Hawassi-ab modelling and simulation of fully dispersive nonlinear waves above bathymetry

Abstract

A challenge in the study of water waves is that the motion can exhibit qualitative differences at different scales such as deep water versus shallow water, long wavelength versus short wavelength, etc.. That leads to a restriction in the applicability of the existing wave models. This dissertation concerns the development of an accurate and efficient model that can simulate wave propagation in any range of wave lengths, in any water depth and moreover can deal with various inhomogeneous problems such as bathymetry and walls, leading to wave structure interactions. Based on a variational principle of water waves, the dynamic equations are of Hamiltonian form for wave elevation and surface potential with non-local operators applied to the canonical surface variables. Since the kinetic energy cannot be expressed explicitly in the basic variables an approximation is required. The approximate Hamilton equations are expressed in pseudo-differential operators (PDO) applied to the surface variables. The PDO has a physical interpretation related to the phase velocity. The phase velocity as function of wave length is specified by a dispersion relation. A spatial-spectral implementation with the global PDO or a generalization with global Fourier integral operators (FIO) can retain the exact dispersion property of the model. To deal with practical applications, the model with localization methods in the FIO can deal with localized effects such as breaking waves, partially or fully reflective walls, submerged bars, run-up on shores, etc. The inclusion of a fixed-structure in the spatial-spectral setting is a challenging task. The method as presented here perhaps serves as a first contribution in this topic. Performance of the model is shown by comparing the simulation result with measurement data of various long crested cases of breaking and non-breaking waves. The model has been extensively tested against at least 50 measurement data. Moreover, 30 measurement data of wave breaking experiments were designed by the accurate wave model. The models and methods presented in this dissertation have been packaged as software under the name HAWASSI-AB; here HAWASSI stands for Hamiltonian Wave-Ship-Structure Interaction, while AB stands for Analytic Boussinesq. Further information of the software can be found on http://hawassi.labmath-indonesia.org.