Study of Relative Roles of Nonlinearity and Depth Refraction in Wave Spectrum Evolution in Shallow Water amg

For mode­lling a series of depth prof­iles cove­ring the rela­tive depth para­meter inte­rval 2 >k p h >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.