Computational and Applied Mathematics seminar

Abstract: In this talk, I will present the development of novel structure-preserving numerical methods for simulating global geophysical fluid dynamics. The methods are derived using a geometric approach to the quasi-geostrophic (QG) equations on a sphere, revealing their Lie-Poisson structure. This leads to energy and enstrophy-conserving numerical methods that also preserve higher-order invariants, known as Casimirs. These methods enable long-time simulations and are applied to study geostrophic turbulence and its properties, zonal jet formation, and critical latitudes in both single- and multi-layer models. I'll discuss both the development of the numerical methods and findings from simulations, including insights into the role of geostrophic balance and stratification in large-scale global fluid dynamics.