title: Logarithmic temperature profiles in turbulent Rayleigh-Bénard convection.
abstract: We report results for the temperature profiles of turbulent Rayleigh-Bénard convection (RBC) in the interior of a cylindrical sample of aspect ratio Γ≡D/L=0.50 (D and L are the diameter and height, respectively). Both in the classical and in the ultimate state of RBC we find that the temperature varies as A×ln(z/L)+B, where z is the distance from the bottom or top plate. In the classical state, the coefficient A decreases in the radial direction as the distance from the side wall increases. For the ultimate state, the radial dependence of A has not yet been determined. These findings are based on experimental measurements over the Rayleigh-number range 4×10(12)≲Ra≲10(15) for a Prandtl number Pr≃0.8 and on direct numerical simulation at Ra=2×10(12), 2×10(11), and 2×10(10), all for Pr=0.7.
authors.affiliation: Department of Physics, University of California, Santa Barbara, California 93106, USA.
authors.forename: Guenter
authors.initials: G
authors.lastname: Ahlers
authors.forename: Eberhard
authors.initials: E
authors.lastname: Bodenschatz
authors.forename: Denis
authors.initials: D
authors.lastname: Funfschilling
authors.forename: Siegfried
authors.initials: S
authors.lastname: Grossmann
authors.forename: Xiaozhou
authors.initials: X
authors.lastname: He
authors.forename: Detlef
authors.initials: D
authors.lastname: Lohse
authors.forename: Richard J A M
authors.initials: RJ
authors.lastname: Stevens
authors.forename: Roberto
authors.initials: R
authors.lastname: Verzicco