Investigation of temperature statistics in turbulent Rayleigh-Bénard convection using PDF methods

Lülff, Johannes; Wilczek, Michael; Friedrich, Rudolf

Abstract

Rayleigh-Bénard 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. The unclosed terms arising in the form of conditional averages are estimated from direct numerical simulations. Focussing on the statistics of temperature, the theoretical framework allows to interpret the statistical results in an illustrative manner, giving deeper insight into the connection between dynamics and statistics of Rayleigh-Bénard convection.