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Volume 23, Issue 2
Dispersive Shallow Water Wave Modelling. Part III: Model Derivation on a Globally Spherical Geometry

Gayaz Khakimzyanov, Denys Dutykh & Zinaida Fedotova

DOI: 10.4208/cicp.OA-2016-0179c

Commun. Comput. Phys., 23 (2018), pp. 315-360.

Published online: 2018-02

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  • 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.

  • Keywords

Motion on a sphere, long wave approximation, nonlinear dispersive waves, spherical geometry, flow on sphere.

  • AMS Subject Headings

76B15, 76B25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-23-315, author = {Gayaz Khakimzyanov, Denys Dutykh and Zinaida Fedotova}, title = {Dispersive Shallow Water Wave Modelling. Part III: Model Derivation on a Globally Spherical Geometry}, journal = {Communications in Computational Physics}, year = {2018}, volume = {23}, number = {2}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2016-0179c}, url = {http://global-sci.org/intro/article_detail/cicp/10529.html} }
TY - JOUR T1 - Dispersive Shallow Water Wave Modelling. Part III: Model Derivation on a Globally Spherical Geometry AU - Gayaz Khakimzyanov, Denys Dutykh & Zinaida Fedotova JO - Communications in Computational Physics VL - 2 SP - 315 EP - 360 PY - 2018 DA - 2018/02 SN - 23 DO - http://doi.org/10.4208/cicp.OA-2016-0179c UR - https://global-sci.org/intro/article_detail/cicp/10529.html KW - Motion on a sphere, long wave approximation, nonlinear dispersive waves, spherical geometry, flow on sphere. AB -

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.

Gayaz Khakimzyanov, Denys Dutykh and Zinaida Fedotova. (2018). Dispersive Shallow Water Wave Modelling. Part III: Model Derivation on a Globally Spherical Geometry. Communications in Computational Physics. 23 (2). 315-360. doi:10.4208/cicp.OA-2016-0179c
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