The Batchelor spectrum for a deterministically driven passive scalar
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908875291099136 |
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| author | Liss, Kyle L. Mattingly, Jonathan C. |
| author_facet | Liss, Kyle L. Mattingly, Jonathan C. |
| contents | We study the long-time behavior of a passive scalar transported by an incompressible flow in the presence of smooth, deterministic forcing. For a specific spatially Lipschitz and time-periodic velocity field, we prove that all sufficiently smooth initial data is attracted to a limiting solution that satisfies a cumulative form of Batchelor's law. To our knowledge, this provides the first example for which a version of Batchelor's law can be established with deterministic forcing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08904 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Batchelor spectrum for a deterministically driven passive scalar Liss, Kyle L. Mattingly, Jonathan C. Analysis of PDEs Dynamical Systems 76F25, 35Q49, 37A25, 37D20 We study the long-time behavior of a passive scalar transported by an incompressible flow in the presence of smooth, deterministic forcing. For a specific spatially Lipschitz and time-periodic velocity field, we prove that all sufficiently smooth initial data is attracted to a limiting solution that satisfies a cumulative form of Batchelor's law. To our knowledge, this provides the first example for which a version of Batchelor's law can be established with deterministic forcing. |
| title | The Batchelor spectrum for a deterministically driven passive scalar |
| topic | Analysis of PDEs Dynamical Systems 76F25, 35Q49, 37A25, 37D20 |
| url | https://arxiv.org/abs/2603.08904 |