Assessment of gradient-diffusion closures for modeling Rayleigh-Taylor and Richtmyer-Meshkov instability-induced mixing

The validity of gradient-diffusion closures for modeling turbulent transport in multi-mode Rayleigh-Taylor and reshocked Richtmyer-Meshkov instability-induced mixing is investigated using data from three-dimensional spectral/tenth-order compact difference and ninth-order weighted essentially non-oscillatory simulations, respectively. Details on the numerical methods, initial and boundary conditions, and validation of the results are discussed elsewhere [2, 3]. First, mean and fluctuating fields are constructed using spatial averaging in the two periodic flow directions. Then, quantities entering eddy viscosity-type gradient-diffusion closures, such as the turbulent kinetic energy and its dissipation rate (or turbulent frequency), and the turbulent viscosity are constructed. The magnitudes of the terms in the turbulent kinetic energy transport equation are examined to identify the dominant processes. It is shown that the buoyancy (or shock) production term is the dominant term in the transport equation, and that the shear production term is relatively small for both the Rayleigh-Taylor and Richtmyer-Meshkov cases. Finally, a priori tests of gradient-diffusion closures of the unclosed terms in the turbulent kinetic energy transport equation are performed by comparing the terms constructed directly using the data to the modeled term. A simple method for estimating the turbulent Schmidt numbers appearing in the closures is proposed. Using these turbulent Schmidt numbers, it is shown that both the shape and magnitude of the profiles of the dominant terms in the turbulent kinetic energy transport equation across the mixing layer are generally well captured.