Hierarchical network of thermal plumes and their dynamics in turbulent Rayleigh–Bénard convection

Abstract

The link between characteristic coherent structures and their statistical properties in turbulent flows remains largely unclear and is thus a central bottleneck for a better understanding of turbulent flows. Here, we demonstrate this link for the important problem of thermal convection. We show how the hierarchical plume network in the near-wall region of the flow, which becomes increasingly sparse with increasing distance away from the wall, is connected to the marginal stability of the thermal boundary layer and the resulting global heat transport. Our results, which are based on a series of direct numerical simulations for Rayleigh numbers up to Ra = 1011 in a relatively shallow layer, suggest a highly fluctuating thermal boundary layer that is composed of local building blocks in terms of plumes, which are the essential drivers of turbulent heat transport. These thermal plumes are found in a dynamically perpetual process of formation and aggregation that can be described, particularly well for Rayleigh numbers Ra ≳ 109, by a von Smoluchowski equation resulting in a gamma distribution of the local plume spacing, consistent with measurements. Similarity manifests with respect to the horizontal extension of the network, the vertical hierarchical plume clustering away from the wall and the number of plumes, over an order of magnitude of the thermal boundary layer thickness. Our findings suggest the dominance of dynamical local processes near the wall, rather than a global boundary layer instability.