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Dispersive shallow water wave modelling. Part III: Model derivation on a globally spherical geometry

Khakimzyanov, Gayaz ; Dutykh, Denys ; Fedotova, Zinaida

Arxiv ID: 1707.01304

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  • Nhan đề:
    Dispersive shallow water wave modelling. Part III: Model derivation on a globally spherical geometry
  • Tác giả: Khakimzyanov, Gayaz ; Dutykh, Denys ; Fedotova, Zinaida
  • Chủ đề: Physics - Fluid Dynamics ; Physics - Atmospheric And Oceanic Physics ; Physics - Classical Physics ; Physics - Computational Physics
  • Mô tả: 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. Comment: 49 pages, 2 figures, 79 references. Published in Commun. Comput. Phys. Some minor typos were corrected. Other author's papers can be downloaded at http://www.denys-dutykh.com/
  • Số nhận dạng: Arxiv ID: 1707.01304

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