Monte Carlo simulation of thermal fluctuations below the onset of Rayleigh-Bénard convection

The density fluctuations below the onset of convection in the Rayleigh-Bénard problem are studied with the direct simulation Monte Carlo method. The particle simulation results clearly show the connection between the static correlation functions of fluctuations below the critical Rayleigh number and the flow patterns above the onset of convection for small Knudsen number flows (Kn=0.01 and Kn=0.005). Furthermore, the physical nature for no convection in the Rayleigh-Bénard problem under large Knudsen number conditions (Kn>0.028) is explained based on the dynamics of fluctuations.