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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2510.13097 |
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| _version_ | 1866908593869029376 |
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| author | Li, Te Zhang, Le |
| author_facet | Li, Te Zhang, Le |
| contents | In this paper, we investigate the long-time behavior of a passive scalar advected by a parallel shear flow in an infinite cylinder with unbounded cross section, in the regime where the viscosity coefficient satisfies $ν\ll 1$, and in arbitrary spatial dimension. Under the assumption of an infinite cylinder, that is, $x \in \mathbb{R}$, the corresponding Fourier frequency $k$ (often referred to as the streamwise wave number) also ranges over the whole real line $\mathbb{R}$. In this setting, the enhanced dissipation phenomenon only occurs for high frequencies $ν\le |k|$, whereas for low frequencies $|k| \le ν$ only the decay of Taylor dispersion appears. It is worth noting that, in the case where $x \in \mathbb{T}$, the Fourier frequency does not contain low frequencies near zero, and thus enhanced dissipation occurs for all nonzero modes. Previously, Coti Zelati and Gallay study in [8] the case of infinite cylinders with bounded cross sections. For the unbounded case considered here, we find that a non-degeneracy condition at infinity is also required. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13097 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Enhanced dissipation and Taylor dispersion by a parallel shear flow in an infinite cylinder with unbounded cross section Li, Te Zhang, Le Analysis of PDEs In this paper, we investigate the long-time behavior of a passive scalar advected by a parallel shear flow in an infinite cylinder with unbounded cross section, in the regime where the viscosity coefficient satisfies $ν\ll 1$, and in arbitrary spatial dimension. Under the assumption of an infinite cylinder, that is, $x \in \mathbb{R}$, the corresponding Fourier frequency $k$ (often referred to as the streamwise wave number) also ranges over the whole real line $\mathbb{R}$. In this setting, the enhanced dissipation phenomenon only occurs for high frequencies $ν\le |k|$, whereas for low frequencies $|k| \le ν$ only the decay of Taylor dispersion appears. It is worth noting that, in the case where $x \in \mathbb{T}$, the Fourier frequency does not contain low frequencies near zero, and thus enhanced dissipation occurs for all nonzero modes. Previously, Coti Zelati and Gallay study in [8] the case of infinite cylinders with bounded cross sections. For the unbounded case considered here, we find that a non-degeneracy condition at infinity is also required. |
| title | Enhanced dissipation and Taylor dispersion by a parallel shear flow in an infinite cylinder with unbounded cross section |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.13097 |