Heat transport and temperature profiles in turbulent convection of fluids heated locally from below

We measured mean-temperature profiles in turbulent convection of fluids heated locally from below in a cylindrical sample with aspect ratio $\Gamma \equiv D/L = 1.00$ (D= 24.1 cm is the diameter and L the height). Heating was near the bottom-plate center over a circular area of diameter $D_h/D = 0.053$, while cooling was over the entire top plate. Rayleigh- and Prandtl-number ranges were $6\times10^{9} \leq Ra \leq 2\times 10^{12}$ and $5 \le Pr \le 12.3$. The measurements were at radial distances $r$ from the vertical center line with $\xi \equiv 1 - 2r/D = 1.00$ (along the center line) and $\xi=0.135$ (near the side wall) and at several vertical locations $z/L$. The center temperature was well below the mean temperature. Near the side wall the mean temperature varied logarithmically with $z/L$ near the bottom and $1-z/L$ near the top plate. Along the center line such a log layer was found near the bottom plate, but not near the top plate.