attaining a Reynolds number of $\sim 32,000$. Mean and fluctuating fields, defined from spatial averages over the two periodic directions of the DNS, are used to construct the profiles across the mixing layer of the terms in the turbulent kinetic energy and turbulent kinetic energy dissipation rate transport equations. The unclosed terms are then compared a priori with the corresponding terms modeled using the gradient-diffusion approximation to assess the validity of this approximation at very large Reynolds numbers. In addition, optimized turbulent Schmidt numbers appearing in the closures are obtained by correlating the unclosed and closed model terms.