Characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh-Bénard convection

Abstract

We study the characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh–Bénard convection in a square cavity by 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 of 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.