Turbulent spherical Rayleigh--Bénard convection: Prandtl number dependence

Direct numerical simulations (DNS) are performed to explore the Prandtl number (Pr) dependence of the turbulent Rayleigh--Bénard convection (RBC) in spherical shells. The simulations are performed for 0.1 ≤ Pr ≤ 10, radius ratio η = 0.2 and 0.6, and for a range of Rayleigh number (Ra) varying between 10⁵ and 5 × 10⁷. A centrally condensed gravity profile, g ∽ 1/r², is employed in this study. Our primary aim is to analyze how Pr influences the global transport properties and flow physics. The scaling behavior of the Nusselt number (Nu) and Reynolds number (Re) with respect to Pr and Ra is investigated. It is observed that the asymmetry in the mean radial profiles of the temperature and velocity is a function of Pr and η. The asymmetry at smaller η has a stronger Pr dependence than at larger η. Various assumptions for quantifying this asymmetry are evaluated, revealing that different assumptions are valid at different Pr. It is shown that the assumption of the equivalency of local thermal boundary layer Rayleigh numbers holds only for Pr > 10. Furthermore, the assumption that the average plume density is the same at the inner and outer boundaries, as well as the assumption of the identical thermal scales between the two boundary layers, holds only for 0.2 < Pr < 1. Additionally, the validity of a new assumption based on the similarity of the average plume volume between the inner and the outer boundaries is proposed for Pr ≈ 0.1, which is validated using our DNS data.