Applicability of the Korteweg-de Vries Equation for Description of the Statistics of Freak Waves

Abstract

The requirements to the numerical model of wind-generated waves in shalow water are discusedin the framework of the Korteweg-de Vries equation. The weakness of nonlinearity and dispersion required forthe Korteweg-de Vries equation applicability is considered for fully developed sea, non-stationary wind wavesand swell, including some experimental data. We note for suficient evaluation of the freak wave statistics it isnecesary to consider more than about 10,0 waves in the wave record, and this leads to the limitation of thenumerical domain and number of realizations. The numerical modelling of iregular water waves is made todemonstrate the posibility of effective evaluation of the statistical properties of freak waves with heights equalto 2.2.3 significant wave height.