Mixing at the Batchelor Scale for White-In-Time Flows
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918230997598208 |
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| author | Chemnitz, Robin Chemnitz, Dennis |
| author_facet | Chemnitz, Robin Chemnitz, Dennis |
| contents | We consider the mixing properties of solutions to the advection-diffusion equation of a white-in-time velocity field on the 2-dimensional torus with four forced modes. As the diffusivity parameter goes to zero, we show that the almost-sure exponential dissipation rate stays bounded from below. Together with the corresponding upper bound established by Gess and Yaroslavtsev, this constitutes an example of a velocity field for which the Batchelor scale conjecture can be verified. In addition, we characterize the exponential mixing rate without diffusion of this system. Our results are not restricted to two dimensions, and we construct a three-dimensional white-in-time velocity field with the same properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04297 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mixing at the Batchelor Scale for White-In-Time Flows Chemnitz, Robin Chemnitz, Dennis Probability Analysis of PDEs Dynamical Systems 35Q35, 37H15, 37L30, 76F25 We consider the mixing properties of solutions to the advection-diffusion equation of a white-in-time velocity field on the 2-dimensional torus with four forced modes. As the diffusivity parameter goes to zero, we show that the almost-sure exponential dissipation rate stays bounded from below. Together with the corresponding upper bound established by Gess and Yaroslavtsev, this constitutes an example of a velocity field for which the Batchelor scale conjecture can be verified. In addition, we characterize the exponential mixing rate without diffusion of this system. Our results are not restricted to two dimensions, and we construct a three-dimensional white-in-time velocity field with the same properties. |
| title | Mixing at the Batchelor Scale for White-In-Time Flows |
| topic | Probability Analysis of PDEs Dynamical Systems 35Q35, 37H15, 37L30, 76F25 |
| url | https://arxiv.org/abs/2512.04297 |