Transformation of a nonlinear wave train passing over a submerged shelf without breaking

Abstract

The decomposition phenomenon of a nonlinear wave train passing over a submerged shelf without breaking has been investigated by a previously developed numerical model. The computed wave profiles at various locations agree favorably with experimental observations. This phenomenon is triggered by higher harmonic generation and nonlinear resonant interaction over the shelf. In the case of a strongly nonlinear wave field over the shelf, the resultant beat length of higher harmonic amplitudes cannot be properly described by weakly nonlinear solutions, in which the linear dispersion relation is employed for free waves. A large amount of energy in bound harmonics over the shelf is abruptly transferred into free higher harmonics in the trailing side of the shelf, where a second-order theory markedly overestimates the first- and the second-harmonic amplitudes. Variations of the decomposition characteristic between the shelf's configuration and the incident wave conditions are also investigated. When the width of the shelf is nearly one half of the beat length of a higher harmonic amplitude, the magnitude of the corresponding component becomes remarkably large in transmitted waves. In the case of large incident waves, significant decomposition takes place even when the shelf is deeply submerged. In addition, the transformation of multicomponent random waves has been studied. The results show that nonlinear interaction among the incident wave components also generates distinct higher harmonics. The power spectrum of the transmitted wave is found to be significantly influenced by the phase differences among the incident components.