A test case for the inviscid shallow-water equations on the sphere
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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.
Scott , R K , Harris , L M & Polvani , L M 2016 , ' A test case for the inviscid shallow-water equations on the sphere ' Quarterly Journal of the Royal Meteorological Society , vol 142 , no. 694 , pp. 488-495 . DOI: 10.1002/qj.2667
Quarterly Journal of the Royal Meteorological Society
© 2015, Publisher / the Author(s). This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at onlinelibrary.wiley.com / https://dx.doi.org/10.1002/qj.2667
DescriptionPartial support for this work was provided through the National Science Foundation award AGS-1333029.
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