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arXiv · 2203.04903

A new implementation of the geometric method for solving the Eady slice equations

Charlie P. Egan·David P. Bourne·Colin J. Cotter·Mike J. P. Cullen·Beatrice Pelloni·Steven M. Roper·Mark Wilkinson
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Abstract

We present a new implementation of the geometric method of Cullen & Purser (1984) for solving the semi-geostrophic Eady slice equations which model large scale atmospheric flows and frontogenesis. The geometric method is a Lagrangian discretisation, where the PDE is approximated by a particle system. An important property of the discretisation is that it is energy conserving. We restate the geometric method in the language of semi-discrete optimal transport theory and exploit this to develop a fast implementation that combines the latest results from numerical optimal transport theory with a novel adaptive time-stepping scheme. Our results enable a controlled comparison between the Eady-Boussinesq vertical slice equations and their semi-geostrophic approximation. We provide further evidence that weak solutions of the Eady-Boussinesq vertical slice equations converge to weak solutions of the semi-geostrophic Eady slice equations as the Rossby number tends to zero.

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Charlie P. Egan, David P. Bourne, Colin J. Cotter, Mike J. P. Cullen, Beatrice Pelloni, Steven M. Roper, Mark Wilkinson. 2022-03-09. A new implementation of the geometric method for solving the Eady slice equations. https://doi.org/10.1016/j.jcp.2022.111542

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