Energy transfer in the spatial evolution of double-wave-group focusing

The linear superposition of the individual wave groups underestimates the bimodal waves, as it overlooks the interactions between these wave groups, which is thought to be connected to the generation of extreme waves. Continuing our previous work Zhou et al., “Experimental study on the interactions between wave groups in double-wave-group focusing,” Phys. Fluids 35(3), 037118 (2023), the energy transfer in the spatial evolution of double-wave-group focusing is highlighted based on a fully nonlinear numerical wave tank with the high-order spectral method. The findings reveal that a sea state with a narrower intermodal distance or an uneven distribution of the bimodal spectrum tends to induce larger waves. The third-order nonlinear interaction is primarily triggered by the transient wave focusing, as opposed to a prolonged evolution like the behavior of even-order components. The configurations of the sea state exert varying impacts on the evolution of harmonical energy, with the most potent nonlinearity observed away from the actual focused position, the nonlinear energy amplified relative to the initial state, and the energy redistributed after wave focus. The study also uncovers that during the wave focus and defocus process, waves experience an irreversible energy exchange, with frequencies shifting from higher to lower, likely due to second-order harmonics. These discoveries broaden our comprehension of the nonlinear characteristics inherent in the interaction between the swell and wind-sea waves.