Nonlinearity of gravity waves in coastal region plays crucial role in the wave evolution and the sediment transport. Parameterization of the nonlinear characteristics of random waves is an efficient and important way to descript the wave process. It is well known that coastal topography has a key effect on the wave transformation. However, the related previous studies have ignored the slope effects. It is the primary motivation of the research.
To implement this aim, physical experiments of random waves propagating over three slopes (1/15, 1/30, 1/45) were carried out in a wave flume with 50m long, 3m wide and used with a water depth of 0.52m. About 20 random wave simulations based on JONSWAP spectra with varying wave height and peak frequency were considered.
The wavelet based bispectrum is adopted to obtain the nonlinear parameters, bicoherence, biphase, skewness and asymmetry. On each slope bottoms, several empirical relationships between these parameters and the local Ursell number are derived using the least square method. The results indicate that the bicoherence and the asymmetry of waves relate to the slope. However, the slopes have negligible effect on the formulae of the skewness. Then, the empirical formulae on the bicoherence and asymmetry combining with the bottom slope are constructed.