A Model for Transformation of Fully Dispersive Nonlinear Waves

Abstract

In this dissertation, we evaluate the performance of nonlinear models, and the effects of bound waves in nearshore wave models are studied mathematically and numerically. The first part of this study concerns the evaluation of different nearshore models and their capability in the estimation of wave spectra and higher order wave statistics. Four different nearshore wave models (three fully dispersive models and a consistent shoaling model) are compared to field and experimental data sets. Comparison of these nearshore models reveals that the nearshore models’ performance in predicting higher frequency energy evolution is not as skillful as at lower frequencies. Therefore, a new wave transformation model is derived. The model includes nonlinear wave interaction effects up to third order in wave steepness and is based on the fully dispersive second order model. Transforming the problem into the frequency domain and using multiple scale analysis in space and perturbation theory, the model is expanded up to third order in wave steepness. The result is a set of evolution equations which explicitly contains quadratic near-resonant interactions, non-resonant bound waves, and cubic resonant interactions. The results of the numerical modeling for the aforementioned nearshore model show that the model is verified reasonably well in terms of the harmonics tests and the spectral analysis for experimental and field data sets. However, the calculation of higher order statistical parameters is quite sensitive to how the free parameters in the model are chosen.

In addition, the dissipation characteristics of the breaking waves has been investigated using the high-resolution laboratory datasets. The free parameter in a probabilistic breaking model and the threshold parameter in the instantaneous dissipation model is parameterized at each gauge location separately, and the dependency of the calculated damping coefficient in the formulation to frequency components is extensively discussed. Moreover, the relationship between the third moments of free surface elevation and the parameterized threshold parameter in the instantaneous dissipation model is represented.