Late Stages in the Development of Modulation Instability of Waves

Abstract

We conducted experimental and theoretical studies on Benjamin-Feir (BF) instability and revealed a number of new features of the development of instability on the late stages of wave’s evolution. We employ the reduced (truncated) version of Zakharov equations — the multi-wave near-neighbor resonance model (NN model), which takes into account the most effective quasi-resonances with minimum detuning from exact resonance conditions. We show that near-neighbor model for wave interactions can adequately describe the number of new prominent features of BF instability observed in experiments and it is much simpler than Zakharov equation for computation and analysis. Numerical simulations of the full Zakharov equations confirm the main predictions obtained by the NN modeling and both reasonably correspond to the results of available physical experiments. Strong permanent downshifting of spectral maximum for gentle waves without wave breaking is revealed for twice as narrow side band spectral width in comparison with the most unstable case. Regime of multiple downshifting accompanied by wave breaking is discovered for steep waves. Discrete energy flow to higher spectral components takes a place in breaking and no breaking regimes. Results of numerical simulations of Zakharov and NN models reasonably correspond to each other and to our experimental and field observations on wave modulation.