To study the nonlinear wave interaction with large submerged, rectangular breakwaters, the writers developed a fully nonlinear numerical wave tank, which is based on the mixed Eulerian-Lagrangian (MEL) formulation. The desingularized boundary element method (DBIEM) is adopted here to circumvent the singular integration in the boundary element methods (BEM) that are based on Green's function formulations. After code verification, our nonlinear numerical wave tank is used to study the nonlinear wave scattering by a submerged rectangular step. In comparison with our experiments, we found that higher harmonic wave components generated by nonlinear wave processes in shallower water over the step are well predicted by our DBIEM numerical wave tank. The reflection coefficients and the transmission coefficients of the second harmonic waves are also modeled satisfactorily. The transmission coefficients of the first harmonic waves predicted by the DBIEM demonstrated improvement over those by linear theory.
Submerged breakwaters are frequently used to provide economic measure in shoreline erosion control. The purpose of a submerged breakwater is not to create completely calm water behind the breakwater, but to reduce the wave intensity behind the breakwater to an acceptable level. Early research on this subject focused on the linear interactions between waves and submerged objects. Following Newman (1965), who first studied the scattering of long waves by submerged obstacles, Mei and Black (1969) investigated the wave scattering by two-dimensional obstacles in waters of finite depth. Recent reviews of linear wave scattering by impermeable submerged steps can be found in Dingemans (2000) or Mei et al. (2005). Ocean waves nearshore are most likely nonlinear in nature and the interactions between waves and the submerged structures are strongly or at least weakly nonlinear as well. It is not always possible to obtain analytical solutions for fully nonlinear problems.