Rare massive eruption of thermal plumes causes random reversals of the large-scale flow in turbulent thermal convection.

We report simultaneous measurements of the mean temperature profile θ(z) and temperature variance profile η(z) near the lower conducting plate of a specially designed quasi-two-dimensional cell for turbulent Rayleigh-Bénard convection. The measured θ(z) is found to have a universal scaling form θ (z/δ) with varying thermal boundary layer (BL) thickness δ, and its functional form agrees well with the recently derived BL equation by Shishkina et al. [Phys. Rev. Lett. 114, 114302 (2015)]. The measured η(z), on the other hand, is found to have a scaling form η(z/δ) only in the near-wall region with z/δ 2. Based on the experimental findings, we derive a BL equation for η(z/δ), which is in good agreement with the experimental results. These BL equations thus provide a common framework for understanding the effect of BL fluctuations.

We report a systematic study of spatial variations of the probability density function (PDF) $P(\unicode[STIX]{x1D6FF}T)$ for temperature fluctuations $\unicode[STIX]{x1D6FF}T$ in turbulent Rayleigh–Bénard convection along the central axis of two different convection cells. One of the convection cells is a vertical thin disk and the other is an upright cylinder of aspect ratio unity. By changing the distance $z$ away from the bottom conducting plate, we find the functional form of the measured $P(\unicode[STIX]{x1D6FF}T)$ in both cells evolves continuously with distinct changes in four different flow regions, namely, the thermal boundary layer, mixing zone, turbulent bulk region and cell centre. By assuming temperature fluctuations in different flow regions are all made from two independent sources, namely, a homogeneous (turbulent) background which obeys Gaussian statistics and non-uniform thermal plumes with an exponential distribution, we obtain the analytic expressions of $P(\unicode[STIX]{x1D6FF}T)$ in four different flow regions, which are found to be in good agreement with the experimental results. Our work thus provides a unique theoretical framework with a common set of parameters to quantitatively describe the effect of turbulent background, thermal plumes and their spatio-temporal intermittency on the temperature PDF $P(\unicode[STIX]{x1D6FF}T)$ .