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- Title
Symmetry group analysis of the shallow water and semi-geostrophic equations.
- Authors
BÎLĂ, NICOLETA; MANSFIELD, ELIZABETH L.; CLARKSON, PETER A.
- Abstract
The two-dimensional shallow water equations and their semi-geostrophic approximation that arise in meteorology and oceanography are analysed from the point of view of symmetry groups theory. A complete classification of their associated classical symmetries, potential symmetries, variational symmetries and conservation laws is found. The semi-geostrophic equations are found to lack conservation of angular momentum. We also show how the particle relabelling symmetry can be used to rewrite the semi-geostrophic equations in such a way that a well-defined formal series solution, smooth only in time, may be carried out. We show that such solutions are in the form of an ‘infinite linear cascade’.
- Subjects
SYMMETRY; EQUATIONS; APPROXIMATION theory; MATHEMATICS; MECHANICS (Physics)
- Publication
Quarterly Journal of Mechanics & Applied Mathematics, 2006, Vol 59, Issue 1, p95
- ISSN
0033-5614
- Publication type
Article
- DOI
10.1093/qjmam/hbi033