Dispersive Shallow Water Wave Modelling. Part III: Model Derivation on a Globally Spherical Geometry (Communications in Computational Physics, 2018)
The present article is the third part of a series of papers devoted to the shallowwater wave modelling. In this part we investigate the derivation of some longwave models on a deformed sphere. We propose first a suitable for our purposesformulation of the full EULER equations on a sphere. Then, by applying the depth-averagingprocedure we derive first a new fully nonlinear weakly dispersive basemodel. After this step we show how to obtain some weakly nonlinear models on thesphere in the so-called BOUSSINESQ regime. We have to say that the proposed basemodel contains an additional velocity variable which has to be specified by a closurerelation. Physically, it represents a dispersive correction to the velocity vector. So, themain outcome of our article should be rather considered as a whole family of longwave models.
Keywords: Motion on a sphere; long wave approximation; nonlinear dispersive waves; spherical geometry; flow on sphere.