Evolution of high frequency waves in shoaling and breaking wave spectra

Abstract

Mathematical derivation and numerical verification of a wave transformation model in the frequency domain are discussed. The model is a fully dispersive nonlinear wave model and is derived based on the boundary value problem. Transforming the problem in the frequency domain and using multiple scale analysis in space and perturbation theory, the model is expanded up to second order in wave steepness. This fully dispersive nonlinear wave model is a set of evolution equations which explicitly contains quadratic near-resonant interactions. The comparison between the presented model, the existing fully dispersive model, and a nearshore model with different sets of laboratory and field data shows that the presented model provides significant improvements particularly at higher frequency.

Ecohydraulics of Surrogate Salt Marshes for Coastal Protection: Wave–Vegetation Interaction and Related Hydrodynamics on Vegetated Foreshores at Sea Dikes

“…The incident and reflected wave parameters (zeroth moment of the wave spectrum m 0 , wave height H m0 , and wave period T m−1,0 ) are determined by reflection analysis according to Mansard and Funke (1980). As the peaks of the generated wave spectra are shifted in shallow water by spectral transformation (Mahmoudof et al 2016;Ardani and Kaihatu 2019), the wave heights and periods were analyzed applying the fast Fourier transform (FFT) technique and the following equations:…”

A Modified Frequency Distribution Function of Wave‐Breaking‐Induced Energy Dissipation

“…The majority of phase‐resolved frequency‐domain models have been employed with a frequency‐squared weighting of the dissipation term proposed by Mase and Kirby ( 1993 ) ‐ for example, Kaihatu and Kirby ( 1995 , 1997 ) with the nonlinear, parabolic mild‐slope equation of Kaihatu and Kirby ( 1995 ); Chen et al. ( 1997 ) with modified Boussinesq equation model of Chen and Liu ( 1995 ); Ardani and Kaihatu ( 2019 ) with their fully dispersive nonlinear wave model. They included the dissipation term of Thornton and Guza ( 1983 ) or an extension of it by Whitford ( 1988 ).…”