Latitudinal Regionalization of Planetary Core Convection

Convection occurs ubiquitously in rotating geophysical and astrophysical bodies. Prior spherical shell studies have shown that the convection dynamics in polar regions can differ significantly from lower latitude dynamics. Yet most spherical shell convective scaling laws use globally-averaged quantities that erase latitudinal differences in the physics. Here we quantify those differences by analyzing spherical shell simulations in terms of their regionalized convective heat transfer properties. This is done by measuring local Nusselt numbers in the polar and the equatorial regions, $Nu_p$ and $Nu_e$, respectively. In rotating spherical shells, convection first sets in outside the tangent cylinder such that equatorial heat transfer dominates at small and moderate supercriticalities. We show that the buoyancy forcing, parameterized by the Rayleigh number $Ra$, must exceed the critical equatorial forcing by a factor of ≈ 20 to trigger polar convection within the tangent cylinder. Once triggered, $Nu_p$ increases with $Ra$ much faster than $Nu_e$. At significantly higher $Ra$, the equatorial and polar heat fluxes tend to become comparable. Comparisons between the polar convection data and Cartesian numerical simulations reveal quantitative agreement between the two geometries in terms of heat transfer and averaged bulk temperature gradient. This agreement indicates that spherical shell rotating convection dynamics are accessible both through spherical simulations and via reduced investigatory pathways, be they theoretical, numerical or experimental.