Large-scale mean patterns in turbulent convection

TL;DR

This study reveals persistent large-scale mean flow patterns in turbulent Rayleigh-Bénard convection at high Rayleigh numbers, showing their robustness and estimating turbulent transport properties through averaging and modeling.

Contribution

It demonstrates the existence of large-scale mean flow patterns in turbulent convection at high Rayleigh numbers and estimates their turbulent transport parameters using Boussinesq closure.

Findings

Large-scale patterns persist at high Rayleigh numbers in turbulent convection.

Turbulent Rayleigh number for mean patterns is within the spiral defect chaos range.

Mean flow patterns are robust to side wall forcing under high turbulence levels.

Abstract

Large-scale patterns, which are well-known from the spiral defect chaos regime of thermal convection at Rayleigh numbers $Ra < 10^4$, continue to exist in three-dimensional numerical simulations of turbulent Rayleigh-B\'{e}nard convection in extended cylindrical cells with an aspect ratio $\Gamma=50$ and $Ra>10^5$. They are uncovered when the turbulent fields are averaged in time and turbulent fluctuations are thus removed. We apply the Boussinesq closure to estimate turbulent viscosities and diffusivities, respectively. The resulting turbulent Rayleigh number $Ra_{\ast}$, that describes the convection of the mean patterns, is indeed in the spiral defect chaos range. The turbulent Prandtl numbers are smaller than one with $0.2\le Pr_{\ast}\le 0.4$ for Prandtl numbers $0.7 \le Pr\le 10$. Finally, we demonstrate that these mean flow patterns are robust to an additional finite-amplitude side wall-forcing when the level of turbulent fluctuations in the flow is sufficiently high.