Analysis of Discrete Shallow-Water Models on Geodesic Delaunay Grids with C-Type Staggering

The properties of C-grid staggered spatial discretizations of the shallow-water equations on regular Delaunay triangulations on the sphere are analyzed. Mass-conserving schemes that also conserve either energy or potential enstrophy are derived, and their features are analogous to those of the C-grid staggered schemes on quadrilateral grids. Results of numerical tests carried out with explicit and semi-implicit time discretizations show that the potential-enstrophy-conserving scheme is able to reproduce correctly the main features of large-scale atmospheric motion and that power spectra for energy and potential enstrophy obtained in long model integrations display a qualitative behavior similar to that predicted by the decaying turbulence theory for the continuous system.