Boundary layer fluctuations and their effects on mean and variance temperature profiles in turbulent Rayleigh-Benard convection

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