The Navier-Stokes equations along with the exact free surface boundary conditions are solved to simulate the deformation of water waves propagating over submerged dikes. The incident waves are generated by a piston-type wavemaker set up in the computation domain. Numerical results have been compared with experimental data to verify the accuracy. Transformations of waves of different Ursell numbers passing over trapezoidal dikes are studied and compared. The Fast Fourier Transform method was applied to decompose the transformed waves and the higher harmonics. The main characteristics of the flow fields are also briefly discussed.
The generation of higher harmonics as waves propagating over submerged dikes has long been known by direct field observations or by experiments (e.g. Johnson et al., 1951; Jolas, 1960). Since the deformation of water waves propagating over a submerged dike is important in the design of submerged breakwaters, this problem has attracted attention of many investigators. The phenomenon of harmonic generation can also be explained theoretically by the nonlinear shallow-water waves theory, usually the Boussrnesq equations. The derivation of Boussinesq equations is based on the assumptions of both weak nonlinearity and weak dispersivity of waves hence they may not be valid for the prediction on the trailing side of the dike: where higher harmonics may arise as deep-water waves. In order to overcome this defect, improvements on the Boussinesq equations have been developed. Peregrine (1967) developed equations of motion for long waves in water of varying depth. Madsen et al. (1991) improved the Boussinesq equation by adding a term to improve the dispersion characteristics. Battiejes and Beji (1991) derived a new set of Boussinesq equations by combining the method used by Madsen et al. (1991) and the equation proposed by Peregrine (1967). Beji and Battjes (1994) employed these equations to study the deformation of water waves passing over a dike.
