Modeling extreme waves based on equations of potential flow with a free surface

A method for numerical investigation of nonlinear wave dynamics based on direct hydrodynamical modeling of 1-D potential periodic surface waves is created. The model is a part of an interactive wind-wave model. Using a non-stationary conformal mapping, the principal equations are rewritten in a surface-following coordinate system and reduced to two simple evolutionary equations for the elevation and the velocity potential of the surface; Fourier expansion is used to approximate these equations. High accuracy was confirmed by validation of the non-stationary model against known solutions, and by comparison between the results obtained with different resolution in the horizontal. The method developed is applied to the simulation of waves evolution with different initial conditions. Numerical experiments with initially monochromatic waves with different steepness show that the model is able to simulate breaking conditions when the surface becomes a multi-valued function of the horizontal coordinate. An estimate of the critical initial wave height that divides between non-breaking and eventually breaking waves is obtained. Simulations of nonlinear evolution of a wave field is represented initially by two modes with close wave numbers (amplitude modulation) and a wave field with a phase modulation. Both runs result in the appearance of large and very steep waves, these also break if the initial amplitudes are sufficiently large.