Abstract
AbstractA conservative spatial discretization scheme is constructed for a shallow‐water system on a geodesic grid with C‐type staggering. It is derived from the original equations written in Nambu form, which is a generalization of Hamiltonian representation. The term ‘conservative scheme’ refers to one that preserves the constitutive quantities, here total energy and potential enstrophy. We give a proof for the non‐existence of potential enstrophy sources in this semi‐discretization. Furthermore, we show numerically that in comparison with traditional discretizations, such schemes can improve stability and the ability to represent conservation and spectral properties of the underlying partial differential equations. Copyright © 2009 Royal Meteorological Society
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