Turbulent boundary layers in thermal convection at moderately high Rayleigh numbers

Abstract

In this work, we perform direct numerical simulations of Rayleigh–Bénard convection in a two-dimensional confined square cell for Rayleigh numbers (Ra) from 109 to 1013 and a Prandtl number (Pr) of 0.7. In contrast to a previous study in a periodic box conducted by Zhu et al. [Phys. Rev. Lett. 120, 144502 (2018)], our simulations apply two adiabatic sidewalls. In particular, boundary layer structures near the heating plates are examined using both mean velocity and temperature profiles in the impacting, shearing, and ejecting regions of the plumes. After an appropriate normalization using the wall units, the friction Reynolds numbers of our simulations exceed the critical value of 200 and follow Reτ∼Ra0.323, and we also observe the logarithmic mean velocity profiles (with the slope κv≈0.35) in the shearing regions and logarithmic mean temperature profiles (with the slope κθ≈2) in the ejecting regions. These logarithmic behaviors indicate that both the thermal and momentum boundary layers may have entered the fully developed turbulent state. However, for the Nusselt number (Nu), our data still follow the trend of classical 1/3 scaling, differing from the ultimate state reported before but agreeing with the three-dimensional results obtained by Iyer et al. [PNAS 117, 14 (2020)] for confined cells.