Internally heated convection with rotation: bounds on heat transport
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909439721734144 |
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| author | Arslan, Ali |
| author_facet | Arslan, Ali |
| contents | This work investigates heat transport in rotating internally heated convection, for a horizontally periodic fluid between parallel plates under no-slip and isothermal boundary conditions. The main results are the proof of bounds on the mean temperature, $\overline{\langle T \rangle }$, and the heat flux out of the bottom boundary, $\mathcal{F}_B$ at infinite Prandtl numbers where the Prandtl number is the nondimensional ratio of viscous to thermal diffusion. The lower bounds are functions of a Rayleigh number quantifying the ratio of internal heating to diffusion and the Ekman number, $E$, which quantifies the ratio of viscous diffusion to rotation. We utilise two different estimates on the vertical velocity, $w$, one pointwise in the domain (Yan 2004, J. Math. Phys., vol. 45(7), pp. 2718-2743) and the other an integral estimate over the domain (Constantin et al . 1999, Phys. D: Non. Phen., vol. 125, pp. 275-284), resulting in bounds valid for different regions of buoyancy-to-rotation dominated convection. Furthermore, we demonstrate that similar to rotating Rayleigh-Bénard convection, for small $E$, the critical Rayleigh number for the onset of convection asymptotically scales as $E^{-4/3}$.This result is combined with heuristic arguments for internally heated and rotating convection to arrive at scaling laws for $\overline{\langle T \rangle }$ and $\mathcal{F}_B$ valid for arbitrary Prandtl numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10975 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Internally heated convection with rotation: bounds on heat transport Arslan, Ali Fluid Dynamics Mathematical Physics This work investigates heat transport in rotating internally heated convection, for a horizontally periodic fluid between parallel plates under no-slip and isothermal boundary conditions. The main results are the proof of bounds on the mean temperature, $\overline{\langle T \rangle }$, and the heat flux out of the bottom boundary, $\mathcal{F}_B$ at infinite Prandtl numbers where the Prandtl number is the nondimensional ratio of viscous to thermal diffusion. The lower bounds are functions of a Rayleigh number quantifying the ratio of internal heating to diffusion and the Ekman number, $E$, which quantifies the ratio of viscous diffusion to rotation. We utilise two different estimates on the vertical velocity, $w$, one pointwise in the domain (Yan 2004, J. Math. Phys., vol. 45(7), pp. 2718-2743) and the other an integral estimate over the domain (Constantin et al . 1999, Phys. D: Non. Phen., vol. 125, pp. 275-284), resulting in bounds valid for different regions of buoyancy-to-rotation dominated convection. Furthermore, we demonstrate that similar to rotating Rayleigh-Bénard convection, for small $E$, the critical Rayleigh number for the onset of convection asymptotically scales as $E^{-4/3}$.This result is combined with heuristic arguments for internally heated and rotating convection to arrive at scaling laws for $\overline{\langle T \rangle }$ and $\mathcal{F}_B$ valid for arbitrary Prandtl numbers. |
| title | Internally heated convection with rotation: bounds on heat transport |
| topic | Fluid Dynamics Mathematical Physics |
| url | https://arxiv.org/abs/2406.10975 |