Decoupling small-scale turbulence generation from a large-scale domain in direct numerical simulations of Rayleigh-Taylor instabilities

Rayleigh-Taylor (RT) instabilities are buoyant-turbulent phenomena of immense practical value in the areas of wildfire modeling, astrophysics, and inertial confinement fusion. Unfortunately, direct numerical simulations (DNS) of the full domain of RT flow, including both reservoirs of heavy and light fluid, may be an inefficient use of computational resources when most turbulence generation is confined to small-scale eddies in the central mixing layer. To isolate these effects in a smaller domain, this study relies on a Reynolds-decomposition of the governing equations into mean and fluctuations. The fluctuations are transformed into variables verified to be spatially homogeneous by leveraging results of previous DNS of RT instabilities, allowing the use of a 3D periodic box for boundary conditions. The equations are closed by assuming the mean flow to be of a form known from previous DNS, resulting in a set of equations similar to Navier-Stokes but with a few additional source terms. These terms act to maintain the turbulent kinetic energy and mixture fraction variance, emulating the effect of the larger-domain flow without having to resolve it in a full-scale simulation. The equations are then implemented in the periodic box DNS and the resulting statistics are compared with those found in a full DNS of RT instabilities.