Parameterization of variations for wave energy over bottom slopes

Wave energy transfer through a shallow water region, produced by nonlinearity, was investigated using random wave simulations based on JONSWAP spectra in a physical experiment. To confirm the role of topography, slopes of β = 1/15, 1/30, and 1/45 were installed in a flume. The shoaling effect was first examined by comparing the experimental data with the theoretically predicted values. A wavelet-based bispectrum was then used to investigate the role of the bottom slope in energy transfer. Next, the evolution of energy transfer in the total, primary, and higher harmonic frequency bands was investigated using the wavelet-based energy spectrum. Based on the data from each slope, empirical formulas expressing the dimensionless energy parameters as a function of the local water depth were derived. The bottom slope was confirmed to have an influence on the variation in the total energy and primary harmonic energy, but its effect was shown to be negligible for the higher harmonic energy. Novel formulas were derived to represent the combined slope effect