Flow organization in laterally unconfined Rayleigh-B\'enard turbulence

TL;DR

This study examines the large-scale circulation in unconfined Rayleigh-Bénard turbulence at high Rayleigh numbers, finding that key properties are similar to confined cases and predicting the transition to turbulence at extremely high Ra.

Contribution

It provides the first detailed analysis of LSC properties in unconfined Rayleigh-Bénard convection at high Ra, showing similarities to confined cases and estimating the critical Ra for boundary layer transition.

Findings

LSC properties are similar to confined domains.

Transition to turbulence predicted at Ra ~ 10^15.

Local heat transport varies with plume regions and Ra.

Abstract

We investigate the large-scale circulation (LSC) of turbulent Rayleigh-B\'enard convection in a large box of aspect ratio $\Gamma =32$ for Rayleigh numbers up to $Ra=10^9$ and at a fixed Prandtl number $Pr=1$. A conditional averaging technique allows us to extract statistics of the LSC even though the number and the orientation of the structures vary throughout the domain. We find that various properties of the LSC obtained here, such as the wall-shear stress distribution, the boundary layer thicknesses and the wind Reynolds number, do not differ significantly from results in confined domains ($\Gamma \approx 1$). This is remarkable given that the size of the structures (as measured by the width of a single convection roll) more than doubles at the highest $Ra$ as the confinement is removed. An extrapolation towards the critical shear Reynolds number of $Re_s^{\textrm{crit}} \approx 420$, at which the boundary layer (BL) typically becomes turbulent, predicts that the transition to the ultimate regime is expected at $Ra_{\textrm{crit}} \approx \mathcal{O}(10^{15})$ in unconfined geometries. This result is in line with the G\"ottingen experimental observations. Furthermore, we confirm that the local heat transport close to the wall is highest in the plume impacting region, where the thermal BL is thinnest, and lowest in the plume emitting region, where the thermal BL is thickest. This trend, however, weakens with increasing $Ra$.