Evolution of sidebands in deep-water bichromatic wave trains

Abstract

Numerical and physical experiments on bichromatic wave trains were conducted in deep water. The evolution of wave trains and corresponding spectra were investigated in this paper. The results indicate that the evolution of bichromatic wave trains strongly depends on the wave steepness and frequency difference between the imposed wave components. The evolutions of wave trains including breaking and non-breaking types were analyzed for different combination of wave steepness and frequency difference. Specifically, for non-breaking cases, the wave trains evolve modulation and demodulation periodically in the experimental data. This phenomenon can be better predicted by the nonlinear Schrödinger (NLS) equation. However, for the free surface displacement, the multi-layer Boussinesq model gives better phase agreement with experimental data. For breaking case, the amplitude of lower sideband frequency is selectively amplified through the breaking process, which can be qualitatively simulated in the NLS model by adding an additional proper damping function. The experimental data also show weak evolution of induced bound long wave during the breaking process

Keywords:

• Nonlinear Schrödinger equation
• Boussinesq model
• spectrum
• bichromatic waves
• sideband frequency
• bound long wave