Turbulent thermal superstructures in Rayleigh-B\'enard convection

TL;DR

This paper reports the discovery of large-scale, long-lived thermal superstructures in highly turbulent Rayleigh-Bénard convection at high Rayleigh numbers, using direct numerical simulations in large aspect ratio domains.

Contribution

It demonstrates the existence and properties of thermal superstructures in turbulent convection at high Rayleigh numbers and analyzes how various statistical measures converge with aspect ratio.

Findings

Thermal superstructures extend six to seven times the height of the domain.

Superstructure size is independent of Rayleigh number in the studied regime.

Convergence of statistical quantities occurs at different aspect ratios, with some requiring very large domains.

Abstract

We report the observation of superstructures, i.e.\ very large-scale and long living coherent structures in highly turbulent Rayleigh-B\'enard convection up to Rayleigh $Ra=10^9$. We perform direct numerical simulations in horizontally periodic domains with aspect ratios up to $\Gamma=128$. In the considered $Ra$ number regime the thermal superstructures have a horizontal extend of six to seven times the height of the domain and their size is independent of $Ra$. Many laboratory experiments and numerical simulations have focused on small aspect ratio cells in order to achieve the highest possible $Ra$. However, here we show that for very high $Ra$ integral quantities such as the Nusselt number and volume averaged Reynolds number only converge to the large aspect ratio limit around $\Gamma \approx 4$, while horizontally averaged statistics such as standard deviation and kurtosis converge around $\Gamma \approx 8$, and the integral scale converges around $\Gamma \approx 32$, and the peak position of the temperature variance and turbulent kinetic energy spectra only around $\Gamma \approx 64$.