Parameterization Of The Nonlinear Characteristics Of Shallow Water Waves On Slope Bottom

The propagation of ocean waves is a nonlinear process. Nonlinearity is an intrinsic feature of the waves and plays an essential role in the waves transformation.Hence it is a key issue in the studies of ocean dynamics. Wave nonlinearity can be classified into weak nonlinearity and strong nonlinearity in term of the intensity of interaction among wave modes. The weak nonlinearity mainly acts on deep and finite water waves. In this circumatance, energy transfer among different wave modes is very slow, significant energy transfer only occur afer hundreds of wave periods length. However, for waves in nearshore regions, it will behave a strong nonlinear characteristic with water depth becoming shallower and this will lead to an obvious energy transfer in a few wave periods. A mount of researches revealed that the nonlinear wave-wave interaction plays an important role inwave deformation and wave breaking; therefore, it is closely related to the nearshore sediment transport. Hence, investigation on the nonlinear characteristics of shallow water waves is very important. In this dissertation, physical experiment of random waves propagating on different bottom slopes are conducted to investigate the nonlinear characteristics of waves; for obliquely incident waves, a well established numerical model is adopted. The major contributions of this dissertation are summarized as follow:Firstly, the transformation of random waves on different bottom slopes is investigated through physical experiment and the effect of bottom slope for the nonlinear interaction of waves is examined based on the wavelet bispectrum; the relationships between nonlinear geometric parameter such as skewness, asymmetry and bicoherence with respect to the local Ursell number are analysised, some new formulae combining the slope effect to the variation of these parameters are derived using the least square method. Through comparingthe present formulae with previous studies, it is found that the new formulae could more accurately dipict the variation of nonlinear characteristics. In addition, the geometric characteristics of extreme waveson slope bottomare investigated. It is found that the water depth and local waveheight may play a crucial role on the spatial development of extreme waves.Through comparing the results in different water depth conditions, it is revealed that the geometric parameters acquired in shallower water could attain to a higher value than those measured in deep water and finite water depth conditions.Some empirical formulae which describe the relationships between the geometric feature of extreme waves and ratio of local waveheight to water depth are presented, also the bottom slope effect are discussed.Then, the nonlinear characteristics of waves on a spatially varying, opposing current are investigated experimentally. The results show that the opposing currents could obviously influence the evolution of nonlinear characteristics. In shoaling region, the opposing currents could intensity the increasing of nonlinear parameters such as steepness, skewness and asymmetry. In deshoaling region, however, the opposing currents will intensify the decreasing of those nonlinear parameters. Moreover, the empirical formulae of nonlinear parameters considering the influence of current adopted in this experiment are presented.At last, the transformations of obliquely incident waves on a bottom slope are simulated by the fully nonlinear Boussinesq model and the effect of incident wave angles to the nonlinear characteristics is examined. It is found that the effect of incident angle may play an important role in the nonlinear interaction. With the increasing of incident angle, the nonlinear interactions are weakened.A set of empirical formulae combining the effect of incident wave angle to the relationships between nonlinear parameters and the local Ursell number are derived.