Supergranule aggregation: a Prandtl number-independent feature of constant heat flux-driven convection flows

Supergranule aggregation, i.e., the gradual aggregation of convection cells to horizontally extended networks of flow structures, is a unique feature of constant heat flux-driven turbulent convection. In the present study, we address the question if this mechanism of self-organisation of the flow is present for any fluid. Therefore, we analyse three-dimensional Rayleigh-Bénard convection at a fixed Rayleigh number $\text{Ra}\approx 2.0\times {10}^5$ across $4$ orders of Prandtl numbers $\mathrm{Pr}\in [{10}^{-2},{10}^2]$ by means of direct numerical simulations in horizontally extended periodic domains with aspect ratio $\mathrm{\Gamma }=60$. Our study confirms the omnipresence of the mechanism of supergranule aggregation for the entire range of investigated fluids. Moreover, we analyse the effect of $\mathrm{Pr}$ on the global heat and momentum transport, and clarify the role of a potential stable stratification in the bulk of the fluid layer. The ubiquity of the investigated mechanism of flow self-organisation underlines its relevance for pattern formation in geophysical and astrophysical convection flows, the latter of which are often driven by prescribed heat fluxes.