Rapidly Rotating Wall-Mode Convection
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911122155634688 |
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| author | Vasil, Geoffrey M. Burns, Keaton J. Lecoanet, Daniel Oishi, Jeffrey S. Brown, Benjamin P. Julien, Keith |
| author_facet | Vasil, Geoffrey M. Burns, Keaton J. Lecoanet, Daniel Oishi, Jeffrey S. Brown, Benjamin P. Julien, Keith |
| contents | In the rapidly rotating limit, we derive a balanced set of reduced equations governing the strongly nonlinear development of the convective wall-mode instability in the interior of a general container. The model illustrates that wall-mode convection is a multiscale phenomenon where the dynamics of the bulk interior diagnostically determine the small-scale dynamics within Stewartson boundary layers at the sidewalls. The sidewall boundary layers feedback on the interior via a nonlinear lateral heat-flux boundary condition, providing a closed system. Outside the asymptotically thin boundary layer, the convective modes connect to a dynamical interior that maintains scales set by the domain geometry. In many ways, the final system of equations resembles boundary-forced planetary geostrophic baroclinic dynamics coupled with barotropic quasi-geostrophic vorticity. The reduced system contains the results from previous linear instability theory but captured in an elementary fashion, providing a new avenue for investigating wall-mode convection in the strongly nonlinear regime. We also derive the dominant Ekman-flux correction to the onset Rayleigh number for large Taylor number, $\textit{Ra} \approx 31.8 \,\textit{Ta}^{1/2} - 4.43 \,\textit{Ta}^{5/12} + \mathcal{O}(\textit{Ta}^{1/3})$ for no-slip boundaries. However, we find that the linear onset in a finite cylinder differs noticeably compared to a Cartesian channel. We demonstrate some of the reduced model's nonlinear dynamics with numerical simulations in a cylindrical container. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_20541 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rapidly Rotating Wall-Mode Convection Vasil, Geoffrey M. Burns, Keaton J. Lecoanet, Daniel Oishi, Jeffrey S. Brown, Benjamin P. Julien, Keith Fluid Dynamics Dynamical Systems Pattern Formation and Solitons In the rapidly rotating limit, we derive a balanced set of reduced equations governing the strongly nonlinear development of the convective wall-mode instability in the interior of a general container. The model illustrates that wall-mode convection is a multiscale phenomenon where the dynamics of the bulk interior diagnostically determine the small-scale dynamics within Stewartson boundary layers at the sidewalls. The sidewall boundary layers feedback on the interior via a nonlinear lateral heat-flux boundary condition, providing a closed system. Outside the asymptotically thin boundary layer, the convective modes connect to a dynamical interior that maintains scales set by the domain geometry. In many ways, the final system of equations resembles boundary-forced planetary geostrophic baroclinic dynamics coupled with barotropic quasi-geostrophic vorticity. The reduced system contains the results from previous linear instability theory but captured in an elementary fashion, providing a new avenue for investigating wall-mode convection in the strongly nonlinear regime. We also derive the dominant Ekman-flux correction to the onset Rayleigh number for large Taylor number, $\textit{Ra} \approx 31.8 \,\textit{Ta}^{1/2} - 4.43 \,\textit{Ta}^{5/12} + \mathcal{O}(\textit{Ta}^{1/3})$ for no-slip boundaries. However, we find that the linear onset in a finite cylinder differs noticeably compared to a Cartesian channel. We demonstrate some of the reduced model's nonlinear dynamics with numerical simulations in a cylindrical container. |
| title | Rapidly Rotating Wall-Mode Convection |
| topic | Fluid Dynamics Dynamical Systems Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2409.20541 |