Modeling waves in fetch-limited and slanting fetch conditions using a quasi-exact method for nonlinear four-wave interactions

The computation of nonlinear four-wave interaction is one of the central issues of the development of operational spectral models for ocean waves prediction. So far, most of the computational models used a very simplified method to evaluate these interactions, namely the Discrete Interaction Approximation (DIA). We consider in this work the effects and implications resulting from the substitution of DIA by a quasi-exact method (namely the Gaussian Quadrature Method, GQM). This improved method for calculating the nonlinear four-wave interactions is applied to fetch-limited and slanting fetch situations, in conjunction with well-established models for the source and sink terms (wind input and dissipation). Four different combinations of the source terms are tested. Results show the significant influence of the method for calculating the Q_nl4 term on the directional properties of the spectrum. Whereas growth curves in fetch limited conditions do not exhibit marked differences (due to the use of a set of source/sink terms that have been properly calibrated for these cases), the analysis of the directional wave spectrum reveals differences both for the spectral shape and the directional distribution.