Laboratory Study On The Modulational Evolution Of Nonlinear Wave Trains

Deep-water gravity waves were proved to be unstable to small perturbations and that the unstable disturbances grow exponentially as the wave trains evolve due to resonance wave interactions. Meanwhile, the initial uniform wave train would be gradually spited into several successive wave groups. This phenomenon is always called the modulational instability or Benjamin-Feir instability. The modulational instability of deep water waves is proved to be related to many instantaneous changes of ocean surfaces, such as breaking events and freak waves. Hence, in recent years, it is one of the hot and key issues in the research on the nonlinear wave dynamics. Hence, Studies on this field is very crucial, and have effects not only on the development of the nonlinear waves, but on the promotion of engineering, significance and value in engineering.In this study, new experiments on the modulational instability have been carried out in a big wave-current tank. Firstly, experiments on the evolution of initial uniform wave trains under quiescent water were carried out. The results show that, due to the instability of the wave front, the initially uniform wave trains are gradually transformed to a series of wave groups, and the wave groupiness increases with the propagation distance. In addition, the modulational evolution for shorter waves is more obvious than that of longer waves in the same effective distance, indicating that wave length plays important role in the modulational evolution. The frequency modulation of the waves is studied using the instantaneous frequencies, which is extracted through the wavelet transform. The instantaneous frequencies reveal that the modulation of frequency occurs at local time firstly, and then gradually expands. Moreover, even without the effective frequency downshift, some local frequency downshift is observed, suggesting that frequency downshift begin at local time.Secondly, a series of wave trains with initially imposed sidebands, varying initial steepness, perturbed amplitudes and frequencies, are physically generated in the long wave flume. Experimental results show that the larger of the wave steepness, the faster of the growth of sidebands. To study the frequency and phase modulation, the Morlet wavelet transform is adopted to extract the instantaneous frequency of wave trains and the phase functions of each wave components. The instantaneous frequency shows that there are local frequency downshifts even the effective frequency downshift was not observed. The frequency modulation increases with increasing the amplitude modulation, and shows abrupt changes at the peak amplitude modulation. The wrapped phase functions show that in the early stage of the modulation, the phase of the upper sideband diverges from that of the carrier waves first. However, at the later stage, the discrepancy phase from the carrier wave transformed to the lower sideband.The phase deviations appear at the front of the peak envelopes.Lastly, experiments on the modulation evolution of nonlinear wave trains in the presence of currents with different velocity are carried out. The experimental results indicate that currents play an important role in the modulational evolution. Opposing currents can speed the modulational evolution and promote the asymmetry growth of the lower and upper sidebands, and following currents have stabilization effect on the evolution.