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

C. P. Egan, D. P. Bourne, C. J. Cotter, M. J. P. Cullen, B. Pelloni, S. M. Roper, M. Wilkinson

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
43 Downloads (Pure)


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.
Original languageEnglish
Article number111542
JournalJournal of Computational Physics
Early online date19 Aug 2022
Publication statusPublished - 15 Nov 2022


  • Adaptive time-stepping
  • Eady model
  • Frontogenesis
  • Geometric method
  • Semi-discrete optimal transport
  • Semi-geostrophic

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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