Probability of the occurrence of freak waves

The statistics of the occurrence of freak waves on a surface of an ideal heavy liquid is studied. The freak (rogue, extreme) waves arise in the course of evolution of a statistically homogeneous random Gaussian wave field. The mean steepness of initial data varies from small (μ² = 1.54 × 10⁻³) to moderate (μ² = 3.08 × 10⁻³) values. The frequency of the occurrence of extreme waves decreases with an increase in the spectral width of the initial distribution, but remains relatively high even for broad spectra (Δ _k /Δ ~ 1).