Second order perturbation theory of two-scale systems in fluid dynamics
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866908465512841216 |
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| author | Debussche, Arnaud Pappalettera, Umberto |
| author_facet | Debussche, Arnaud Pappalettera, Umberto |
| contents | In the present paper we study slow-fast systems of coupled equations from fluid dynamics, where the fast component is perturbed by additive noise. We prove that, under a suitable limit of infinite separation of scales, the slow component of the system converges in law to a solution of the initial equation perturbed with transport noise, and subject to the influence of an additional Itō-Stokes drift. The obtained limit equation is very similar to turbulent models derived heuristically. Our results apply to the Navier-Stokes equations in dimension $d=2,3$; the Surface Quasi-Geostrophic equations in dimension $d=2$; and the Primitive equations in dimension $d=2,3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_07775 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Second order perturbation theory of two-scale systems in fluid dynamics Debussche, Arnaud Pappalettera, Umberto Probability In the present paper we study slow-fast systems of coupled equations from fluid dynamics, where the fast component is perturbed by additive noise. We prove that, under a suitable limit of infinite separation of scales, the slow component of the system converges in law to a solution of the initial equation perturbed with transport noise, and subject to the influence of an additional Itō-Stokes drift. The obtained limit equation is very similar to turbulent models derived heuristically. Our results apply to the Navier-Stokes equations in dimension $d=2,3$; the Surface Quasi-Geostrophic equations in dimension $d=2$; and the Primitive equations in dimension $d=2,3$. |
| title | Second order perturbation theory of two-scale systems in fluid dynamics |
| topic | Probability |
| url | https://arxiv.org/abs/2206.07775 |