PLAIN INTERPRETATION OF FREAK WAVES PHENOMENON

An extremely large ('freak') wave is a typical though quite a rare phenomenon observed in the sea. Special theories (for example, the modulational instability theory) were developed to explain the mechanics and appearance of freak waves as a result of nonlinear wave-wave interactions. This paper demonstrates that freak wave appearance can be also explained by superposition of linear modes with a realistic spectrum. The integral probability of trough-to-crest waves is calculated by two methods: the first one is based on the results of a numerical simulation of wave field evolution, performed with one-dimensional and two-dimensional nonlinear models. The second method is based on the calculation of the same probability over ensembles of wave fields, constructed as a superposition of linear waves with random phases and a spectrum similar to that used in nonlinear simulations. It is shown that the integral probabilities for nonlinear and linear cases are of the same order of values. One-dimensional model was used for performing thousands of exact short-term simulations of evolution of two superposed wave trains with different steepness and wavenumbers to investigate the effect of wave crests merging. The nonlinear sharpening of merging crests is demonstrated. It is suggested that such effect may be responsible for appearance of typical sharp crests of surface waves, as well as for the wave breaking.