  We studied the properties of the large-scale circulation (LSC) in turbulent
Rayleigh-B\'enard (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 orientation 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 $Ra=1\times10^8$ and $5\times10^8$ 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 $Ra=1\times10^8$ 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
$Ra=1\times10^8$ 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.
