On the Importance of the Exact Nonlinear Interactions in the Spectral Characterization of Rogue Waves

This work is focused on the analysis of the wave action equation with full 4-wave interactions (Snl4). For this purpose, we have applied a state-of-the-art spectral wave model (Wave Watch III), using an exact method for the calculation of the full nonlinear Boltzmann interactions in the evolution of the wave spectrum. We emphasize the use of the exact WRT method [Van Vledder, 2006] for the computation of the Snl4 interactions instead of the approximate DIA method. The WRT algorithm includes the full Boltzmann integrations. We discuss how the WRT method is important in any assessment of rogue waves in the ocean and discuss how the enhanced spectral peak assists the formation of rogue waves packets. We demonstrate how the most nonlinear part of the peak of the spectrum is reduced in amplitude when the nonlinear interactions are instead computed using the DIA interactions. These results suggest that a clear understanding of the physics of nonlinear interactions and of rogue wave dynamics requires the use of the full Boltzmann interactions. Future work would include faster WRT computations so that practical forecasting/hindcasting can become possible using the full four-wave interactions.