A conservative scheme for the shallow-water system on a staggered geodesic grid based on a Nambu representation



A 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