Boundary layers in thermal convection are fluctuation-dominated

We study the dynamics of thermal and momentum boundary layers in three-dimensional direct numerical simulations of Rayleigh-Bénard convection for the Rayleigh number range 10^5 ≤ Ra ≤ 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 an infinitely extended system. We observe that upon canonical use of long-time and area averages, a coherent mean flow is practically absent. Instead, the velocity field close to the wall is a collection of differently oriented local shear patches interspersed by shear-free, incoherent flow regions. These shear patches occupy an area fraction of approximately 40% for all Ra. Rather than resulting in a pronounced mean with small fluctuations about it, the velocity field is dominated by strong fluctuations of all three components around a non-existent or weak mean. This feature is particularly pronounced for Ra ≥ 10^9. We discuss the consequences of these observations for convection layers with larger aspect ratios, including boundary layer instabilities and the resulting turbulent heat transport.