Modified shallow water equations for significantly varying seabeds

Abstract

Abstract. 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.

Non-dispersive conservative regularisation of nonlinear shallow water (and isentropic Euler equations)

“…As anti-aliasing we use an eight-order Erfc-Log filter [5]. In order to compare the regularised solutions with entropic solutions to the original hyperbolic system, we employ the finite volume scheme described in some detail in [12]. Thus, we do not reproduce the numerical details in the present study.…”

On the modelling of shallow turbidity flows

“…Consequently, some high order finite volume well-balanced schemes have to be developed to solve numerically the density current models proposed in our study. This technology is relatively well mastered nowadays [14][15][16]31].…”

Experimental and numerical study of the propagation of focused wave groups in the nearshore zone

“…In the dispersive focusing technique, the wave speed depends on the wavelength. For this reason, Boussinesq equations capture more physical effects than the classical shallow water equations [22].…”