Fourier mass lower bounds for Batchelor-regime passive scalars
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910864987127808 |
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| author | Cooperman, William Rowan, Keefer |
| author_facet | Cooperman, William Rowan, Keefer |
| contents | Batchelor predicted that a passive scalar $ψ^ν$ with diffusivity $ν$, advected by a smooth fluid velocity, should typically have Fourier mass distributed as $|\hat ψ^ν|^2(k) \approx |k|^{-d}$ for $|k| \ll ν^{-1/2}$. For a broad class of velocity fields, we give a quantitative lower bound for a version of this prediction summed over constant width annuli in Fourier space. This improves on previously known results, which require the prediction to be summed over the whole ball. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_05885 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fourier mass lower bounds for Batchelor-regime passive scalars Cooperman, William Rowan, Keefer Analysis of PDEs Batchelor predicted that a passive scalar $ψ^ν$ with diffusivity $ν$, advected by a smooth fluid velocity, should typically have Fourier mass distributed as $|\hat ψ^ν|^2(k) \approx |k|^{-d}$ for $|k| \ll ν^{-1/2}$. For a broad class of velocity fields, we give a quantitative lower bound for a version of this prediction summed over constant width annuli in Fourier space. This improves on previously known results, which require the prediction to be summed over the whole ball. |
| title | Fourier mass lower bounds for Batchelor-regime passive scalars |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.05885 |