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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.17501 |
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Table of Contents:
- 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-Bénard convection (RRBC) framework with tilted rotation and gravity axes to model convection at different latitudes $φ$ in the geostrophic regime. We derive scaling relations for the latitude dependence of convective length scales $\ell(φ)$ and the Nusselt number $Nu(φ)$. At high latitudes, the scalings $Nu \sim \sin^{-4/3}φ$ (near onset) and $Nu \sim \sin^{-4}φ$ (above onset) emerge, while at low latitudes $Nu \sim \cos^{4}φ$. 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.