Dispersive shallow water wave modelling. Part III: Model derivation on a globally spherical geometry

Abstract : The present article is the third part of a series of papers devoted to the shallow water wave modelling. In this part, we investigate the derivation of some long wave models on a deformed sphere. We propose first a suitable for our purposes formulation of the full Euler equations on a sphere. Then, by applying the depth-averaging procedure we derive first a new fully nonlinear weakly dispersive base model. After this step, we show how to obtain some weakly nonlinear models on the sphere in the so-called Boussinesq regime. We have to say that the proposed base model contains an additional velocity variable which has to be specified by a closure relation. Physically, it represents a dispersive correction to the velocity vector. So, the main outcome of our article should be rather considered as a whole family of long wave models.
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Contributeur : Denys Dutykh <>
Soumis le : samedi 1 juillet 2017 - 14:49:00
Dernière modification le : jeudi 11 janvier 2018 - 06:12:26
Document(s) archivé(s) le : jeudi 14 décembre 2017 - 19:54:38


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  • HAL Id : hal-01552229, version 1
  • ARXIV : 1707.01304



Gayaz Khakimzyanov, Denys Dutykh, Zinaida Fedotova. Dispersive shallow water wave modelling. Part III: Model derivation on a globally spherical geometry. 49 pages, 2 figures, 79 references. Accepted to Commun. Comput. Phys. Other author's papers can b.. 2017. 〈hal-01552229〉



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