Turbulent superstructures in Rayleigh-B\xe9nard convection

Ambrish Pandey,Janet D Scheel,Jörg Schumacher

doi:10.1038/s41467-018-04478-0

Ambrish Pandey, Janet D Scheel + Show 1 more

Open Access

https://doi.org/10.1038/s41467-018-04478-0

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Abstract

Turbulent Rayleigh-Bénard 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. Here we report numerical simulations of turbulent convection in fluids at different Prandtl number ranging from 0.005 to 70 and for Rayleigh numbers up to 107. 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 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.

Highlights

Turbulent Rayleigh-Bénard 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
Rayleigh-Bénard convection (RBC) is the simplest turbulent convection flow evolving in a planar fluid layer of height H that is uniformly heated with a temperature T = Tb from below and cooled from above with T = Tt such that Tb – Tt = ΔT > 0
Roll and cell patterns of the velocity field in a turbulent RBC for Ra ≳ 105 that are reminiscent of the flow structures in the weakly nonlinear regime at Ra ≲ 5 × 103 have been observed in recent direct numerical simulations (DNS) at Pr ≳ 119, 20

Summary

Introduction

Turbulent Rayleigh-Bénard 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. This plume formation process is determined by two aspects: (i) the molecular diffusivity of the temperature field (and the resulting differences in the thicknesses of thermal and viscous boundary layers) and (ii) the typical variation scale of the horizontal velocity field near the walls that forms the plume ridges by temperature field advection.

Results

Conclusion