Boundary layer fluctuations in turbulent Rayleigh-Benard convection

We report a combined experimental and numerical study of the effect of boundary layer (BL) fluctuations on the scaling properties of the mean temperature profile theta(z) and temperature variance profile eta(z) in turbulent Rayleigh-Benard convection in a thin disk cell and an upright cylinder of aspect ratio unity. Two scaling regions are found with increasing distance z away from the bottom conducting plate. In the BL region, the measured theta(z) and eta(z) are found to have the scaling forms theta(z/delta) and eta(z/delta), respectively, with varying thermal BL thickness delta. The functional forms of the measured theta(z/delta) and eta(z/delta) in the two convection cells agree well with the recently derived BL equations by Shishkina et al. (Phys. Rev. Lett., vol. 114, 2015, 114302) and by Wang et al. (Phys. Rev. Fluids, vol. 1, 2016, 082301). In the mixing zone outside the BL region, the measured theta(z) remains approximately constant, whereas the measured eta(z) is found to scale with the cell height H in the two convection cells and follows a power law, eta(z) similar to (z/H)(is an element of), with the obtained values of is an element of being close to -1. Based on the experimental and numerical findings, we derive a new equation for eta(z) in the mixing zone, which has a power-law solution in good agreement with the experimental and numerical results. Our work demonstrates that the effect of BL fluctuations can be adequately described by the velocity-temperature correlation functions and the new BL equations capture the essential physics.