Two-dimensional Rayleigh-Bénard convection in an annulus with radial gravity

Thermal convection in annulus domains with gravitational acceleration g that decreases with the radial coordinate r is commonly observed in astrophysical and geophysical flows. In these systems, the annulus radius ratio η is a control parameter, in addition to the Rayleigh number Ra and Prandtl number Pr. To study the effect of η, we conduct direct numerical simulations of Rayleigh-Bénard convection in a two-dimensional annulus. Keeping the inner shell hot and the outer shell cold, η is varied from 0.2 to 0.8, Ra from 10⁷ to 10¹⁰, and Pr is kept constant at unity. The gravity profile assigned is g ∼ 1/r. For some parameter ranges, we observe zonal flows, which were not previously seen in systems without imposed external rotation. We demonstrate how the disproportionately strong inner plumes cause the zonal flow. Interestingly, the asymmetry in the properties of the inner and outer thermal boundary layers (TBLs) follows different scaling laws than those previously observed in three-dimensional systems. We develop scaling laws to quantify the asymmetry in the TBL widths and temperature drops in the inner and outer shells. By conditionally averaging the flow fields, we isolate the inner and outer plumes in the system and illustrate how the system’s curvature affects the boundary layer profiles.