The large-scale footprint in small-scale Rayleigh-B\'enard turbulence

TL;DR

This study investigates the relationship between small-scale turbulence and large-scale flow structures in Rayleigh-Bénard convection at high Rayleigh number, revealing significant correlations and variations in turbulence properties linked to large-scale circulation.

Contribution

It provides the first detailed analysis of how small-scale turbulence characteristics vary with large-scale flow in high Rayleigh number convection, using large aspect ratio simulations.

Findings

Small-scale turbulence correlates with large-scale flow variations.

Enhanced temperature fluctuations occur in plume impacting regions.

Local wavenumbers are higher near plume emitting regions.

Abstract

Turbulent convection systems are known to give rise to prominent large scale circulation. At the same time, the `background' (or `small-scale') turbulence is also highly relevant and e.g. carries the majority of the heat transport in the bulk of the flow. Here, we investigate how the small-scale turbulence is interlinked with the large-scale flow organization of Rayleigh-B\'enard convection. Our results are based on a numerical simulation at Rayleigh number $Ra = 10^8$ in a large aspect ratio ($\Gamma=32$) cell to ensure a distinct scale separation. We extract local magnitudes and wavenumbers of small scale turbulence and find significant correlation of large scale variations in these quantities with the large-scale signal. Most notably, we find stronger temperature fluctuations and increased small scale transport (on the order of $10\%$ of the global Nusselt number $Nu$) in plume impacting regions and opposite trends in the plume emitting counterparts. This concerns wall distances up to $2\delta_\theta$ (thermal boundary layer thickness). Local wavenumbers are generally found to be higher on the plume emitting side compared to the impacting one. A second independent approach by means of conditional averages confirmed these findings and yields additional insight into the large-scale variation of small-scale properties. Our results have implications for modelling small-scale turbulence.