### HYBRID FREQUENCY-DOMAIN KDV EQUATION FOR RANDOM WAVE TRANSFORMATION

#### Abstract

This paper develops a hybrid model for random wave transformation by employing a modified spectral model of the KdV equation and a probabilistic bore-type wave breaking model, and compares the numerical predictions with experimental observations. Main results are as follows: 1) Original frequency-domain KdV equation overestimates energy densities, due to over-shoaling term by Green's law in the equation, even in a region where wave breaking is not seen; 2) Modification of the original KdV equation in order to represent shoaling for linear-dispersive component waves leads to better predictions in the non-breaking region; 3) Damping coefficients in the model equation, either estimated from measured spectral densities or the numerically predicted, are in inverse proportion to the water depth and in proportion to the square of frequency, similar to the viscous damping term of the Burgers equation; 4) The hybrid model developed here can predict transformations of random waves satisfactorily, as indicated by comparison of energy spectra, representative wave heights, periods, and crest heights.

#### Keywords

random wave; wave transformation; KdV equation; frequency domain

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