Implementation and test of improved methods for evaluation of nonlinear quadruplet interactions in a third generation wave model

Nonlinear quadruplets wave-wave interactions play a dominant role in the evolution of ocean and coastal wave spectra. Although the theoretical model equation representing these interactions is available for more than 40 years, most of existing operational and applied wave models rely on a rather crude and very simplified computing scheme to evaluate these interactions, namely the Discrete Interaction Approximation (DIA). Recent research results suggest that improved or quasi-exact techniques can be available to estimate this transfer term quite accurately within a computational time ratio in the order of 20 to 200, compared to DIA (depending on the level of approximation). This leads us to consider the possibility to use such improved computational techniques in wave models applied on real cases (not only academic simplified 1D cases as it used to be up to now). To that end the present study address several issues related to the inclusion of improved techniques for computing the quadruplet interactions term in a real wave model environment. Test simulations are performed to examine and quantify the effects of several parameters and choices, such as physics for wind input and white-capping dissipation, wave growth limiter, prognostic limit of the discrete spectrum. Results are presented for homogeneous wind and wave conditions (one single sea point) in deep water under constant wind (duration-limited case) and turning wind conditions (instantaneous shift of wind direction).