Boundary layer fluctuations and their effects on mean and variance temperature profiles in turbulent Rayleigh-Bénard 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)PRLTAO0031-900710.1103/PhysRevLett.114.114302]. 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.