The Obukhov--Corrsin spectrum of passive scalar turbulence through anomalous regularization
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917119339266048 |
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| author | Rowan, Keefer |
| author_facet | Rowan, Keefer |
| contents | The Obukhov--Corrsin spectrum predicts the distribution of Fourier mass for a passive scalar field advected by a "turbulent" velocity field with spatial regularity $C^α_x$ for $α\in (0,1)$ and subject to a time-stationary forcing. We prove the Obukhov--Corrsin spectrum holds after summing over geometric annuli in Fourier space -- up to logarithmic corrections -- as a consequence of a sharp anomalous regularization result. We then prove this anomalous regularization for a broad class of Kraichnan-type models. The proof of anomalous regularization relies on a Fourier space $\ell^p$ energy equality and a weighted lattice Poincaré inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02853 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Obukhov--Corrsin spectrum of passive scalar turbulence through anomalous regularization Rowan, Keefer Analysis of PDEs Mathematical Physics Probability The Obukhov--Corrsin spectrum predicts the distribution of Fourier mass for a passive scalar field advected by a "turbulent" velocity field with spatial regularity $C^α_x$ for $α\in (0,1)$ and subject to a time-stationary forcing. We prove the Obukhov--Corrsin spectrum holds after summing over geometric annuli in Fourier space -- up to logarithmic corrections -- as a consequence of a sharp anomalous regularization result. We then prove this anomalous regularization for a broad class of Kraichnan-type models. The proof of anomalous regularization relies on a Fourier space $\ell^p$ energy equality and a weighted lattice Poincaré inequality. |
| title | The Obukhov--Corrsin spectrum of passive scalar turbulence through anomalous regularization |
| topic | Analysis of PDEs Mathematical Physics Probability |
| url | https://arxiv.org/abs/2512.02853 |