# Geometry of shallow-water dynamics with thermodynamics

@inproceedings{BeronVera2021GeometryOS, title={Geometry of shallow-water dynamics with thermodynamics}, author={F. Beron-Vera}, year={2021} }

We review the geometric structure of the ILPE model, a rotating shallow-water model with variable buoyancy, thus sometimes called “thermal” shallow-water model. We start by discussing the Euler–Poincaré equations for rigid body dynamics and the generalized Hamiltonian structure of the system. We then reveal similar geometric structure for the ILPE. We show, in particular, that the model equations and its (Lie– Poisson) Hamiltonian structure can be deduced from Morrison and Greene’s (1980… Expand

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