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.
Domains
Fluid mechanics [physics.class-ph] Atmospheric and Oceanic Physics [physics.ao-ph] Fluid Dynamics [physics.flu-dyn] Classical Physics [physics.class-ph] Computational Physics [physics.comp-ph] Geophysics [physics.geo-ph] Mathematical Physics [math-ph] Exactly Solvable and Integrable Systems [nlin.SI] Pattern Formation and Solitons [nlin.PS] Analysis of PDEs [math.AP]Origin | Files produced by the author(s) |
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