Aspect-ratio dependency of Rayleigh-Bénard convection in box-shaped containers

We report on a numerical study of the aspect-ratio dependency of Rayleigh-Bénard convection, using direct numerical simulations. The investigated domains have equal height and width while the aspect ratio Γ of depth per height is varied between 1/10 and 1. The Rayleigh numbers 12ptminimaldocument RadocumentRa for this study variate between 105 and 109, while the Prandtl number is 12ptminimaldocument Pr = 0. 786documentPr=0. 786. The main focus of the study concerns the dependency of the Nusselt number 12ptminimaldocument NudocumentNu and the Reynolds number 12ptminimaldocument RedocumentRe on 12ptminimaldocument RadocumentRa and Γ. It turns out that due to Γ, differences to the cubic case (i. e. , Γ = 1) in 12ptminimaldocument NudocumentNu of up to 55% and in 12ptminimaldocument RedocumentRe of up to 97% occur, which decrease for increasing 12ptminimaldocument RadocumentRa. In particular for small Γ sudden drops in the 12ptminimaldocument RadocumentRa-scaling of 12ptminimaldocument NudocumentNu and 12ptminimaldocument RedocumentRe appear for 12ptminimaldocument Ra 10⁶documentRa≈106. Further analysis reveals that these correspond to the onset of unsteady motion accompanied by changes in the global flow structure. The latter is investigated by statistical analysis of the heat flux distribution on the bottom and top plates and a decomposition of the instantaneous flow fields into two-dimensional modes. For 12ptminimaldocument RadocumentRa slightly above the onset of unsteady motion (i. e. , 12ptminimaldocument Ra 10⁶documentRa≈106) for all considered Γ ⩽ 1/3 a four-roll structure is present, which corresponds to thermal plumes moving vertically through the domain's center. For 12ptminimaldocument Ra 10⁷documentRa≥107, also for small Γ, a single-roll structure is dominant, in agreement with two-dimensional simulations and experiments at larger 12ptminimaldocument RadocumentRa and 12ptminimaldocument PrdocumentPr.