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

Abstract

We report measurements of logarithmic temperature profiles Θ(z, r) = A(r) × ln(z/L) + B(r) in the bulk of turbulent Rayleigh-Bénard convection (here Θ is a scaled and timeaveraged 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 Γ ≡ 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 × 10 10 Ra 2 × 10 11 for Γ = 1.00 and 3 × 10 11 Ra 2 × 10 12 for Γ = 0.50. In contradistinction to what had been found for Γ = 0.50 and Pr = 0.78 by Ahlers et al. (Phys. 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 Γ . 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 Γ = 1 2 by a factor that depended slightly upon Ra but was close to 2.

Logarithmic Mean Temperature Profiles and Their Connection to Plume Emissions in Turbulent Rayleigh-Bénard Convection

“…In between exists a wind-sheared region, where the large scale wind shears the boundary layer and the flow is predominantly horizontal close to the plates. The profiles of the mean temperature differ stongly between these regions, which explains the radial dependence of the profiles found in cylindrical experiments [28][29][30]. In these experiments, the amplitude and the quality of the logarithmic fit to the data decreases from the sidewall to the central region of the domain.…”

“…Lateral local mean temperature log profiles have been found in experiments and direct numerical simulations (DNS) down to a Rayleigh number of Ra = 10 12 [28][29][30]; a Ra where the BL is expected to more closely resemble a laminar profile instead of a logarithmic (turbulent) profile. The log profiles were found near the sidewall in the experiments and numerics, with the log amplitude and fit quality decreasing towards the center of the cell.…”

Boundary layer structure in a rough Rayleigh–Bénard cell filled with air

“…This is larger than the increase due to the increase in heating area caused by the roughness (Shen, Tong & Xia 1996;Du & Tong 1998Qiu, Xia & Tong 2005). The result has been extended recently to the case where roughness is added on one plate only (Wei et al 2014).…”

“…The observation of logarithmic profiles of velocity reported at high Rayleigh numbers in this work is direct evidence of the destabilization of the boundary layers. This is not to be confused with the logarithmic profiles of temperature that have been observed above smooth plates, in both the classical and ultimate states (Ahlers et al 2012a;Ahlers, Bodenschatz & He 2014;Wei & Ahlers 2014), and which do not necessarily imply a transition to turbulent boundary layers.…”

Heat-flux enhancement by vapour-bubble nucleation in Rayleigh–Bénard turbulence

“…These thermistors were calibrated against the water-bath thermistors. More details about the use and performance of these thermistors are given by He et al (2014) and Wei & Ahlers (2014) and in appendix B. We estimate that the uncertainty of the vertical position of each thermistor is approximately ±0.01L.…”