2023/06/27 by Arnout Franken, Martino Caliaro, Franken, Arnout +5 · 2 citations
Computer Science · Earth and Planetary Sciences · Engineering · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Meteorological Phenomena and Simulations #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.2306.15481
openalex publication_date 2023/06/27 · openalex created_date 2023/06/29 · openalex updated_date 2026/07/28
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 → ∞; 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.