Modified Shallow Water Equations for significantly varying seabeds
This work provides a new hyperbolic model for wave propagation over complex seabeds, relevant for coastal engineering and tsunami modeling, but the improvements over existing methods are not quantified.
The authors propose a modified version of the Nonlinear Shallow Water Equations for irrotational surface waves over significantly varying seabeds, derived from a variational principle without small parameters. The new hyperbolic model extends classical Saint-Venant equations and is validated with test cases, showing potential for tsunami modeling.
In the present study, we propose a modified version of the Nonlinear Shallow Water Equations (Saint-Venant or NSWE) for irrotational surface waves in the case when the bottom undergoes some significant variations in space and time. The model is derived from a variational principle by choosing an appropriate shallow water ansatz and imposing some constraints. Our derivation procedure does not explicitly involve any small parameter and is straightforward. The novel system is a non-dispersive non-hydrostatic extension of the classical Saint-Venant equations. A key feature of the new model is that, like the classical NSWE, it is hyperbolic and thus similar numerical methods can be used. We also propose a finite volume discretisation of the obtained hyperbolic system. Several test-cases are presented to highlight the added value of the new model. Some implications to tsunami wave modelling are also discussed.