On dispersion of directional surface gravity waves

Using a nonlinear evolution equation we examine the dependence of the dispersion of directional surface gravity waves on the Benjamin-Feir index (BFI) and crest length. A parameter for describing the deviation between the dispersion of simulated waves and the theoretical linear dispersion relation is proposed. We find that for short crests the magnitude of the deviation parameter is low while for long crests the magnitude is high and depends on the BFI. In the present paper we also consider laboratory data of directional waves from the Marine Research Institute of the Netherlands (MARIN). The MARIN data confirm the simulations for three cases of BFI and crest length.