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This paper deals with the implementation of a new, efficient,non-perturbative, Hamiltonian coupled-mode theory (HCMT) for the fullynonlinear, potential flow (NLPF) model of water waves over arbitrarybathymetry, Papoutsellis and Athanassoulis (2017) (arXiv:1704.03276).Applications considered herein concern the interaction of solitary waves withbottom topographies and vertical walls both in two- and three-dimensionalenvironments. The essential novelty is a new representation of theDirichlet-to-Neumann operator, needed to close the Hamiltonian evolutionequations. This representation emerges from the treatment of the substratekinematical problem by means of exact semi-separation of variables in theirregular fluid domain, established recently by Athanassoulis & Papoutsellis(2017) (https://doi.org/10.1098/rspa.2017.0017). The HCMT ensures an efficientdimensional reduction of the exact NLFP, being able to treat an arbitrarybathymetry as simply as the flat-bottom case. A key point for the efficientimplementation of HCMT is the fast and accurate evaluation of the space-timevarying coefficients appearing in some of its equations. All varyingcoefficients are calculated analytically, resulting in a refined version of thetheory, characterized by improved accuracy at significantly reducedcomputational time. This improved version of HCMT is first validated againstexisting experimental results and other computations, and subsequently appliedto new solitary wave-bottom interaction problems. The latter include: i) theinvestigation of a new type of Bragg scattering effect, appearing when asolitary wave propagates over a seabed with a sinusoidal patch, and ii) thedisintegration, focusing and reflection of a solitary wave moving over athree-dimensional bathymetry consisting of parallel banks and troughs, andimpinging on a vertical wall.

Implementation of a fully nonlinear Hamiltonian Coupled-Mode Theory, and application to solitary wave problems over bathymetry