We studied the properties of the large-scale circulation (LSC) in turbulent Rayleigh-Benard (RB) convection by using results from direct numerical simulations in which we placed a large number of numerical probes close to the sidewall. The LSC orient
ation is determined by either a cosine or a polynomial fit to the azimuthal temperature or azimuthal vertical velocity profile measured with the probes. We study the LSC in Gamma=D/L=1/2 and Gamma=1 samples, where D is the diameter and L the height. For Pr=6.4 in an aspect ratio Gamma=1 sample at $Ra=1times10^8$ and $5times10^8$ the obtained LSC orientation is the same, irrespective of whether the data of only 8 or all 64 probes per horizontal plane are considered. In a Gamma=1/2 sample with $Pr=0.7$ at $Ra=1times10^8$ the influence of plumes on the azimuthal temperature and azimuthal vertical velocity profiles is stronger. Due to passing plumes and/or the corner flow the apparent LSC orientation obtained using a cosine fit can result in a misinterpretation of the character of the large-scale flow. We introduce the relative LSC strength, which we define as the ratio between the energy in the first Fourier mode and the energy in all modes that can be determined from the azimuthal temperature and azimuthal vertical velocity profiles, to further quantify the large-scale flow. For $Ra=1times10^8$ we find that this relative LSC strength is significantly lower in a Gamma=1/2 sample than in a Gamma=1 sample, reflecting that the LSC is much more pronounced in a Gamma=1 sample than in a Gamma=1/2 sample. The determination of the relative LSC strength can be applied directly to available experimental data to study high Rayleigh number thermal convection and rotating RB convection.
Results from direct numerical simulation for three-dimensional Rayleigh-Benard convection in samples of aspect ratio $Gamma=0.23$ and $Gamma=0.5$ up to Rayleigh number $Ra=2times10^{12}$ are presented. The broad range of Prandtl numbers $0.5<Pr<10$ i
s considered. In contrast to some experiments, we do not see any increase in $Nu/Ra^{1/3}$, neither due to $Pr$ number effects, nor due to a constant heat flux boundary condition at the bottom plate instead of constant temperature boundary conditions. Even at these very high $Ra$, both the thermal and kinetic boundary layer thicknesses obey Prandtl-Blasius scaling.
