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

Egan, C.P., Bourne, D.P., Cotter, C.J., Cullen, M.J.P., Pelloni, B., Roper, S.M. and Wilkinson, M. (2022) A new implementation of the geometric method for solving the Eady slice equations. Journal of Computational Physics, 469, 111542. (doi: 10.1016/j.jcp.2022.111542)

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.

• Item Type: Articles
• Additional Information: C. P. Egan is supported by The Maxwell Institute Graduate School in Analysis and its Applications, a Centre for Doctoral Training funded by the UK Engineering and Physical Sciences Research Council (EPSRC) via the grant EP/L016508/01, the Scottish Funding Council, Heriot-Watt University and the University of Edinburgh. D. P. Bourne is supported by the EPSRC via the grant EP/V00204X/1 Mathematical Theory of Polycrystalline Materials. C. J. Cotter would like to acknowledge the NERC grants NE/K012533/1 and NE/M013634/1. B. Pelloni and M. Wilkinson gratefully acknowledge the support of the EPSRC via the grant EP/P011543/1 Analysis of models for large-scale geophysical flows.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Roper, Dr Steven
• Authors: Egan, C.P., Bourne, D.P., Cotter, C.J., Cullen, M.J.P., Pelloni, B., Roper, S.M., and Wilkinson, M.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Computational Physics
• Publisher: Elsevier
• ISSN: 0021-9991
• ISSN (Online): 1090-2716
• Published Online: 19 August 2022
• Copyright Holders: Copyright © 2022 The Authors
• First Published: First published in Journal of Computational Physics 469: 111542
• Publisher Policy: Reproduced under a Creative Commons License