No sustained mean velocity in the boundary region of plane thermal convection

TL;DR

This study uses high-resolution simulations to show that in large-aspect-ratio Rayleigh-Bénard convection, the boundary region lacks a sustained mean velocity, being dominated by fluctuating, incoherent shear patches rather than a coherent flow.

Contribution

It provides new insights into the boundary layer dynamics in large-aspect-ratio convection, highlighting the absence of a sustained mean velocity and the prevalence of incoherent shear regions.

Findings

Velocity fluctuations exceed mean velocities by up to 100 times.

Incoherent shear-free regions occupy about 60% of the area.

No sustained mean flow is observed in the boundary region.

Abstract

We study the dynamics of thermal and momentum boundary regions in three-dimensional direct numerical simulations of Rayleigh-B\'enard convection for the Rayleigh number range $10^5 \le Ra \le 10^{11}$ and $Pr=0.7$. Using a Cartesian slab with horizontal periodic boundary conditions and an aspect ratio of 4, we obtain statistical homogeneity in the horizontal $x$- and $y$-directions, thus approximating best an extended convection layer relevant for most geo- and astrophysical flow applications. We observe upon canonical use of combined long-time and area averages, with averaging periods of at least 100 free-fall times, that a global coherent mean flow is practically absent and that the magnitude of the velocity fluctuations is larger than the mean by up to 2 orders of magnitude. The velocity field close to the wall is a collection of differently oriented local shear-dominated flow patches interspersed by extensive shear-free incoherent regions which can be as large as the whole cross section, unlike for a closed cylindrical convection cell of aspect ratio of the order 1. The incoherent regions occupy a $60\%$ area fraction for all Rayleigh numbers investigated here. Rather than resulting in a pronounced mean with small fluctuations about such a mean, as found in small-aspect-ratio convection, the velocity field is dominated by strong fluctuations of all three components around a non-existent or weak mean. We discuss the consequences of these observations for convection layers with larger aspect ratios, including boundary layer instabilities and the resulting turbulent heat transport.