关键词: Rayleigh-Bénard, temperature fluctuation, distribution patterns, critical value

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 ${1\times }{{10}}^{{8}}\le Ra\le 1\times {{10}}^{{13}}$, 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 $\theta_{\rm rms}/\theta_{\rm rms,max}$ is independent of Ra and a power law relation is identified, $i.e.$, $\theta _{\rm rms}/\theta_{\rm rms,max}\sim \left( z / \delta \right)^{0.99\pm 0.01}$, where $z / \delta $ is a dimensionless distance to the boundary ($\delta $ is the thickness of thermal boundary layer). Out of the boundary layer, when $Ra\le 5\times {10}^{9}$, the profiles of $\theta _{\rm rms}/\theta_{\rm rms,max}$ descend, then ascend, and finally drop dramatically as $z / \delta $ increases. While for $Ra\ge 1\times {10}^{10}$, 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 $\langle \theta_{\rm rms}\rangle _{V}$ has a power law dependence on Ra, given by $\langle \theta_{\rm rms}\rangle _{V}{\sim }{Ra}^{-0.14\pm 0.01}$.

Key words: Rayleigh-Bénard, temperature fluctuation, distribution patterns, critical value