Computational and Applied Mathematics seminar

Abstract: Geophysical fluid dynamics (GFD) describes flows of fluids on a planetary scale. We will discuss the recent contribution to the hierarchy of GFD models developed in [1], called thermal quasi-geostrophic (TQG) equations on the sphere. We will give Arnold’s formulation of TQG. Surprisingly, the TQG equations are formulated in terms of Morrison-Greene brackets (semidirect product brackets) discovered long ago for another theory - magnetohydrodynamics (MHD). Further, we will discuss the structure-preserving discretisation for TQG based on Zeitlin’s matrix equations and the Lie-Poisson time integrator developed for semidirect products, and finally we will see some simulations.

[1] M. Roop, S. Ephrati. Thermal quasi-geostrophic model on the sphere: Derivation and structure-preserving simulation. Phys. Fluids. 37, 096601. 2025.