Diffraction and Refraction of Nonlinear Waves by the Green–Naghdi Equations

Abstract Diffraction and refraction of nonlinear shallow water waves due to uneven bathymetry are studied by use the Green–Naghdi (GN) equations in three dimensions. A numerical wave tank consisting deep, transitional, regions is created. Various forms three-dimensional bathymetry, ramps with nonuniform profiles large slopes, used connect deep-water side shelf. wavemaker placed at upwave domain, capable generating solitary cnoidal GN equations. absorber located downwave domain minimize reflection back into domain. The system solved numerically time a second-order finite-difference approach for spatial discretization, boundary-fitted coordinate system, modified Euler method marching. Results include surface elevation particle velocities compared existing solutions where possible. Overall, very good agreement observed. Discussion provided on nonlinearity dispersion effects diffraction various ramps, as well performance solving these problems.