Phase convergence and crest enhancement of modulated wave trains

Hidetaka Houtani; Hiroshi Sawada; Takuji Waseda

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arXiv · 2207.08176

Phase convergence and crest enhancement of modulated wave trains

Hidetaka Houtani·Hiroshi Sawada·Takuji Waseda

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Abstract

The Akhmediev breather (AB) solution of the nonlinear Schr$ö$dinger equation (NLSE) shows that the maximum crest height of modulated wave trains reaches triple the initial amplitude as a consequence of nonlinear long-term evolution. Several fully nonlinear numerical studies have indicated that the amplification can exceed 3, but its physical mechanism has not been clarified. This study shows that spectral broadening, bound-wave production, and phase convergence are essential to crest enhancement beyond the AB solution. The free-wave spectrum of modulated wave trains broadens owing to nonlinear quasi-resonant interaction. This enhances bound-wave production at high wavenumbers. The phases of all the wave components nearly coincide at peak modulation and enhance amplification. We find that the phase convergence observed in linear-focusing waves can also occur due to nonlinear wave evolution. These findings are obtained by numerically investigating the modulated wave trains using the higher-order spectral method (HOSM) up to the fifth order, which allows investigations of nonlinearity and spectral bandwidth beyond the NLSE framework. Moreover, we confirm the crest enhancement through a tank experiment wherein waves are generated in the transition region from non-breaking to breaking. Owing to strong nonlinearity, the maximum crest height observed in the tank begins to exceed the HOSM prediction at an initial wave steepness of 0.10.

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Hidetaka Houtani, Hiroshi Sawada, Takuji Waseda. 2022-07-17. Phase convergence and crest enhancement of modulated wave trains. https://arxiv.org/abs/2207.08176

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