Stability of laminar monotone shear flows in a channel for high Reynolds number
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918104282431488 |
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| author | Almog, Yaniv Helffer, Bernard |
| author_facet | Almog, Yaniv Helffer, Bernard |
| contents | We consider the stability of a laminar flow $U\in C^4([-1,1])$ in the two-dimensional channel $\mathbb{R} \times[-1,1]$ in the large Reynolds number limit. Assuming that $U$ is strictly monotone but allowing $U^{\prime\prime}$ to vanish, we obtain that if the operator
$$
{\mathcal K}_ν=-\frac{d^2}{dx^2}+\frac{U^{\prime\prime}}{U-ν} \,, $$ is strictly positive for all $ν\in\mathbb{R}$ for which $U^{\prime\prime}(U^{-1}(ν))=0$,then $U$ is stable for sufficiently large Reynolds number. This contribution generalizes previous results mostly by allowing long wave perturbations (but much shorter than the Reynolds number). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19106 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability of laminar monotone shear flows in a channel for high Reynolds number Almog, Yaniv Helffer, Bernard Analysis of PDEs Mathematical Physics 35P15, 76E05 We consider the stability of a laminar flow $U\in C^4([-1,1])$ in the two-dimensional channel $\mathbb{R} \times[-1,1]$ in the large Reynolds number limit. Assuming that $U$ is strictly monotone but allowing $U^{\prime\prime}$ to vanish, we obtain that if the operator $$ {\mathcal K}_ν=-\frac{d^2}{dx^2}+\frac{U^{\prime\prime}}{U-ν} \,, $$ is strictly positive for all $ν\in\mathbb{R}$ for which $U^{\prime\prime}(U^{-1}(ν))=0$,then $U$ is stable for sufficiently large Reynolds number. This contribution generalizes previous results mostly by allowing long wave perturbations (but much shorter than the Reynolds number). |
| title | Stability of laminar monotone shear flows in a channel for high Reynolds number |
| topic | Analysis of PDEs Mathematical Physics 35P15, 76E05 |
| url | https://arxiv.org/abs/2507.19106 |