Ekman boundary layers in a domain with topography
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866916334994980864 |
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| author | Chemin, Jean-Yves Fanelli, Francesco Gallagher, Isabelle |
| author_facet | Chemin, Jean-Yves Fanelli, Francesco Gallagher, Isabelle |
| contents | We investigate the asymptotic behaviour of fast rotating incompressible fluids with vanishing viscosity, in a {three dimensional} domain with topography including the case of land area. Assuming the initial data is well-prepared, we prove a convergence theorem of the velocity fields to a two-dimensional vector field solving a linear, damped ordinary differential equation.The proof is based on a weak-strong uniqueness argument, combinedwith an abstract result implying that the weak convergence of a familyof weak solutions to the Navier-Stokes-Coriolis system can be translated into a form of uniform-in-time convergence.This argument yields strong convergence of the velocity fields, without a precise rate though. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17050 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ekman boundary layers in a domain with topography Chemin, Jean-Yves Fanelli, Francesco Gallagher, Isabelle Analysis of PDEs We investigate the asymptotic behaviour of fast rotating incompressible fluids with vanishing viscosity, in a {three dimensional} domain with topography including the case of land area. Assuming the initial data is well-prepared, we prove a convergence theorem of the velocity fields to a two-dimensional vector field solving a linear, damped ordinary differential equation.The proof is based on a weak-strong uniqueness argument, combinedwith an abstract result implying that the weak convergence of a familyof weak solutions to the Navier-Stokes-Coriolis system can be translated into a form of uniform-in-time convergence.This argument yields strong convergence of the velocity fields, without a precise rate though. |
| title | Ekman boundary layers in a domain with topography |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.17050 |