Turbulent superstructures in Rayleigh-B\'enard convection

TL;DR

This paper investigates large-scale turbulent superstructures in Rayleigh-Bénard convection through numerical simulations across various Prandtl and Rayleigh numbers, revealing their characteristic scales, dynamics, and correlation with boundary layer behavior.

Contribution

It provides a detailed analysis of turbulent superstructures, identifying their scales and connection to boundary layer dynamics, offering insights into simplified modeling in geophysical and astrophysical contexts.

Findings

Superstructures are characterized by specific scales and times.

Large-scale patterns correlate with boundary layer plume clustering.

Scale separation enables simplified descriptions of turbulence.

Abstract

Turbulent Rayleigh-B\'enard convection displays a large-scale order in the form of rolls and cells on lengths larger than the layer height once the fluctuations of temperature and velocity are removed. These turbulent superstructures are reminiscent of the patterns close to the onset of convection. They are analyzed by numerical simulations of turbulent convection in fluids at different Prandtl number ranging from 0.005 to 70 and for Rayleigh numbers up to $10^7$. For each case, we identify characteristic scales and times that separate the fast, small-scale turbulent fluctuations from the gradually changing large-scale superstructures. The characteristic scales of the large-scale patterns, which change with Prandtl and Rayleigh number, are also found to be correlated with the boundary layer dynamics, and in particular the clustering of thermal plumes at the top and bottom plates. Our analysis suggests a scale separation and thus the existence of a simplified description of the turbulent superstructures in geo- and astrophysical settings.