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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | https://arxiv.org/abs/2306.15481 |
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| _version_ | 1866929332457308160 |
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| author | Franken, Arnout Caliaro, Martino Cifani, Paolo Geurts, Bernard |
| author_facet | Franken, Arnout Caliaro, Martino Cifani, Paolo Geurts, Bernard |
| contents | In this work, we consider a Shallow-Water Quasi Geostrophic equation on the sphere, as a model for global large-scale atmospheric dynamics. This equation, previously studied by Verkley (2009) and Schubert et al. (2009), possesses a rich geometric structure, called Lie-Poisson, and admits an infinite number of conserved quantities, called Casimirs. In this paper, we develop a Casimir preserving numerical method for long-time simulations of this equation. The method develops in two steps: firstly, we construct an N-dimensional Lie-Poisson system that converges to the continuous one in the limit $N \to \infty$; secondly, we integrate in time the finite-dimensional system using an isospectral time integrator, developed by Modin and Viviani (2020). We demonstrate the efficacy of this computational method by simulating a flow on the entire sphere for different values of the Lamb parameter. We particularly focus on rotation-induced effects, such as the formation of jets. In agreement with shallow water models of the atmosphere, we observe the formation of robust latitudinal jets and a decrease in the zonal wind amplitude with latitude. Furthermore, spectra of the kinetic energy are computed as a point of reference for future studies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_15481 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Zeitlin truncation of a Shallow Water Quasi-Geostrophic model for planetary flow Franken, Arnout Caliaro, Martino Cifani, Paolo Geurts, Bernard Fluid Dynamics In this work, we consider a Shallow-Water Quasi Geostrophic equation on the sphere, as a model for global large-scale atmospheric dynamics. This equation, previously studied by Verkley (2009) and Schubert et al. (2009), possesses a rich geometric structure, called Lie-Poisson, and admits an infinite number of conserved quantities, called Casimirs. In this paper, we develop a Casimir preserving numerical method for long-time simulations of this equation. The method develops in two steps: firstly, we construct an N-dimensional Lie-Poisson system that converges to the continuous one in the limit $N \to \infty$; secondly, we integrate in time the finite-dimensional system using an isospectral time integrator, developed by Modin and Viviani (2020). We demonstrate the efficacy of this computational method by simulating a flow on the entire sphere for different values of the Lamb parameter. We particularly focus on rotation-induced effects, such as the formation of jets. In agreement with shallow water models of the atmosphere, we observe the formation of robust latitudinal jets and a decrease in the zonal wind amplitude with latitude. Furthermore, spectra of the kinetic energy are computed as a point of reference for future studies. |
| title | Zeitlin truncation of a Shallow Water Quasi-Geostrophic model for planetary flow |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2306.15481 |