The characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh-Bénard convection

Abstract

Abstract We study the characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh-Bénard convection in a suqare cavity by means of direct numerical simulations. The Rayleigh number range is 1×108 ≤ Ra ≤ 1×1013, and the Prandtl number is selected as Pr=0.7 and Pr=4.3. It is found that, the temperature fluctuation profiles with respect to Ra exhibit two different distribution patterns. In the thermal boundary layer, the normalized fluctuation θ rms /θ rms,max is independent on Ra and a power law relation is identified, i.e., θ rms /θ rms,max ~(z/δ)0.99±0.01, where z/δ is a dimensionless distance to the boundary (δ is the thickness of thermal boundary layer). Out of the boundary layer, when Ra ≤ 5×109, the profiles of θ rms /θ rms,max descend, then ascend, and finally drop dramatically as z/δ increases. While for Ra ≥ 1×1010, the profiles continuously decrease and finally overlap with each other. The two different characteristics of temperature fluctuations are closely related to the formation of stable large-scale circulations and corner rolls. Besides, there is a critical value of Ra indicating the transition, beyond which the fluctuation <θ rms > V has a power law dependence on Ra, given by <θ rms > V ~Ra -0.14±0.01.