Abstract:A review of physical mechanisms of the rogue wave phenomenon is given. The data of marine observations as well as laboratory experiments are briefly discussed. They demonstrate that freak waves may appear in deep and shallow waters. Simple statistical analysis of the rogue wave probability based on the assumption of a Gaussian wave field is reproduced. In the context of water wave theories the probabilistic approach shows that numerical simulations of freak waves should be made for very long times on large spatial domains and large number of realizations. As linear models of freak waves the following mechanisms are considered: dispersion enhancement of transient wave groups, geometrical focusing in basins of variable depth, and wave-current interaction. Taking into account nonlinearity of the water waves, these mechanisms remain valid but should be modified. Also, the influence of the nonlinear modulational instability (BenjaminFeir instability) on the rogue wave occurence is discussed. Specific numerical simulations were performed in the framework of classical nonlinear evolution equations: the nonlinear Schrödinger equation, the Davey -Stewartson system, the Korteweg -de Vries equation, the Kadomtsev -Petviashvili equation, the Zakharov equation, and the fully nonlinear potential equations. Their results show the main features of the physical mechanisms of rogue wave phenomenon.

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International audienceNumerical simulations describing plunging breakers including the splash-up phenomenon are presented. The motion is governed by the classical, incompressible, two-dimensional Navier–Stokes equation. The numerical modeling of this two-phase flow is based on a piecewise linear version of the volume of fluid method. Capillary effects are taken into account such as a nonisotropic stress tensor concentrated near the interface. Results concerning the time evolution of liquid–gas interface and velocity field are given for short waves, showing how an initial steep wave undergoes breaking and successive splash-up cycles. Breaking processes including overturning, splash-up and gas entrainment, and breaking induced vortex-like motion beneath the surface and energy dissipation, are presented and discussed. It is found that strong vorticities are generated during the breaking process, and that more than 80% of the total pre-breaking wave energy is dissipated within three wave periods. The numerical results are compared with some laboratory measurements, and a favorable agreement is found