Radial boundary layer structure and Nusselt number in Rayleigh-Benard convection

Results from direct numerical simulations for three dimensional Rayleigh-Benard convection in a cylindrical cell of aspect ratio 1/2 and Pr=0.7 are presented. They span five decades of Ra from $2\times 10^6$ to $2 \times10^{11}$. Good numerical resolution with grid spacing $\sim$ Kolmogorov scale turns out to be crucial to accurately calculate the Nusselt number, which is in good agreement with the experimental data by Niemela et al., Nature, 404, 837 (2000). In underresolved simulations the hot (cold) plumes travel further from the bottom (top) plate than in the fully resolved case, because the thermal dissipation close to the sidewall (where the grid cells are largest) is insufficient. We compared the fully resolved thermal boundary layer profile with the Prandtl-Blasius profile. We find that the boundary layer profile is closer to the Prandtl Blasius profile at the cylinder axis than close to the sidewall, due to rising plumes in that region.