Comparison of Reynolds-Averaged and Analytical Self-Similar Solutions of Four-Equation Models of Small Atwood Number Rayleigh–Taylor Mixing Driven by Power-Law Accelerations

Quantities obtained from previously derived analytical self-similar solutions to two-, three-, and four-equation Reynolds-averaged turbulence models describing Rayleigh–Taylor mixing driven by a temporal power-law acceleration in the small Atwood number limit [O. Schilling, Phys. Fluids 36, 075170 (2024)] are compared to the corresponding quantities obtained from numerical solutions of the Reynolds-averaged equations. The equations are solved numerically for power-law accelerations g(t) = g₀ (t/t₀)^θ_RT^-2 with θ_RT = 1, 2, and 3 corresponding to a deceleration, constant acceleration, and linear in time acceleration, respectively. It is shown that the mixing layer widths grow as h(t) = α At g(t) t² ∝ t^θ_RT at late times, with α depending on the model coefficients and on the exponent θ_RT. Other self-similar quantities are also compared and shown to be in good agreement between the numerical values and analytical predictions. Mean and turbulent fields and equation budgets are compared between the cases to illustrate the effects of different time-dependent accelerations on the evolution of Rayleigh−Taylor mixing.