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

We study the characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh-Benard convection in a square cavity by direct numerical simulations. The Rayleigh number range is 1 x 10(8) <= Ra <= 1 x 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 (rms)/theta (rms,max) is independent of Ra and a power law relation is identified, i.e., theta (rms)/theta (rms,max)similar to (z / delta)(0.99 +/- 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 <= 5 x 10(9), the profiles of theta (rms)/theta (rms,max) descend, then ascend, and finally drop dramatically as z/delta increases. While for Ra >= 1 x 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 theta (rms)( V ) has a power law dependence on Ra, given by theta (rms)( V ) similar to Ra (-0.14 +/- 0.01).