Numerical Study of Trapped Waves Propagation over a Submerged Step

In this paper, propagation of trapped waves traveling along a submerged step is investigated numerically. Within the framework of the exact model of surface gravity waves, a numerical model based on a conformal mapping method is developed to simulate nonlinear wave propagation. Regular incident waves over a range of driving frequencies and ratio of the depth in shallower water (h2) and deeper water (h1) are designed to generate the first four trapped modes. For each of the trapped modes considered, the time and spatial domain structure of the wave trapping are obtained and analysed. The trapped harmonic wave amplitude is characterized by reflection coefficients and Fourier series coefficients, as well as the parameters of skewness and kurtosis. The results of reflection coefficients are found to agree well with the theoretical predictions. In addition, the linear and weakly nonlinear trapped waves induced by weak resonant interactions of water waves are identified by the apparent variation of the higher harmonic components. It is found that the nonlinearity grows with the increase of trapped modes and wave steepnesses but has little effect on the reflection.