Estimation of Broadening of the Spectra of Short Surface Waves in the Presence of Long Waves

We perform a numerical simulation of evolution of the wind waves, which is based on solving the Euler equations for a two-dimensional potential flow and, therefore, allows for the nonlinear effects. Analysis of the obtained realizations of the surface profiles shows that the proposed direct numerical simulation allows one to reproduce the features of modulation of short surface waves. The model dependence, which describes the characteristic deviation of the spectral density from the dispersion curve on the frequency–wave number plane, is obtained. Comparison with the wave spectra measured under natural conditions is indicative of a qualitative agreement between the calculated and experimental results.