Julien Touboul

Numerical Simulations of Water Waves' Modulational Instability Under the Action of Wind and Dissipation

Since the work of Benjamin & Feir (1967), water waves propagating in infinite depth are known to be unstable to modulational instability. The evolution of such wave trains is well described through fully nonlinear simulations, but also by means of simplified models, such as the nonlinear Schrodinger equation. Segur et al. (2005) and Wu et al. (2006) studied theoretically and numerically the evolution of this instability, and both concluded that a long term restabilization occurs in these conditions. More recently, Kharif et al. (2010) considered wind forcing and viscous dissipation within the framework of a forced and damped nonlinear Schrodinger equation, and discussed the range of parameters for which this behavior is still valid. This work aims to demonstrate how numerical simulations are useful to analyze their theoretical predictions. Since we are dealing with long term stability, results are especially complicated to obtain experimentally. Thus, numerical simulations of the fully nonlinear equations turn out to be a very useful tool to provide a validation for the model. Here, the evolution of the modulational instability is investigated within the framework of the two-dimensional fully non linear potential equations, modified to include wind forcing and viscous dissipation. The wind model corresponds to the Miles theory. The introduction of dissipation in the equations is briefly discussed. The marginal stability curve derived from the fully nonlinear numerical simulations coincides with the curve obtained by Kharif et al. (2010) from a linear stability analysis. Furthermore, the long term evolution of the wave trains can be obtained through the numerical simulations, and it is found that the presence of wind forcing promotes the occurrence of a permanent frequency-downshifting without invoking damping due to breaking wave phenomenon.

Les vagues scélérates : mécanismes de génération et prédictibilité

EnglishThe scientific community has been concerned about rogue waves for the last thirty years. During this period of time, several accidents, sometimes serious, have occurred. Initially, mechanisms amenable to explain the formation of such waves were beyond understanding. However, nowadays, several physical processes can explain the generation of such giant waves. Using this new knowledge, the scientific community now focuses its attention on the possibility of building warning systems. francaisLes vagues scelerates preoccupent la communaute scientifique depuis une trentaine dannees. Pendant cette periode, plusieurs accidents, parfois graves, sont survenus. Dans un premier temps, les mecanismes pouvant conduire a la formation de telles vagues sont restes mysterieux. Pourtant, aujourdhui, plusieurs processus physiques permettent dexpliquer la formation de ces vagues geantes. En sappuyant sur cette connaissance nouvelle, la communaute scientifique sinterroge a present sur la possibilite de mettre au point des systemes dalertes.