Numerical experiments based on a three-wave quasi-kinetic model for describing the evolution of the spectrum of shallow-water waves

A model for the evolution of the spectrum of nonlinear shallow-water gravit y waves is numerically tested and verified using the data of flume experime nts. On the basis of the three-wave quasi-kinetic theory developed by the a uthor and Zaslavskii [1, 2], the simplest representation is found for the n onlinear term of the source function of the spectral model of shallow-water waves in the case of a unidirectional wave spectrum. The features of spect rum evolution are numerically studied using a number of testing computation s carried out both in the absence of wave breaking and with allowance for w ave breaking. In the latter case, the spectral representation obtained in [ 3] for the "breaking" term of the source function proposed in [4] is employ ed. The contribution of each term of the model source function is determine d. Strong evidence of a high efficiency of the three-wave quasi-kinetic app roximation used to describe the evolution of the spectrum of shallow-water waves is obtained from a comparison of the results of numerical modeling to those of flume experiments [5, 6].