Compressible turbulent convection at very high Rayleigh numbers
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arXiv
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| Format: | Preprint |
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2024
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| author | Tiwari, Harshit Sharma, Lekha Verma, Mahendra K. |
| author_facet | Tiwari, Harshit Sharma, Lekha Verma, Mahendra K. |
| contents | Heat transport in highly turbulent convection is not well understood. In this paper, we simulate compressible convection in a box of aspect ratio 4 using computationally-efficient MacCormack-TVD finite difference method on single and multi-GPUs, and reach very high Rayleigh number ($\mathrm{Ra}$) -- $10^{15}$ in two dimensions and $10^{11}$ in three dimensions. We show that the Nusselt number $\mathrm{Nu} \propto \mathrm{Ra}^{0.3}$ (classical scaling) that differs strongly from the ultimate-regime scaling, which is $\mathrm{Nu} \propto \mathrm{Ra}^{1/2}$. The bulk temperature drops adiabatically along the vertical even for high $\mathrm{Ra}$, which is in contrast to the constant bulk temperature in Rayleigh-Bénard convection (RBC). Unlike RBC, the density decreases with height. In addition, the vertical pressure-gradient ($-dp/dz$) nearly matches the buoyancy term ($ρg$). But, the difference, $-dp/dz-ρg$, is equal to the nonlinear term that leads to Reynolds number $\mathrm{Re} \propto \mathrm{Ra}^{1/2}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_10372 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compressible turbulent convection at very high Rayleigh numbers Tiwari, Harshit Sharma, Lekha Verma, Mahendra K. Fluid Dynamics Solar and Stellar Astrophysics Heat transport in highly turbulent convection is not well understood. In this paper, we simulate compressible convection in a box of aspect ratio 4 using computationally-efficient MacCormack-TVD finite difference method on single and multi-GPUs, and reach very high Rayleigh number ($\mathrm{Ra}$) -- $10^{15}$ in two dimensions and $10^{11}$ in three dimensions. We show that the Nusselt number $\mathrm{Nu} \propto \mathrm{Ra}^{0.3}$ (classical scaling) that differs strongly from the ultimate-regime scaling, which is $\mathrm{Nu} \propto \mathrm{Ra}^{1/2}$. The bulk temperature drops adiabatically along the vertical even for high $\mathrm{Ra}$, which is in contrast to the constant bulk temperature in Rayleigh-Bénard convection (RBC). Unlike RBC, the density decreases with height. In addition, the vertical pressure-gradient ($-dp/dz$) nearly matches the buoyancy term ($ρg$). But, the difference, $-dp/dz-ρg$, is equal to the nonlinear term that leads to Reynolds number $\mathrm{Re} \propto \mathrm{Ra}^{1/2}$. |
| title | Compressible turbulent convection at very high Rayleigh numbers |
| topic | Fluid Dynamics Solar and Stellar Astrophysics |
| url | https://arxiv.org/abs/2411.10372 |