Large-scale patterns in Rayleigh–Bénard convection

Rayleigh–Bénard convection at large Rayleigh number is characterized by the presence of intense, vertically moving plumes. Both laboratory and numerical experiments reveal that the rising and descending plumes aggregate into separate clusters so as to produce large-scale updrafts and downdrafts. The horizontal scales of the aggregates reported so far have been comparable to the horizontal extent of the containers, but it has not been clear whether that represents a limitation imposed by domain size. In this work, we present numerical simulations of convection at sufficiently large aspect ratio to ascertain whether there is an intrinsic saturation scale for the clustering process when that ratio is large enough. From a series of simulations of Rayleigh–Bénard convection with Rayleigh numbers between 105 and 108 and with aspect ratios up to 12π, we conclude that the clustering process has a finite horizontal saturation scale with at most a weak dependence on Rayleigh number in the range studied.