Heat and momentum transfer in Rayleigh-Bénard convection within a two-dimensional annulus under radial gravity

We conduct direct numerical simulations (DNS) to explore Rayleigh-B & eacute;nard convection (RBC) within a twodimensional (2D) annular domain, where the radius ratio (n) plays a crucial role in shaping the flow dynamics. In this study, we examine how varying n impacts the convection patterns when the inner shell is maintained at a higher temperature than the outer shell. Our simulations cover abroad range of radius ratios (n = 0.2 to 0.8) and Rayleigh numbers (Ra = 10 7 to 10 10 ), with a fixed Prandtl number of unity. To generate the buoyancy force, a gravity profile proportional to g similar to 1/r is applied, reflecting the radial dependence. Our findings reveal a distinct asymmetry in the flow field, which we further analyze by isolating the plume structures through conditional averaging. This approach allows us to examine how these structures influence the boundary layer behavior. Additionally, with the applied gravity profile, we derive exact relations between the driving forces and the kinetic and thermal dissipation rates. Using the Grossmann-Lohse theory, we incorporate these exact relations to determine prefactors specific to each n value, offering new insights into how geometry influences convection in this non-rotating cylindrical system.