Infinite Prandtl number convection with Navier-slip boundary conditions
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914413911474176 |
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| author | Seis, Christian |
| author_facet | Seis, Christian |
| contents | We are concerned with infinite Prandtl number Rayleigh--Bénard convection with Navier-slip boundary conditions. The goal of this work is to estimate the average upward heat flux measured by the nondimensional Nusselt number $Nu$ in terms of the Rayleigh number $Ra$, which is a nondimensional quantity measuring the imposed temperature gradient. We derive bounds on the Nusselt number that coincide for relatively small slip lengths with the optimal Nusselt number scaling for no-slip boundaries, $Nu\lesssim Ra^{1/3}$; for relatively large slip lengths, we recover scaling estimates for free-slip boundaries, $Nu\lesssim Ra^{5/12}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11051 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infinite Prandtl number convection with Navier-slip boundary conditions Seis, Christian Analysis of PDEs We are concerned with infinite Prandtl number Rayleigh--Bénard convection with Navier-slip boundary conditions. The goal of this work is to estimate the average upward heat flux measured by the nondimensional Nusselt number $Nu$ in terms of the Rayleigh number $Ra$, which is a nondimensional quantity measuring the imposed temperature gradient. We derive bounds on the Nusselt number that coincide for relatively small slip lengths with the optimal Nusselt number scaling for no-slip boundaries, $Nu\lesssim Ra^{1/3}$; for relatively large slip lengths, we recover scaling estimates for free-slip boundaries, $Nu\lesssim Ra^{5/12}$. |
| title | Infinite Prandtl number convection with Navier-slip boundary conditions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.11051 |