A new approximation for nonlinear wave–wave interactions

Modern wave models require an accurate computation of the nonlinear wave–wave interactions. This is because nonlinear wave–wave interactions play an important role in the evolution of wind waves, accounting for nonlinear transfer of wave energy to lower and higher frequencies within the spectrum. Presently, in almost all operational state-of-the-art wave models, nonlinear transfer due to wave–wave interactions are evaluated by the discrete interaction approximation (DIA), which was developed by pioneering studies led by Hasselmann more than two decades ago. Although many efforts have tried to develop new methodologies to improve DIA, its basic formulation has not changed. In this study, we present a new computational method by evaluating the dominant nonlinear wave transfer along the wavenumber and the wave directional axes, and by approximating the contributions along the resonance loci. The new method is denoted the Advanced Dominant Interaction (AvDI) method. We show that AvDI is sufficiently efficient that it can be implemented within an operational wave model. As a validation of the approach, we compare simulations of hurricane Juan with observed wave data.