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

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