On dispersion of directional surface gravity waves

Using a nonlinear evolution equation, this paper examines the dependence of the dispersion of directional surface gravity waves on the Benjamin-Feir index (BFI) and crest length. A novel parameter is introduced to describe the deviation between the dispersion of simulated waves and the theoretical linear dispersion relation. The findings indicate that for short crests, the magnitude of the deviation parameter is low; conversely, for long crests, the magnitude increases significantly and correlates with the BFI. Additionally, this study incorporates laboratory data on directional waves from the Marine Research Institute of the Netherlands (MARIN), which verify the simulation results across three different cases of BFI and crest length. This comprehensive analysis contributes to understanding the behavior of gravity waves in various contexts of ocean engineering, emphasizing the influence of nonlinearity in wave dynamics.