Threshold model on the evolution of Stokes wave side-band instability

Evolution of Stokes wave side-band instability along a super tank was studied experimentally and theoretically. The initial exponential growth of the resonant side-bands is followed by asymmetrical growth rates for the side-bands: lower side-band growth is much faster, and finally the main energy is concentrated in 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 stabilization takes place during the final post-breaking stages of the process and can be characterized by a sharp decreasing of wave breaking activity and stabilization of wave modulations with essentially high characteristic steepness. The adjusted dissipative model based on the Nonlinear Schrödinger Equation is suggested for adequate description of the obtained experimental data. Sink/Source terms due to wave breaking processes in its right side correspond to the well known Tulin (1996) [20] model. The wave dissipation function includes the wave steepness threshold function and is applied only in the regions with active wave breaking. Permanent frequency downshift as a result of wave breaking process and post-breaking wave modulations described by the model have the satisfactory quantitative correspondence to results of experiments conducted along a super tank.