Statistics of velocity and temperature fluctuations in two-dimensional Rayleigh-Bénard convection

Abstract

We investigate fluctuations of the velocity and temperature fields in two-dimensional (2D) Rayleigh-Bénard (RB) convection by means of direct numerical simulations (DNS) over the Rayleigh number range 10^{6}≤Ra≤10^{10} and for a fixed Prandtl number Pr=5.3 and aspect ratio Γ=1. Our results show that there exists a counter-gradient turbulent transport of energy from fluctuations to the mean flow both locally and globally, implying that the Reynolds stress is one of the driving mechanisms of the large-scale circulation in 2D turbulent RB convection besides the buoyancy of thermal plumes. We also find that the viscous boundary layer (BL) thicknesses near the horizontal conducting plates and near the vertical sidewalls, δ_{u} and δ_{v}, are almost the same for a given Ra, and they scale with the Rayleigh and Reynolds numbers as ∼Ra^{-0.26±0.03} and ∼Re^{-0.43±0.04}. Furthermore, the thermal BL thickness δ_{θ} defined based on the root-mean-square (rms) temperature profiles is found to agree with Prandtl-Blasius predictions from the scaling point of view. In addition, the probability density functions of turbulent energy ɛ_{u^{'}} and thermal ɛ_{θ^{'}} dissipation rates, calculated, respectively, within the viscous and thermal BLs, are found to be always non-log-normal and obey approximately a Bramwell-Holdsworth-Pinton distribution first introduced to characterize rare fluctuations in a confined turbulent flow and critical phenomena.