Symmetry group analysis of the shallow water and semi-geostrophic equations

Bila, Nicoleta and Mansfield, Elizabeth L. and Clarkson, Peter (2006) Symmetry group analysis of the shallow water and semi-geostrophic equations. Quarterly Journal of Mechanics and Applied Mathematics, 59 (1). pp. 95-123. ISSN 0033-5614. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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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'.

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Peter A Clarkson
Date Deposited: 30 Aug 2008 19:34
Last Modified: 28 Apr 2014 15:53
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