A test case for the inviscid shallow‐water equations on the sphere. (3rd November 2015)

• Record Type: Journal Article
• Authors: Scott, R. K.; Harris, L. M.; Polvani, L. M.
• Is Part Of: Quarterly journal of the Royal Meteorological Society. Volume 142:Number 694(2016)
• Page Start: 488
• Page End: 495
• Publication Date: 2015-11-03
• Subjects: shallow‐water flow -- numerical modelling -- potential vorticity; Meteorology -- Periodicals; 551.5
• DOI: 10.1002/qj.2667
• Languages: English
• ISSNs: 0035-9009

Abstract

Abstract : 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.