Abstract
Rayleigh–Bénard (RB) convection in the turbulent regime is studied using statistical methods. Exact evolution equations for the probability density function of temperature and velocity are derived from first principles within the framework of the Lundgren–Monin–Novikov hierarchy known from homogeneous isotropic turbulence. The unclosed terms arising in the form of conditional averages are estimated from direct numerical simulations. Focusing on the statistics of temperature, the theoretical framework allows us to interpret the statistical results in an illustrative manner, giving deeper insights into the connection between dynamics and statistics of RB convection. The results are discussed in terms of typical flow features and the relation to the heat transfer.