Localization for spatial-spectral implementations of 1D Analytic Boussinesq equations

Accurate simulations of waves in oceanic and coastal areas should take dispersive effects over a large range of frequencies into account in the relevant order of nonlinearity of the equation. Taking the exact Hamiltonian-Boussinesq formulation of surface waves as starting point, a fully Hamiltonian consistent spatial-spectral approximation of the kinetic energy leads to a model that has exact dispersion above constant depth and can deal with arbitrary depth, for nonlinearity in second, third and fourth order of the surface elevation (Kurnia and van Groesen, 2014). In this paper we describe and show with simulations of various 1D cases of breaking and non-breaking waves how localized effects of partially or fully reflective walls, run-up on a coast and the dam-break problem can be dealt with in the implementation with global Fourier integral operators; a dynamic or post-processing step will show the interior flow properties.