Study On Nonliearity Of Waves By Contionous Wavelet Transform

Wavelet transform is an ideal tool for time-frequency analysis of nonstational signals. In recent years, this method has been used successfully in many scientific and engineering applications. However, applications of wavelet transform in nonlinearity of ocean waves are rare. Even though some studies have used the new method to slove some issues, the advantages of it are not revealed in depth. The goal of this dissertation is to apply the Morlet wavelet transform and some related definitions for analyzing the nonlinear ocean waves, digging the advantages of the new method in analyzing the nonlinear signals deeply. Furthermore, some new methods, which are suitable to process signals in nonlinear ocean wave analysis, will be proposed based on the Morlet wavelet transform.In this thesis, based on a brief introduction of the signal processing technology, the definition, properties and advantages of the Morlet wavelet transform are introduced carfully. Then, some typical nonstational signals in physical experimental models are analyzed in detail using the Morlet wavelet transform. The major creative contributions of this dissertation are summarized as follows:1. A new groupiness factor(GF), which is the main parameter to measure groupiness of waves, is proposed based on the local wavelet energy history. The main advantage of the new GF is that the effect of the operational definition on it is much smaller than on other GF. Therefore, this new GF is much more suitable to unify wave groupiness.2. To analyze the nonlinear phase coupling in short duration series, the wavelet bicoherence spectrum is introduced. Thus, the concept of bispectrum can be used to analysis series of physical models in ocean engineering. Then, the wavelet bicoherence spectrum is used to study the nonlinear evolutions of both irregular waves propagating over a submerged sill and focusing waves over a constant depth.3. A new method to measure the instantaneous harmonic components of nonstational signals, which can not be resolved using the traditional methods, is proposed using the local wavelet scale-averaged energy.4. The evolution of wave modulations on a spatially varying, opposing current has been studied experimentally. In this study, the wave frequency modulations are represented by the instantaneous peak frequencies which are extracted by the Morlet wavelet ridges, avoiding the difficulties for obtaining instaneaneous frequencies of complicated signals using the traditional methods. The criterion for the occurrence of frequency downshift in opposing currents has been investigated. Furthermore, the characteristic and the physical mechanism for frequency downshift have also been studied.5. A new method for separating nonstationary waves into incident and reflected low-frequecy waves in time domain has been proposed based on the Morlet wavelet transform. Hence, the problem about separating nonstational wave fields accuately by the methods based on Fourier transform is sloved. A new method for separating low-frequency waves in time domain has also been proposed. The method can accurately obtain the time series of bound low-frequency waves, incident and reflected low-frequecy waves. Hence, this method can be used to investigate the cross-shore variations of phase lag of bound low-frequency waves behind short wave envelops.