Self-Similar Solutions of Two-, Three-, and Four-Equation RANS Models of Small Atwood Number Rayleigh–Taylor Mixing Driven by Power-Law Accelerations*

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 are derived in the small Atwood number limit. The solutions generalize those previously derived for constant acceleration Rayleigh–Taylor mixing for models based on the turbulent kinetic energy and its dissipation rate, together with the scalar variance and its dissipation rate [O. Schilling, Phys. Fluids 33, 085129 (2021)]. The turbulent fields are expressed in terms of the model coefficients and power-law exponent. Mixing layer growth parameters and other physical observables are obtained as functions of the model coefficients and parameterized by the exponent of the power-law acceleration. The four-equation model is then used to numerically reconstruct the mean and turbulent fields, and turbulent equation budgets across the mixing layer for several values of the power-law exponent.