Long space-time evolution of the stokes-wave sideband instability

The sideband instability of Stokes waves was analyzed both experimentally and theoretically. The initial exponential growth of the resonant sidebands is followed by asymmetrical growth rates for the sidebands: lower sideband growth is much faster and finally the main energy exchange takes place between it and the primary wave. An active breaking process increases the frequency downshift during the latter stages of the wave propagation. Some type of wave saturation takes place during the final stages of the process and can be characterized by a restabilization and a decrease of wave modulations to more or less constant values for the considered sidebands and the main wave. Tulin & Landrini's modification of (NLS) model can satisfactory describe the wave instability, the side band asymmetry and the wave breaking effects during the wave train evolution. The suggested saturation model, beside the earlier stages of wave instability and sideband asymmetrical growth rates, can quantitatively describe the restabilization of waves at large distances of propagation.