Logarithmic temperature profiles in turbulent Rayleigh-B\'enard convection

TL;DR

This study investigates the temperature profiles in turbulent Rayleigh-Bénard convection, revealing a logarithmic variation with height and analyzing how these profiles change with radial position and state of convection.

Contribution

It provides experimental and numerical evidence of logarithmic temperature profiles in RBC across different states and explores their radial dependence.

Findings

Temperature varies as A*ln(z/L) + B in RBC.

The coefficient A decreases radially towards the sample center.

Logarithmic profiles are present in both classical and ultimate states.

Abstract

We report results for the temperature profiles of turbulent Rayleigh-B\'enard convection (RBC) in the interior of a cylindrical sample of aspect ratio $\Gamma \equiv D/L = 0.50$ ($D$ and $L$ are the diameter and height respectively). Results from experiment over the Rayleigh number range $4\times 10^{12} \alt Ra \alt 10^{15}$ for a Prandtl number $\Pra \simeq 0.8$ and from direct numerical simulation (DNS) at $Ra = 2 \times 10^{12}$ for $\Pra = 0.7$ are presented. We find that the temperature varies as $A*ln(z/L) + B$ where $z$ is the distance from the bottom or top plate. This is the case in the classical as well as in the ultimate state of RBC. From DNS we find that $A$ in the classical state decreases in the radial direction as the distance from the side wall increases and becomes small near the sample center.