  We numerically investigate the structures of the near-plate temperature
profiles close to the bottom and top plates of turbulent Rayleigh-B\'{e}nard
flow in a cylindrical sample at Rayleigh numbers Ra=10^8 to Ra=2\times10^{12}
and Prandtl numbers Pr=6.4 and Pr=0.7 with the dynamical frame method [Q. Zhou
and K.-Q. Xia, Phys. Rev. Lett. 104, 104301 (2010)] thus extending previous
results for quasi-2-dimensional systems to 3D systems for the first time. The
dynamical frame method shows that the measured temperature profiles in the
spatially and temporally local frame are much closer to the temperature profile
of a laminar, zero-pressure gradient boundary layer according to Pohlhausen
than in the fixed reference frame. The deviation between the measured profiles
in the dynamical reference frame and the laminar profiles increases with
decreasing Pr, where the thermal BL is more exposed to the bulk fluctuations
due to the thinner kinetic BL, and increasing Ra, where more plumes are passing
the measurement location.
