Direct numerical simulation of a statistically stationary Rayleigh-Taylor mixing layer

Rayleigh-Taylor (RT) instabilities are known to show a strong dependence on the initial conditions at early stages before transiting to a self-similar turbulent regime at high Reynolds numbers. In this study, the late time self-similar nature of the RT mixing layer is exploited to enforce a statistically stationary solution at a prescribed mixing layer width. The governing equations are solved in a transformed coordinate system, where the vertical coordinate is first shifted by δ to account for flow asymmetries, then normalized by a mixing layer width, q. In the transformed coordinates, the governing transport equations resemble the original ones in physical coordinates but with additional terms involving q'/q and δ' – both of which are computed from vertically integrated, ensemble-averaged quantities that are extracted directly from the simulation. The solution is periodic and homogeneous in both horizontal directions, does not require resolution of the initial transients and exhibit statistical convergence over time. Growth rates, mean profiles, velocity anisotropy and conditional means of velocity on density are extracted and compared against other direct numerical simulation and experimental results.