| The thesis is composed of three subjects, independent yet interrelated. The first part deals with the surface wave breaking problem, in which a mechanism of wave-breaking through intrinsic hydrodynamic instability is discovered. The second part is a general theory for non-linear evolution of three-dimensional resonant side-band wave systems. In part three, dynamics of nonlinear wave systems is generalized for non-conservative systems, and applied to model energetic ocean wave systems by taking the real effects into account of wind and dissipation due to nonlinear breaking and large scale diffusion at sea.; In Part I, a physical picture, how waves deform and break, is presented by employing energy approaches, where both inter- and intra-wave interactions within the side-band wave system are distinguished, and corresponding energy transfer through inter- and intra-wave interactions is demonstrated. It is shown that the result of inter-wave interaction is directly related to the instability of the Benjamin-Feir type; and the consequence of intra-wave interaction is principally responsible for the asymmetric deformation of a wave profile which leads to wave-breaking.; In Part II, a general theory by a united approach is schematized for any resonant or near-resonant three-dimensional side-band multi-wave systems. A set of parabolic evolution equations is derived for the case n = 2, which includes the Benjamin-Feir system as a special case. Based on the new evolution equations, analytic results are developed for instability and temporal evolution of the system; also a global picture of its dynamics and bifurcation in a phase space is provided. Finally, bifurcation of planar wave solutions into 3-d non-interactive solutions of permanent form is studied.; In Part III, modelling of energetic ocean wind-waves as a dynamical system is developed, in the light of the Kahma's (1981) wind-wave growth formulation relevant to the most energetic part in the Kitaigorodskii-Toba spectrum, and Toba's (1972) observational law. Based on the resulting equation of complex Ginzburg-Landau type, combined effects of pumping and damping on the modulational instability and temporal evolution of the side-band system are investigated. It is shown, over certain ranges of the parameters, that the asymptotic wave solutions could be either (i) a stable limiting cycle or (ii) a pair of equilibria, or (iii) a new discovered complex attractor in the phase space; they correspond respectively to (i) periodic, (ii) stationary, or chaotic modulation of waves in physical space. The results suggest that wind forcing and dissipation play a key role in contributing to the observed stochastic nature of wind-waves at sea. Finally, we discuss the formation of solitary wind-wave groups and their stability, and the theory is in good agreement with ocean observations of energetic wave groups. In addition, existence of ocean wave envelope front solutions is also discussed. |
