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.