Boundary driven instabilities of Couette flows
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866912010077208576 |
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| author | Bian, Dongfen Grenier, Emmanuel Masmoudi, Nader Zhao, Weiren |
| author_facet | Bian, Dongfen Grenier, Emmanuel Masmoudi, Nader Zhao, Weiren |
| contents | In this article, we prove that the threshold of instability of the classical Couette flow in $H^s$ for large $s$ is $ν^{1/2}$. The instability is completely driven by the boundary. The dynamic of the flow creates a Prandtl type boundary layer of width $ν^{1/2}$ which is itself linearly unstable. This leads to a secondary instability which in turn creates a sub-layer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00307 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Boundary driven instabilities of Couette flows Bian, Dongfen Grenier, Emmanuel Masmoudi, Nader Zhao, Weiren Analysis of PDEs In this article, we prove that the threshold of instability of the classical Couette flow in $H^s$ for large $s$ is $ν^{1/2}$. The instability is completely driven by the boundary. The dynamic of the flow creates a Prandtl type boundary layer of width $ν^{1/2}$ which is itself linearly unstable. This leads to a secondary instability which in turn creates a sub-layer. |
| title | Boundary driven instabilities of Couette flows |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.00307 |