Self-Similar Solutions to Three- and Four-Equation Reynolds-Averaged Models for Rayleigh−Taylor Mixing and Comparisons to Numerical Simulation and Experimental Data

Analytical self-similar solutions to three- and four-equation mechanical/scalar turbulence models [Schilling and Mueschke, Physical Review E 96, 063111 (2017)], similar to those used in turbulent combustion, are presented for Rayleigh-Taylor mixing. The mechanical turbulence is described by the turbulent kinetic energy, K, and its dissipation rate, ε, and the scalar turbulence is described by a scalar variance, S, and its dissipation rate, χ. The addition of the scalar variables gives a prediction for the molecular mixing parameter, θ, as a function of the model coefficients. The spatiotemporal evolution of the mean and turbulent fields is illustrated. The growth and mixing parameters, ratio of turbulent kinetic energy to released potential energy, and production-to-dissipation ratios are obtained as a function of the model coefficients and are compared to their values from direct numerical simulation of a small Atwood number Rayleigh−Taylor mixing experiment. The agreement between the model and data are quite good, with the four-equation model predictions in better agreement with data than the three-equation model predictions.