2012 , Volume 17, № 5, p.3-11

In this paper, an asymptotic mathematical modeling of the surface wave breaking due to the influence of wind loads is addressed. We only consider the motion of the free surface, motions of the medium inside the wave are not accounted for. For this model, we only use strictly defined mathematical facts about the free surface movement with the gas-vacuum interface. In this case, in order to describe the motion of the surface in the breaking waves, it is necessary to construct solutions of the corresponding system of PDE, which in this case are written explicitly. The two facts always accompanying overturning waves are described:1) appearance of the cusp of waves, when the free boundary becomes ambiguous function of the horizontal variable, 2) sharpening of the cusp .Simulation is carried out until the complete fall of the wave on the underlying horizontal layer of water.