Premium
A conservative scheme for the shallow‐water system on a staggered geodesic grid based on a Nambu representation
Author(s) -
Sommer Matthias,
Névir Peter
Publication year - 2009
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.368
Subject(s) - shallow water equations , discretization , geodesic , enstrophy , grid , mathematics , conservation law , hamiltonian (control theory) , partial differential equation , mathematical analysis , mathematical optimization , geometry , physics , meteorology , vorticity , vortex
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