Numerical instabilities of spherical shallow water models considering small equivalent depths
Peixoto, PS; Thuburn, J; Bell, MJ
Date: 30 October 2017
Article
Journal
Quarterly Journal of the Royal Meteorological Society
Publisher
Wiley / Royal Meteorological Society
Publisher DOI
Abstract
Shallow water models are often adopted as an intermediate step in the development of
atmosphere and ocean models, though they are usually tested only with fluid depths
relevant to barotropic fluids. Here we investigate numerical instabilities emerging in
shallow water models considering small fluid depths, which are relevant for ...
Shallow water models are often adopted as an intermediate step in the development of
atmosphere and ocean models, though they are usually tested only with fluid depths
relevant to barotropic fluids. Here we investigate numerical instabilities emerging in
shallow water models considering small fluid depths, which are relevant for baroclinic
fluids. Different numerical instabilities of similar nature are investigated. The first one is
due to the adoption of the vector invariant form of the momentum equations, related to
what is known as the Hollingsworth instability. We provide examples of this instability
with finite volume and finite element schemes used in modern quasi-uniform spherical
grid based models. The second is related to an energy conserving form of discretization
of the Coriolis term in finite difference schemes on latitude-longitude global models.
Simple test cases with shallow fluid depths are proposed as a means of capturing and
predicting stability issues that can appear in three-dimensional models using only twodimensional
shallow-water codes.
Mathematics and Statistics
Faculty of Environment, Science and Economy
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