Statistics of Heat Transfer in Two-Dimensional Turbulent Rayleigh-Bénard Convection at Various Prandtl Number

Statistics of heat transfer in two-dimensional (2D) turbulent Rayleigh-Bénard (RB) convection for [Formula: see text] and [Formula: see text] are investigated using the lattice Boltzmann method (LBM). Our results reveal that the large scale circulation is gradually broken up into small scale structures plumes with the increase of [Formula: see text] , the large scale circulation disappears with increasing [Formula: see text] , and a great deal of smaller thermal plumes vertically rise and fall from the bottom to top walls. It is further indicated that vertical motion of various plumes gradually plays main role with increasing [Formula: see text]. In addition, our analysis also shows that the thermal dissipation is distributed mainly in the position of high temperature gradient, the thermal dissipation rate [Formula: see text] already increasingly plays a dominant position in the thermal transport, [Formula: see text] can have no effect with increase of [Formula: see text]. The kinematic viscosity dissipation rate and the thermal dissipation rate gradually decrease with increasing [Formula: see text]. The energy spectrum significantly decreases with the increase of [Formula: see text]. A scope of linear scaling arises in the second order velocity structure functions, the temperature structure function and mixed structure function(temperature-velocity). The value of linear scaling and the 2nd-order velocity decrease with increasing [Formula: see text] , which is qualitatively consistent with the theoretical predictions.