Zeitlin truncation of a Shallow Water Quasi-Geostrophic model for planetary flow
| Autor: | Franken, Arnout, Caliaro, Martino, Cifani, Paolo, Geurts, Bernard |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: Second version, 19 pages, 5 figures, accepted at JAMES |
| Databáze: | arXiv |
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