Dispersive shallow water wave modelling. Part III: Model derivation on a globally spherical geometry
Résumé
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.
Domaines
- Mécanique des fluides [physics.class-ph]
- Physique Atmosphérique et Océanique [physics.ao-ph]
- Dynamique des Fluides [physics.flu-dyn]
- Physique Classique [physics.class-ph]
- Physique Numérique [physics.comp-ph]
- Géophysique [physics.geo-ph]
- Physique mathématique [math-ph]
- Systèmes Solubles et Intégrables [nlin.SI]
- Formation de Structures et Solitons [nlin.PS]
- Equations aux dérivées partielles [math.AP]
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