Nonlinear Diffraction of Waves by a Submerged Shelf in Shallow Water

Abstract

The diffraction of water waves by submerged obstacles in shallow water generally requires the use of a nonlinear theory since both dispersive and nonlinear effects are important. In this work, wave diffraction is studied in a numerical wave tank using the Level I Green-Naghdi (GN) equations. Cnoidal waves are generated numerically by a wave maker situated at one end of a two-dimensional numerical wave tank. At the downwave end of the tank, an open-boundary condition is implemented to simulate a wave-absorbing beach, and thus to reduce reflections. The GN equations are solved in the time-domain by employing a finite-difference method. The numerical method is applied to diffraction of cnoidal waves by a submerged shelf, or a sand bar, of considerable height relative to water depth. The predicted results are compared with the available experimental data which indicate the importance of nonlinearity for the shallow-water conditions.