Abstract
In this study, mathematical derivation and numerical verification of a wave transformation model in frequency domain is discussed. This wave model is fully dispersive and nonlinear; and is derived based on the WKB assumptions. Transforming the problem into 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 set of laboratory and field data shows that the presented model provides significant improvements particularly at higher frequencies.
Highlights
Studies of nearshore waves originate from the modeling of Boussinesq equations (Boussinesq 1872)
Both weak nonlinearity and weak dispersive effects of waves are taken into account for constant depth; dispersive and nonlinearity parameters are kept at first order
By transforming the varying-bottom Boussinesq equations in frequency domain, Freilich and Guza (1984) derived two nearshore nonlinear models (a "consistent" model and a "dispersive" model) for the shoaling region where the water depth is approximately in the range of 3 to 10m
Summary
Studies of nearshore waves originate from the modeling of Boussinesq equations (Boussinesq 1872). By transforming the varying-bottom Boussinesq equations in frequency domain, Freilich and Guza (1984) derived two nearshore nonlinear models (a "consistent" model and a "dispersive" model) for the shoaling region where the water depth is approximately in the range of 3 to 10m. They used the result of Benney (1962) which used multiple scale expansion to formulate a series of equations which account for significant energy exchange even in only near-resonant conditions. Bredmose et al (2004) enhanced the efficiency of the time domain Boussinesq models by applying Fast Fourier Transforms for calculation of nonlinear interaction terms
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