Spectrum-Based Prediction Model for Random Wave Transformation over Arbitrary Bottom Topography

Abstract

This paper proposes a one-dimensional and a horizontally two-dimensional random wave transformation models based on a spectral wave equation with a probabilistic bore-type energy dissipation term, and examines the validity of the wave models by comparing the predictions with the observations. The present spectrum-based prediction models with a probabilistic dissipation term axe rather heuristic but robust to use. Since the present random wave transformation models consist of spectral and probabilistic models, the wave model can be called as a hybrid random wave transformation model. The model solves the spatial evolution of complex Fourier amplitudes from which energy spectra are calculated. In addition, water surface elevations are obtained from the calculated complex amplitudes by using the inverse Fast Fourier Transform. Furthermore, representative wave heights and periods are obtained from the water surface elevations.We apply the one-dimensional wave model to predict transformations of double peak spectral waves, small and prototype scales' experimental waves and field waves over uniform slope and arbitrary bathymetry. In addition, the horizontally two-dimensional wave model is applied to predict transformations over an elliptic shoal, a conic shoal and field bathymetry, and also employed to investigate the mach-reflection. The comparison between the various observations by laboratory and field experiments and the predictions by the wave models shows good agreements.