Near coast tsunami waveguiding: simulations for various wave models

Shallow parts in a sloping bottom toward the coast can be expected to act as a waveguide, in partial analogy with optical waveguiding. We will present numerical simulations that convincingly show that large enhanced wave amplification happens for tsunami waves in certain geometries and bathymetries. Since this is even the case for shallow regions that have cross sections of the order of badly resolved numerical scales, this phenomenon may at least partly explain that tsunami heights and coastal effects as observed in reality show such high variability along the coastline. This report, following [1], supports a more concise publication that will be published soon [2]. In this report we will provide detailed results of extensive simulations using various wave models and different gridsizes. We will show results obtained with the commonly used Shallow Water Equations and with a more accurate dispersive wave model. For the latter simulations we use a recently derived Variational Boussinesq model. We will also show that relatively small gridsizes are needed to capture the transversal flow near the waveguide; on grids that are too coarse, the enhanced amplification will not be observable. This may provide a partial explanation that spatial variability due to relatively shallow bottom variations will not be present in most simulations.