Dispersive Shallow Water Wave Modelling. Part III: Model Derivation on a Globally Spherical Geometry
Year: 2018
Communications in Computational Physics, Vol. 23 (2018), Iss. 2 : pp. 315–360
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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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2016-0179c
Communications in Computational Physics, Vol. 23 (2018), Iss. 2 : pp. 315–360
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 46
Keywords: Motion on a sphere long wave approximation nonlinear dispersive waves spherical geometry flow on sphere.
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