Dispersive Shallow Water Wave Modelling. Part III: Model Derivation on a Globally Spherical Geometry

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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.