Study of relative role of nonlinearity and depth refraction in wave spectrum evolution in shallow water

For modelling a series of depth profiles covering the relative depth parameter interval 2>kph>0.3, evolution of two-dimensional gravity wave spectra is calculated in the frame of three-wave quasi-kinetic approximation derived by Zaslavskii and Polnikov (1988). The relative impact of refraction and nonlinearity on a change of two-dimensional spectra shape for gravity waves is estimated. It is shown that on the background of refraction impact on the spectrum shape, the three-wave nonlinearity results in a remarkable change of angular and frequency distribution for a wave energy spectrum. Herewith, in the spectral peak domain the nonlinearity reduces the value of the angular narrowness parameter by 20–30%, counteracting the refraction during the wave propagation into a shoal zone. In contrast to the high frequency domain of the spectrum, the angular narrowness parameter is increased due to the nonlinearity. For this reason, the nonlinearity can result in more than 10% change of wave energy in a shallow water zone with respect to the linear wave evolution case. These conclusions were checked by using the SWAN model under the same conditions. It was found that the SWAN model describes some of the main peculiarities of nonlinear waves in shallow water. Some recommendations were made to elaborate the three-wave nonlinear term in the source function of the SWAN model.