Small-Peclet-number approximation for stellar turbulent mixing zones

The purpose of this work is to derive a small turbulent Péclet-small turbulent Mach number approximation for hydroradiative turbulent mixing zones encountered in stellar interiors where the radiative conductivity can overwhelms the turbulent transport. To this end, we proceed to an asymptotic analysis and determine orders of magnitude for the fluctuating temperature and pressure, as well as closed expressions for the fluctuating conduction and velocity divergence. The latter is used to extend a Reynolds stress model to the small-Péclet regime. Three-dimensional direct numerical simulations of radiative Rayleigh-Taylor turbulent mixing zones are performed, first, to validate the asymptotic predictions and, second, to validate their use in the Reynolds stress model.