Sea-well interaction as a mechanism for the generation of freak waves

The probability of freak waves in an inhomogeneous ocean is studied by integration of Alber's equation. The special phase structure of the inhomogeneous disturbance, required for instability, is provided by bound waves, generated by the quadratic interaction of the stochastic sea with a deterministic, long swell. The probability of freak waves higher than twice the significant wave height increases by a factor of up to 20 compared to the classical value given by Rayleigh's distribution. The probability of exceptionally high freak waves, with height larger than three times the significant wave height, is shown to increase some 30 000-fold compared to that given by the Rayleigh distribution, which renders their encounter feasible.