Latitudinal dependence of heat transport in turbulent geostrophic convection

Abstract

Latitudinal variations in turbulent heat flux play a key role in the thermal and magnetic evolution of rapidly rotating planets and stars. Although global spherical-shell simulations have documented such variations, explicit latitude-dependent scaling relations for heat transport have remained elusive. Here we employ the rotating Rayleigh-B\'enard convection (RRBC) framework with tilted rotation and gravity axes to model convection at different latitudes $\varphi$ in the geostrophic regime. We derive scaling relations for the latitude dependence of convective length scales $\ell(\varphi)$ and the Nusselt number $Nu(\varphi)$. At high latitudes, the scalings $Nu \sim \sin^{-4/3}\varphi$ (near onset) and $Nu \sim \sin^{-4}\varphi$ (above onset) emerge, while at low latitudes $Nu \sim \cos^{4}\varphi$. These predictions are validated against direct numerical simulations of convection in a spherical shell. The results provide a quantitative framework for regional thermal transport in planetary and stellar interiors and establish a unified interpretation of spherical convection that connects naturally with planar RRBC turbulence.