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A test case for the inviscid shallow‐water equations on the sphere
Author(s) -
Scott R. K.,
Harris L. M.,
Polvani L. M.
Publication year - 2015
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.2667
Subject(s) - inviscid flow , shallow water equations , finite volume method , mathematics , interval (graph theory) , flow (mathematics) , convergence (economics) , grid , mathematical analysis , infimum and supremum , vorticity , mechanics , vortex , geometry , physics , combinatorics , economics , economic growth
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.