Wave statistics in unimodal and bimodal seas from a second-order model

A second-order surface wave model is used to investigate the effects of the spectral distribution on the statistical properties of the surface elevation. To this end single and double peaked directional wave spectra are considered at different water depths. For unimodal seas (i.e. single peaked), the addition of directional components reduces the effects of the second-order interactions in deep water and increases them in shallower depths. For a bimodal sea (i.e. double peaked), on the other hand, a large angle between the wave trains decreases systematically the vertical asymmetry of the wave profile. However, the nonlinear interactions seem to reach their maximum strength when the two wave spectra are slightly separated in direction. This produces an evident deviation of the wave crest distribution at low probability levels if compared with the unimodal condition.