Heat transport enhancement in confined Rayleigh-Bénard convection feels the shape of the container

Moderate spatial confinement enhances the heat transfer in turbulent Rayleigh-Bénard (RB) convection [Chong et al., PRL 115, 264503 (2015)]. Here, by performing direct numerical simulations, we answer the question how the shape of the RB cell affects this enhancement. We compare three different geometries: a box with rectangular base (i.e., stronger confined in one horizontal direction), a box with square base (i.e., equally confined in both horizontal directions), and a cylinder (i.e., symmetrically confined in the radial direction). In all cases the confinement can be described by the same confinement parameter Γ-1, given as height-over-width aspect ratio. The explored parameter range is 1≤Γ-1≤64, 107≤Ra≤1010 for the Rayleigh number, and a Prandtl number of Pr=4.38. We find that both the optimal confinement parameter Γ-1opt for maximal heat transfer and the actual heat transfer enhancement strongly depend on the cell geometry. The differences can be explained by the formation of different vertically-coherent flow structures within the specific geometries. The enhancement is largest in the cylindrical cell, owing to the formation of a domain-spanning flow structure at the optimal confinement parameter Γ-1opt.