Improvement of Parabolic Nonlinear Dispersive Wave Model

Abstract

Improvements to a previously published nonlinear parabolic wave model are developed and implemented. A second-order correction to a free-surface boundary condition used to develop the original model is formulated. The correction takes into account the complete second-order transformation between amplitudes of the velocity potential and those of the free-surface elevation. Additionally, wide-angle propagation terms are included in the model. It is shown that the model with the second-order correction retains the properties of third-order Stokes theory quite well in deep water. Comparisons of model behavior to data reveal that both nonlinearity and wide-angle propagation effects need to be included in the model for general wave transformation problems in shallow water. Skewness predictions are considerably improved by using both the second-order correction and by retaining a greater number of frequency components in the calculation. Asymmetry calculations are aided by incorporation of frequency-squared weighting for distribution of the dissipation function. Further improvement may entail a different form of the breaking model.