Parameterization of nonlinear shallow water waves over sloping bottoms

Abstract

Investigation of the bottom slope effects on the nonlinear transformation of irregular waves, which are generated based on JONSWAP spectra, is carried out in a physical wave flume with three slopes (β=1/15, 1/30, 1/45). The slope effects on the estimation of representative wave height are examined first. To obtain a better estimation of wave height, the slope effect should be considered when slope is larger than 1/30. The nonlinear parameters (bicoherence, skewness and asymmetry) are estimated by using the wavelet-based bispectrum, and the empirical formulae regarding these nonlinear parameters as a function of the local Ursell number are derived based on the present data measured on each slope. The results indicate that the slopes have a negligible effect on the variations of the skewness. The fitted coefficients of the formulae for the other parameters on slope β=1/15 are clearly different from the results on the slopes β=1/30 and 1/45, indicating that slope influence on the parameterization cannot be ignored when β>1/30. Hence, new formulae considering the slope effect are presented. Furthermore, the empirical formulae for the data in surf zone are recommended.