Stochastic interpretations of the oceanic primitive equations with relaxed hydrostatic assumptions
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909985182580736 |
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| author | Debussche, Arnaud Mémin, Étienne Moneyron, Antoine |
| author_facet | Debussche, Arnaud Mémin, Étienne Moneyron, Antoine |
| contents | In this paper, we investigate how weakening the classical hydrostatic balance hypothesis impacts the well-posedness of the stochastic LU primitive equations. The models we consider are intermediate between the incompressible 3D LU Navier-Stokes equations and the LU primitive equations with standard hydrostatic balance. As such, they are expected to be numerically tractable, while accounting well for phenomena within the grey zone between hydrostatic balance and non-hydrostatic processes. Our main result is the well-posedness of a low-pass filtering-based stochastic interpretation of the LU primitive equations, with rigid-lid type boundary conditions, in the limit of ``quasi-barotropic'' flow. This assumption is linked to the structure assumption proposed in the work of Agresti et al., which can be related to the dynamical regime where the primitive equations remain valid. Furthermore, we present and study two eddy-(hyper)viscosity-based models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14946 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic interpretations of the oceanic primitive equations with relaxed hydrostatic assumptions Debussche, Arnaud Mémin, Étienne Moneyron, Antoine Analysis of PDEs Mathematical Physics Probability In this paper, we investigate how weakening the classical hydrostatic balance hypothesis impacts the well-posedness of the stochastic LU primitive equations. The models we consider are intermediate between the incompressible 3D LU Navier-Stokes equations and the LU primitive equations with standard hydrostatic balance. As such, they are expected to be numerically tractable, while accounting well for phenomena within the grey zone between hydrostatic balance and non-hydrostatic processes. Our main result is the well-posedness of a low-pass filtering-based stochastic interpretation of the LU primitive equations, with rigid-lid type boundary conditions, in the limit of ``quasi-barotropic'' flow. This assumption is linked to the structure assumption proposed in the work of Agresti et al., which can be related to the dynamical regime where the primitive equations remain valid. Furthermore, we present and study two eddy-(hyper)viscosity-based models. |
| title | Stochastic interpretations of the oceanic primitive equations with relaxed hydrostatic assumptions |
| topic | Analysis of PDEs Mathematical Physics Probability |
| url | https://arxiv.org/abs/2502.14946 |