Fine-scale statistics of temperature and its derivatives in convective turbulence

We study the fine-scale statistics of temperature and its derivatives in turbulent Rayleigh–Bénard convection. Direct numerical simulations are carried out in a cylindrical cell with unit aspect ratio filled with a fluid with Prandtl number equal to 0.7 for Rayleigh numbers between 107 and 109. The probability density function of the temperature or its fluctuations is found to be always non-Gaussian. The asymmetry and strength of deviations from the Gaussian distribution are quantified as a function of the cell height. The deviations of the temperature fluctuations from the local isotropy, as measured by the skewness of the vertical derivative of the temperature fluctuations, decrease in the bulk, but increase in the thermal boundary layer for growing Rayleigh number, respectively. Similarly to the passive scalar mixing, the probability density function of the thermal dissipation rate deviates significantly from a log-normal distribution. The distribution is fitted well by a stretched exponential form. The tails become more extended with increasing Rayleigh number which displays an increasing degree of small-scale intermittency of the thermal dissipation field for both the bulk and the thermal boundary layer. We find that the thermal dissipation rate due to the temperature fluctuations is not only dominant in the bulk of the convection cell, but also yields a significant contribution to the total thermal dissipation in the thermal boundary layer. This is in contrast to the ansatz used in scaling theories and can explain the differences in the scaling of the total thermal dissipation rate with respect to the Rayleigh number.