Logarithmic temperature profiles in the bulk of turbulent Rayleigh–Bénard convection for a Prandtl number of 12.3

We report measurements of logarithmic temperature profiles $ #1{} #1{ {#1}} ≤ = ≤ = ≥ = ≥ = {Pr} {Fr} {Re} (z,r) = A(r)× ln (z/L) + B(r)$ in the bulk of turbulent Rayleigh–Bénard convection (here $ $ 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 $ ≡ 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 $2× 10¹⁰ Ra 2× 10¹¹$ for $ = 1.00$ and $3× 10¹¹ Ra 2× 10¹²$ for $ = 0.50$ . In contradistinction to what had been found for $ = 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 $ $ . It varied with $r$ in a manner consistent with the function $A(ξ ) = A_1/√2ξ - ξ ^2$ , where $ξ ≡ (R-r)/R$ with $R=D/2$ and $A_1 0.0016$ . 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 $ = 1/2$ by a factor that depended slightly upon $Ra$ but was close to $2$ .