No sustained mean velocity in the boundary region of plane thermal convection
Roshan J. Samuel, Mathis Bode, Janet D. Scheel, Katepalli R. Sreenivasan, Jörg Schumacher
Abstract
We study the dynamics of thermal and momentum boundary regions in three-dimensional direct numerical simulations of Rayleigh–Bénard convection for the Rayleigh-number range $10^5\leq Ra \leq 10^{11}$ 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 flow 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.