Rigorous ultimate scaling in rapidly rotating steady convection
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866918486974922752 |
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| author | Hadjerci, Gabriel Motoki, Shingo Kawahara, Genta |
| author_facet | Hadjerci, Gabriel Motoki, Shingo Kawahara, Genta |
| contents | Rapidly rotating Rayleigh-Bénard convection admits a class of exact steady single-mode solutions describing high-amplitude convection cells. Using a matched asymptotic analysis in the high-Rayleigh-number limit, we obtain a rigorous characterization of their bulk and boundary-layer structure, yielding explicit scaling laws for the Nusselt and Reynolds numbers, including their dependence on the horizontal wavenumber. We show that, for suitable wavenumbers, these solutions attain the diffusivity-free ultimate scalings frequently assumed for geophysical and astrophysical convection, with additional enhancing logarithmic corrections. This reveals a specific mechanism through which rapidly rotating convection can approach ultimate heat transport via coherent columnar structures with well-defined horizontal scales. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05574 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rigorous ultimate scaling in rapidly rotating steady convection Hadjerci, Gabriel Motoki, Shingo Kawahara, Genta Fluid Dynamics Rapidly rotating Rayleigh-Bénard convection admits a class of exact steady single-mode solutions describing high-amplitude convection cells. Using a matched asymptotic analysis in the high-Rayleigh-number limit, we obtain a rigorous characterization of their bulk and boundary-layer structure, yielding explicit scaling laws for the Nusselt and Reynolds numbers, including their dependence on the horizontal wavenumber. We show that, for suitable wavenumbers, these solutions attain the diffusivity-free ultimate scalings frequently assumed for geophysical and astrophysical convection, with additional enhancing logarithmic corrections. This reveals a specific mechanism through which rapidly rotating convection can approach ultimate heat transport via coherent columnar structures with well-defined horizontal scales. |
| title | Rigorous ultimate scaling in rapidly rotating steady convection |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2605.05574 |