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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2508.17501 |
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| _version_ | 1866915460871618560 |
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| author | Kannan, Veeraraghavan Mathai, Varghese Zhu, Xiaojue |
| author_facet | Kannan, Veeraraghavan Mathai, Varghese Zhu, Xiaojue |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17501 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Latitudinal dependence of heat transport in turbulent geostrophic convection Kannan, Veeraraghavan Mathai, Varghese Zhu, Xiaojue Earth and Planetary Astrophysics Solar and Stellar Astrophysics 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. |
| title | Latitudinal dependence of heat transport in turbulent geostrophic convection |
| topic | Earth and Planetary Astrophysics Solar and Stellar Astrophysics |
| url | https://arxiv.org/abs/2508.17501 |