Centrifugally driven spherical gap convection with polar angle-dependent boundary condition: Can the Nusselt number fall below unity?

This study investigates centrifugally driven convection in a rotating spherical gap with a latitudinally varying temperature boundary condition, maximal at the equator and decreasing toward the poles. We first analyze the steady basic flow across a range of Taylor numbers, Ta, radii ratios, η=Rin/Rout, where Rin and Rout denote the inner and outer radii, respectively, and Prandtl numbers, Pr. The flow's stability is then examined using linear instability theory to determine the critical Taylor number, Tac, critical azimuthal wave number, mc, and the frequency of the critical perturbation ωc. A subsequent analysis of the 3D flow reveals that the onset of instability occurs via a supercritical Hopf bifurcation. A central focus of this study is heat transfer, with particular attention to thermal boundary layers and heat fluxes. Remarkably, the Nusselt number, Nu, evaluated as a function of the Taylor number, Ta, exhibits a non-monotonic trend and drops below unity, which is a rare and fundamentally intriguing phenomenon. Quantitatively, Nu decreases by up to 40% with increasing Prandtl number, Pr, and shows a secondary dependence on η, with variations of 13%–17%. To validate this result, we perform a comprehensive numerical analysis employing three independent methods: pseudospectral, finite volume, and finite element. All approaches yield consistent results, confirming the robustness of the observed behavior.