Modeling freak waves from the North Sea

Four freak events registered in the North Sea during a storm are presented and studied. The spatial evolution of the freak waves backward and forward wave propagation is simulated within the framework of the Dysthe equation. The lifetimes and travel distances of the freak waves are determined based on the results of the simulations. The wave evolution predicted by the Dysthe model is compared with the simulations of the nonlinear Schrödinger and kinematical equations. The contributions of the effects of the nonlinear self-focusing (Benjamin-Feir instability) and quasi-linear wave grouping are discovered with the help of the nonlinear Schrödinger approximation and the linear theory. It is found that though the Benjamin-Feir instability is important for the description of freak wave evolution, the significant wave enhancement by itself may be achieved even in the linear approximation.