Latitudinal regionalization of rotating spherical shell convection

TL;DR

This study investigates how heat transfer varies latitudinally in rotating spherical shell convection, revealing that polar convection is delayed and accelerates with increasing Rayleigh number, and finds agreement with Cartesian models.

Contribution

It quantifies latitudinal differences in convective heat transfer in spherical shells, showing the conditions for polar convection onset and comparing spherical and Cartesian simulation results.

Findings

Polar convection requires higher Rayleigh number to initiate.

Polar heat transfer increases faster than equatorial with Ra.

Spherical and Cartesian models show quantitative agreement.

Abstract

Convection occurs ubiquitously on and in rotating geophysical and astrophysical bodies. Prior spherical shell studies have shown that the convection dynamics in polar regions can differ significantly from the lower latitude, equatorial dynamics. Yet most spherical shell convective scaling laws use globally-averaged quantities that erase latitudinal differences in the physics. Here we quantify those latitudinal differences by analyzing spherical shell simulations in terms of their regionalized convective heat transfer properties. This is done by measuring local Nusselt numbers in two specific, latitudinally separate, portions of the shell, 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 $\approx 20$ to trigger polar convection within the tangent cylinder. Once triggered, $Nu_p$ increases with $Ra$ much faster than does $Nu_e$. The equatorial and polar heat fluxes then tend to become comparable at sufficiently high $Ra$. 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.