Logarithmic temperature profiles in the ultimate regime of thermal convection

TL;DR

This paper develops a theoretical framework for logarithmic temperature profiles in highly turbulent thermal convection within a Rayleigh-Benard cell, comparing predictions with recent experimental data.

Contribution

It introduces a theoretical model for logarithmic temperature profiles in the ultimate regime of thermal convection and analyzes their physical interpretation and radial dependence.

Findings

Theoretical parameters match experimental profiles.

Profiles exhibit logarithmic dependence on radial position.

Physical interpretation of the log-profile parameters is provided.

Abstract

We report on the theory of logarithmic temperature profiles in very strongly developed thermal convection in the geometry of a Rayleigh-Benard cell with aspect ratio one and discuss the degree of agreement with the recently measured profiles in the ultimate state of very large Rayleigh number flow. The parameters of the log-profile are calculated and compared with the measure ones. Their physical interpretation as well as their dependence on the radial position are discussed.