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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | https://arxiv.org/abs/2403.17854 |
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| _version_ | 1866910384587276288 |
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| author | Tong, Chenning |
| author_facet | Tong, Chenning |
| contents | We propose a phenomenological model for thermal convection at high Rayleigh numbers. It hypothesizes existence of a high-Reynolds-number turbulent boundary layer near each horizontal plate, which is shown to be convective. The convective logarithmic friction law of Tong and Ding (2020) is used to relate the large-scale velocity to the induced friction velocity. The predicted scaling relations of the Nusselt ($Nu$) and Reynolds numbers ($Re$) on the Rayleigh number ($Ra$) do not have a power law form, each being a single function, suggesting a single flow regime with no transition, instead of multiple regimes. However, the predicted $Nu$ and $Re$ scaling is close to $Ra^{1/3}$ and $Ra^{4/9}$ for $Ra \sim 10^9$ to $10^{17}$, consistent with direct numerical simulation (DNS) results up to $Ra\sim 10^{15}$. For $Ra<10^9$, the model also correctly predicts the deviations observed in DNS from the above power law scaling. The model predicts deviations from $Ra^{1/3}$ beyond $Ra \sim 10^{17}$ with the local scaling exponent approaching $1/2$, which would likely require data at $Ra>10^{18}$ to verify. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17854 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scaling of high-Rayleigh-number convection based on internal convective boundary layer Tong, Chenning Fluid Dynamics We propose a phenomenological model for thermal convection at high Rayleigh numbers. It hypothesizes existence of a high-Reynolds-number turbulent boundary layer near each horizontal plate, which is shown to be convective. The convective logarithmic friction law of Tong and Ding (2020) is used to relate the large-scale velocity to the induced friction velocity. The predicted scaling relations of the Nusselt ($Nu$) and Reynolds numbers ($Re$) on the Rayleigh number ($Ra$) do not have a power law form, each being a single function, suggesting a single flow regime with no transition, instead of multiple regimes. However, the predicted $Nu$ and $Re$ scaling is close to $Ra^{1/3}$ and $Ra^{4/9}$ for $Ra \sim 10^9$ to $10^{17}$, consistent with direct numerical simulation (DNS) results up to $Ra\sim 10^{15}$. For $Ra<10^9$, the model also correctly predicts the deviations observed in DNS from the above power law scaling. The model predicts deviations from $Ra^{1/3}$ beyond $Ra \sim 10^{17}$ with the local scaling exponent approaching $1/2$, which would likely require data at $Ra>10^{18}$ to verify. |
| title | Scaling of high-Rayleigh-number convection based on internal convective boundary layer |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2403.17854 |