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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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https://hal.archives-ouvertes.fr/hal-01552229
Contributor : Denys Dutykh <>
Submitted on : Wednesday, May 2, 2018 - 7:11:46 PM
Last modification on : Wednesday, February 19, 2020 - 2:00:17 PM
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Gayaz Khakimzyanov, Denys Dutykh, Zinaida Fedotova. Dispersive shallow water wave modelling. Part III: Model derivation on a globally spherical geometry. Communications in Computational Physics, Global Science Press, 2018, 23 (2), pp.315-360. ⟨10.4208/cicp.OA-2016-0179c⟩. ⟨hal-01552229v2⟩

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