Logarithmic temperature profiles in the bulk of turbulent Rayleigh-Benard convection for a Prandtl number of 12.3

We report measurements of logarithmic temperature profiles Theta(z, r) = A(r) x ln(z/L) + B(r) in the bulk of turbulent Rayleigh-Benard convection (here Theta is a scaled and time-averaged local temperature in the fluid, z is the vertical and r the radial position, and L is the sample height). Two samples had aspect ratios Gamma equivalent to D/L = 1.00 and 0.50 (where D = 190 mm is the diameter). The fluid was a fluorocarbon with a Prandtl number of Pr = 12.3. The measurements covered the Rayleigh-number range 2 x 10(10) less than or similar to Ra less than or similar to 2 x 10(11) for Gamma = 1.00 and 3 x 10(11) less than or similar to Ra less than or similar to 2 x 10(12) for Gamma = 0.50. In contradistinction to what had been found for Gamma = 0.50 and Pr = 0.78 by Ahlers et al. (Phys. Rev. Lett., vol. 109, 2012, art. 114501; J. Fluid Mech., 2014, in press), the measurements revealed no Ra dependence of the amplitude A(r) of the logarithmic term. Within the experimental resolution, the amplitude was also found to be independent of Gamma. It varied with r in a manner consistent with the function A(xi) = A(1)/root 2 xi - xi(2), where xi equivalent to (R - r)/R with R = D/2 and A(1) similar or equal to 0.0016. The results for A(r) are smaller than those obtained from experiments and direct numerical simulations (Ahlers et al., Phys. Rev. Lett., vol. 109, 2012, art. 114501) at similar values of Ra for Pr = 0.7 and Gamma = 1/2 by a factor that depended slightly upon Ra but was close to 2.