Latitudinal dependence of heat transport in turbulent geostrophic convection

TL;DR

This paper develops and validates scaling relations for how turbulent heat transport varies with latitude in rotating planetary and stellar interiors, linking spherical and planar convection models.

Contribution

It introduces explicit latitude-dependent scaling laws for heat transport in geostrophic convection, validated through numerical simulations.

Findings

High-latitude Nusselt number scales as sin^{-4/3}φ

Low-latitude Nusselt number scales as cos^{4}φ

Provides a unified framework connecting spherical and planar 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.