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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Soumis le : mercredi 2 mai 2018 - 19:11:46
Dernière modification le : dimanche 6 mai 2018 - 01:06:25
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  • HAL Id : hal-01552229, version 2
  • 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. Published in Commun. Comput. Phys. Some minor typos were corr.. 2018. 〈hal-01552229v2〉



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