Energy dissipation near the outflow boundary in the vanishing viscosity limit
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911005779427328 |
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| author | Yang, Jincheng Martinez, Vincent R. Mazzucato, Anna L. Vasseur, Alexis F. |
| author_facet | Yang, Jincheng Martinez, Vincent R. Mazzucato, Anna L. Vasseur, Alexis F. |
| contents | We consider the incompressible Navier-Stokes and Euler equations in a bounded domain with non-characteristic boundary condition, and study the energy dissipation near the outflow boundary in the zero-viscosity limit. We show that in a general setting, the energy dissipation rate is proportional to $\bar U \bar V ^2$, where $\bar U$ is the strength of the suction and $\bar V$ is the tangential component of the difference between the Euler and the Navier-Stokes solutions on the outflow boundary. Moreover, we show that the enstrophy within a layer of order $ν/ \bar U$ is comparable with the total enstrophy. The rate of enstrophy production near the boundary is inversely proportional to $ν$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13127 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Energy dissipation near the outflow boundary in the vanishing viscosity limit Yang, Jincheng Martinez, Vincent R. Mazzucato, Anna L. Vasseur, Alexis F. Analysis of PDEs 76D05, 35Q30 We consider the incompressible Navier-Stokes and Euler equations in a bounded domain with non-characteristic boundary condition, and study the energy dissipation near the outflow boundary in the zero-viscosity limit. We show that in a general setting, the energy dissipation rate is proportional to $\bar U \bar V ^2$, where $\bar U$ is the strength of the suction and $\bar V$ is the tangential component of the difference between the Euler and the Navier-Stokes solutions on the outflow boundary. Moreover, we show that the enstrophy within a layer of order $ν/ \bar U$ is comparable with the total enstrophy. The rate of enstrophy production near the boundary is inversely proportional to $ν$. |
| title | Energy dissipation near the outflow boundary in the vanishing viscosity limit |
| topic | Analysis of PDEs 76D05, 35Q30 |
| url | https://arxiv.org/abs/2410.13127 |