A quantitative theory is developed for the vertical mean temperature profile (MTP) in turbulent Rayleigh-Benard convection (RBC), which explains the recent experimental and numerical observations of a logarithmic law by Ahlers et al. [1]. A multi-layer model is formulated and quantified, whose predictions agree with DNS and experimental data for the Rayleigh-number (Ra) over seven decades. In particular, a thermal buffer layer follows a 1/7 scaling like the previously postulated mixing zone [2], and yields a Ra-dependent log law constant. A new parameterization of N u(Ra) dependence is proposed, based on the present multi-layer quantification of the bulk MTP. .

The logarithmic law of mean temperature profile has been observed in different regions in Rayleigh-Bénard turbulence. However, how thermal plumes correlate to the log law of temperature and how the velocity profile changes with pressure gradient are not fully understood. Here, we performed three-dimensional simulations of Rayleigh-Bénard turbulence in a slim-box without the front and back walls with aspect ratio, width : depth : height = L : D : H = 1 : 1/6 : 1 (respectively corresponding to x, y and z coordinates), in the Rayleigh number Ra = [1 × 10 8 , 1 × 10 10 ] for Prandtl number Pr = 0.7. To investigate the structures of the viscous and thermal boundary layers, we examined the velocity profiles in the streamwise and vertical directions (i.e. U and W) along with the mean temperature profile throughout the plume-impacting, plumeejecting, and wind-shearing regions. The velocity profile is successfully quantified by a two-layer function of a stress length,, as proposed by She et al. (She 2017), though neither a Prandtl-Blasius-Pohlhausen type nor the log-law is seen in the viscous boundary layer. In contrast, the temperature profile in the plume-ejecting region is logarithmic for all simulated cases, being attributed to the emission of thermal plumes. The coefficient of the temperature log-law, A can be described by composition of the thermal stress length * θ0 and the thicknesses of thermal boundary layer z * sub and z * bu f , i.e. A z * sub / * θ0 z * bu f 3/2 . The adverse pressure gradient responsible for turning the wind direction contributes to thermal plumes gathering at the ejecting region and thus the log-law of temperature profile. The Nusselt number scaling and local heat flux of the present simulations are consistent with previous results in confined cells. Therefore, the slim-box RBC is a preferable system for investigating in-box kinetic and thermal structures of turbulent convection with the large-scale circulation on a fixed plane.

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