A terrain-following Boussinesq system
dispersive waves | inhomogeneous media | asymptotic theory
A long wave model is derived asymptotically from the nonlinear potential theory equations. The flow regime of interest is incompressible, irrotational and inviscid. Asymptotic analysis leads to a weakly nonlinear, weakly dispersive (variable coefficient) Boussinesq system valid for a wide class of topographies. The mild slope hypothesis is not required and rapidly varying topographies are also considered. In analogy with atmospheric models we use a terrain-following coordinate system. The novelty being that this coordinate system naturally suggests the weighted averaging of terrain-following velocity components, as opposed to the depth-average of horizontal velocity components found in standard shallow water formulations. Furthermore, a Schwarz-Christoffel Toolbox is used to provide additional insight on these new results. Regarding applications the proposed model can be used for studying solitary waves interacting with fine scale inhomogeneities, a theme of great interest. The terrain-following model also presents potential numerical advantages for Boussinesq solvers.