Prandtl-Blasius temperature and velocity boundary layer profiles in turbulent Rayleigh-Benard convection*

The shapes of the velocity and temperature profiles near the horizontal conducting plates' center regions in turbulent Rayleigh-Benard convection are studied numerically and experimentally over the Rayleigh number range spanning from 10$^8$ to 3x10$^{11}$ and the Prandtl number range 0.7$\sim $5.4. The results show that both the temperature and velocity profiles well agree with the classical Prandtl-Blasius laminar boundary-layer profiles, if they are re-sampled in the respective dynamical reference frames that fluctuate with the instantaneous thermal and velocity boundary-layer thicknesses. The study further shows that the Prandtl-Blasius boundary layer in turbulent thermal convection not only holds in a time-averaged sense, but is also valid in an instantaneous sense most of the time.