A Comparison of Turbulent Thermal Convection Between Conditions of Constant Temperature and Constant Flux

TL;DR

This study uses high-resolution simulations to compare turbulent heat transport in Rayleigh-Bénard convection under constant temperature and constant flux boundary conditions, revealing similar scaling laws and flow dynamics at high Rayleigh numbers.

Contribution

It provides the first detailed comparison of turbulent convection under fixed flux and fixed temperature conditions at very high Rayleigh numbers, showing their asymptotic similarity.

Findings

Heat transport follows a power law with similar scaling in both conditions.

Flow dynamics and temperature profiles are indistinguishable at high Rayleigh numbers.

Results align with recent three-dimensional simulation findings.

Abstract

We report the results of high resolution direct numerical simulations of two-dimensional Rayleigh-B\'enard convection for Rayleigh numbers up to $\Ra=10^{10}$ in order to study the influence of temperature boundary conditions on turbulent heat transport. Specifically, we considered the extreme cases of fixed heat flux (where the top and bottom boundaries are poor thermal conductors) and fixed temperature (perfectly conducting boundaries). Both cases display identical heat transport at high Rayleigh numbers fitting a power law $\Nu \approx 0.138 \times \Ra^{.285}$ with a scaling exponent indistinguishable from $2/7 = .2857...$ above $\Ra = 10^{7}$. The overall flow dynamics for both scenarios, in particular the time averaged temperature profiles, are also indistinguishable at the highest Rayleigh numbers. The findings are compared and contrasted with results of recent three-dimensional simulations.