Transient and steady convection in two dimensions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913953636941824 |
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| author | Pandey, Ambrish Sreenivasan, Katepalli R. |
| author_facet | Pandey, Ambrish Sreenivasan, Katepalli R. |
| contents | We simulate thermal convection in a two-dimensional square box using the no-slip condition on all boundaries, and isothermal bottom and top walls and adiabatic sidewalls. We choose 0.1 and 1 for the Prandtl number $Pr$ and vary the Rayleigh number $Ra$ between $10^6$ and $10^{12}$. We particularly study the temporal evolution of integral transport quantities towards their steady states. Perhaps not surprisingly, the velocity field evolves more slowly than the thermal field, and its steady state -- which is nominal in the sense that large-amplitude low-frequency oscillations persist around plausible averages -- is reached exponentially. We study these oscillation characteristics. The transient time for the velocity field to achieve its nominal steady state increases almost linearly with the Reynolds number. For large $Ra$, the Reynolds number itself scales almost as $Ra^{2/3} Pr^{-1}$, and the Nusselt number as $Ra^{2/7}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_03080 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Transient and steady convection in two dimensions Pandey, Ambrish Sreenivasan, Katepalli R. Fluid Dynamics Solar and Stellar Astrophysics We simulate thermal convection in a two-dimensional square box using the no-slip condition on all boundaries, and isothermal bottom and top walls and adiabatic sidewalls. We choose 0.1 and 1 for the Prandtl number $Pr$ and vary the Rayleigh number $Ra$ between $10^6$ and $10^{12}$. We particularly study the temporal evolution of integral transport quantities towards their steady states. Perhaps not surprisingly, the velocity field evolves more slowly than the thermal field, and its steady state -- which is nominal in the sense that large-amplitude low-frequency oscillations persist around plausible averages -- is reached exponentially. We study these oscillation characteristics. The transient time for the velocity field to achieve its nominal steady state increases almost linearly with the Reynolds number. For large $Ra$, the Reynolds number itself scales almost as $Ra^{2/3} Pr^{-1}$, and the Nusselt number as $Ra^{2/7}$. |
| title | Transient and steady convection in two dimensions |
| topic | Fluid Dynamics Solar and Stellar Astrophysics |
| url | https://arxiv.org/abs/2503.03080 |