Title: Symmetry analysis and exact solutions of multi-layer quasi-geostrophic problem

Speaker: Serhii Koval

Abstract: After a brief introduction to the theory of symmetries of differential equations, I will discuss symmetry analysis of the multi-layer quasi-geostrophic problem. This model is given by a system of arbitrary number of coupled barotropic vorticity equations. Using original methods, we compute the maximal Lie invariance algebra and the complete pseudogroup of point symmetries of the model. After classifying one- and two-dimensional subalgebras of the Lie invariance algebra, we exhaustively study codimension-one, -two and -three Lie reductions. Notably, among invariant submodels of the original nonlinear model, we obtain systems of well-known linear equations, including Helmholtz, Klein-Gordon, Whittaker, Bessel and linearized Benjamin-Bona-Mahony equations. Integration of these systems depends heavily on spectral properties of the model's vertical coupling matrix, which we also revisit in detail. As a result, we construct wide families of exact solutions, including rediscovered representations of stationary and travelling baroclinic Rossby waves, coherent baroclinic eddies and localized dipolar vortices. We illustrate relevant physical solutions using real-world geophysical data for a three-layer ocean model.

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Location: HH3017

Date and Time: Thursday, Feb. 12 at 01:00 PM - 01:50 PM (NST)

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