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作者机构:Austrian Acad Sci Johann Radon Inst Computat & Appl Math A-4040 Linz Austria Inst Math Stat & Actuarial Sci Canterbury CT3 1BD Kent England
出 版 物:《QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS》 (力学和应用数学季刊)
年 卷 期:2006年第59卷第1期
页 面:95-123页
核心收录:
学科分类:08[工学] 0701[理学-数学] 0801[工学-力学(可授工学、理学学位)]
基 金:Engineering and Physical Sciences Research Council, EPSRC, (GR/M28866) Isaac Newton Trust
主 题:DECOMPOSITION ALGORITHMS DIFFERENTIAL-EQUATIONS CONSERVATION-LAWS ALGEBRA COMPUTATION
摘 要: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 .