Influence of uniform currents on nonlinear characteristics of double-wave-group focusing

Current is considered to be a crucial environmental factor in producing extreme waves. The study of nonlinear characteristics in wave-current interactions has been explored, but the role of currents in the more complex interaction processes of double-wave-group focusing is not yet known. Based on our previous research about the nonlinear interactions between wave groups, the impact of uniform current on nonlinear characteristics of double-wave-group focusing is to be investigated in this paper. A fully nonlinear numerical model using the high-order spectral method is developed to simulate various currents interacting with focused bimodal waves. Three ranges of variation exist: strongly opposing current, weakly opposing current, and following current. Unlike the conclusion in the unimodal waves, the asymmetries of the wave crest and that of the wave envelope influenced by currents are not synchronous, which is explained by the changes in the asymmetry of the secondary crests received energy from the currents, in addition to those of the magnitude of the maximum crest and the adjacent secondary crests. When opposing currents enhance to a certain level, a dynamic equilibrium between the energy of waves and currents would be achieved, in which the proportion of the linear components to their own is almost equivalent to that in the non-current state, revealing that the majority of nonlinearity generated by wave-current interaction is blocked at that time. These findings can promote an understanding of nonlinear characteristics due to wave-current interactions.