On the nonlinear energy transfer in the unidirected adiabatic surface waves

The results of numerical simulation of the adiabatic evolution of waves are presented. The model is based on the fully nonlinear 1D equations of potential waves written in conformal coordinates. It is shown that a wave spectrum is subject to strong fluctuations. Most of such fluctuations are reversible, however a residual effect of the fluctuations causes downshifting of the spectrum. The rate of downshifting depends on nonlinearity.