A test case for the inviscid shallow-water equations on the sphere

R. K. Scott*, L. M. Harris, L. M. Polvani

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)
1 Downloads (Pure)


A numerically converged solution to the inviscid global shallow-water equations for a predefined time interval is documented to provide a convenient benchmark for model validation. The solution is based on the same initial conditions as a previously documented solution for the viscous equations. The solution is computed using two independent numerical schemes, one a pseudospectral scheme based on an expansion in spherical harmonics and the other a finite-volume scheme on a cubed-sphere grid. Flow fields and various integral norms are documented to facilitate model comparison and validation. Attention is drawn to the utility of the potential vorticity supremum as a convenient and sensitive test of numerical convergence, in which the exact value is known a priori over the entire time interval.

Original languageEnglish
Pages (from-to)488-495
Number of pages8
JournalQuarterly Journal of the Royal Meteorological Society
Issue number694
Early online date3 Nov 2015
Publication statusPublished - Jan 2016


  • Shallow-water flow
  • Numerical modelling
  • Potential vorticity


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