TRANSFORMATION OF A NONLINEAR-WAVE TRAIN PASSING OVER A SUBMERGED SHELF WITHOUT BREAKING

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 loca tions agree favorably with experimental observations. This phenomenon is triggered by higher harmonic generation and nonlinear resonant inte raction over the shelf. In the case of a strongly nonlinear wave field over the shelf, the resultant beat length of higher harmonic amplitud es cannot be properly described by weakly nonlinear solutions, in whic h the linear dispersion relation is employed for free waves. A large a mount of energy in bound harmonics over the shelf is abruptly transfer red into free higher harmonics in the trailing side of the shelf, wher e a second-order theory markedly overestimates the first- and the seco nd-harmonic amplitudes. Variations of the decomposition characteristic between the shelf's configuration and the incident wave conditions ar e 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 transf ormation of multicomponent random waves has been studied. The results show that nonlinear interaction among the incident wave components als o generates distinct higher harmonics. The power spectrum of the trans mitted wave is found to be significantly influenced by the phase diffe rences among the incident components.