Boundary layer analysis in turbulent Rayleigh-Bénard convection in air: Experiment versus simulation

Abstract

We report measurements and numerical simulations of the three-dimensional velocity and temperature fields in turbulent Rayleigh-B\'enard convection in air. Highly resolved velocity and temperature measurements inside and outside the boundary layers have been directly compared with equivalent data obtained in direct numerical simulations (DNSs). This comparison comprises a set of two Rayleigh numbers at $\mathrm{Ra}=3\ifmmode\times\else\texttimes\fi{}{10}^{9}$ and $3\ifmmode\times\else\texttimes\fi{}{10}^{10}$ and a fixed aspect ratio; this is the ratio between the diameter and the height of the Rayleigh-B\'enard cell of $\ensuremath{\Gamma}=1$. We find that the measured velocity data are in excellent agreement with the DNS results while the temperature data slightly differ. In particular, the measured mean temperature profile does not show the linear trend as seen in the DNS data, and the measured gradients at the wall are significantly higher than those obtained from the DNS. Both viscous and thermal boundary layer thickness scale with respect to the Rayleigh number as ${\ensuremath{\delta}}_{v}\ensuremath{\sim}{\mathrm{Ra}}^{\ensuremath{-}0.24}$ and ${\ensuremath{\delta}}_{\ensuremath{\theta}}\ensuremath{\sim}{\mathrm{Ra}}^{\ensuremath{-}0.24}$, respectively.