We are concerned by a special mechanism that can explain the formation of freak waves. We study numerically the long time evolution of a surface gravity wave packet, comparing a fully nonlinear model with Schrodinger-like simplified equations. We observe that the interaction between envelope solitons generates large waves. This is predicted by both models. The fully nonlinear simulations show a qualitative behaviour that differs significantly from the ones preticted by Schrodinger models, however. Indeed, the occurence of freak waves is much more frequent with the fully nonlinear model. This is a consequence of the long-time interaction between envelope solitons, which, in the fully nonlinear model, is totally different from the Schrodinger scenario. The fundamental differences appear for times when the simplified equations cease to be valid. Possible statistical models, based on the latter, should hence under-estimate the probability of freak wave formation. To cite this article: D. Clamond, J. Grue, C. R. Mecanique 330 (2002) 575-580.
On s'interresse a un mecanisme particulier pouvant expliquer l'apparition de vagues de grandes amplitudes (freak waves). On etudie numeriquement l'evolution a long terme de paquets d'onde de gravite surfaciques. On compare un modele completement non lineaire avec des equations simplifiees de type Schrodinger. On observe que l'interaction d'ondes solitaires enveloppes generent des vagues de grandes amplitudes. Cela est predit par tous les modeles. Toutefois, le modele completement non lineaire exhibe un comportement a long terme tres different des modeles simplifies. L'apparition de freak waves y est beaucoup plus frequente. C'est une consequence de l'interaction a long terme de solitons enveloppes, qui est totalement differente de celle predite par les scenario derives des equations de type Schrodinger. Les differences fondamentales apparaissent pour des temps superieurs aux domanes de validite des equations simplifiees. D'envisageable modeles statistiques, bases sur ces dernieres, devraient donc sous-estimer la probabilite d'apparition de freak waves. Pour citer cet article : D. Clamond, J. Grue, C. R. Mecanique 330 (2002) 575-580.