Spectral wave modeling using a quasi-exact method for nonlinear wave-wave interactions

Numerical wave models describe the evolution of the wave energy spectrum under the combined action of several physical processes that generate, transfer or dissipate energy. A more accurate modeling of nonlinear four-wave interactions is necessary to improve these spectral sea state models. Based on a method initially introduced by Lavrenov (2001), we developed and optimized a quasi-exact method for computing the nonlinear four-wave interactions in deep water. This method, called GQM (for "Gaussian Quadrature Method"), uses Gaussian quadrature formulas for the different integrations in the computation of the nonlinear interaction term, and provides very accurate estimates of the nonlinear transfer term with acceptable CPU times. In the present study, we first consider the temporal evolution of a homogeneous wave field when there is no energy input from the wind or dissipation. Then we consider a more realistic situation still with a simple geometry, the fetch-limited case, where wind input, white-capping dissipation and wave propagation are taken into account. This work confirms the need to accurately model the nonlinear wave-wave interactions in spectral wave models and shows that these improvements are now feasible, thanks to the GQM method and the newly developed algorithm.