Efficient algorithms for non-linear four-wave interactions

This paper addresses the on-going activities in the development of efficient methods for computing the non-linear four-wave interactions in operational discrete third-generation wind-wave models. It is generally assumed that these interactions play an important role in the evolution of wind generated surface gravity waves. Therefore, present day wave models contain parameterizations of these interactions. Despite the fact that a closed mathematical formulation is available for the description of these interactions, a full solution is not applicable in operational modelling as it requires excessive computational requirements. To overcome this limitation, various approximate methods have been developed that retain most of the basic properties of the full solution. However, the present operational parameterisations of these interactions have various weaknesses that degrade model performance and which generally lead to too broad spectra. Efficient and more accurate algorithms are therefore needed to improve model performance. As with each approximate method, a gain in computational speed goes together with a loss in accuracy in evaluating the basic integral, but this may not translate in less accurate wave model results. Therefore the definition of efficiency in the context of approximate methods for computing the four-wave interactions is addressed. Two main lines of development are identified in the development of efficient algorithms: extended Discrete Interaction Approximations, and reduced quasi-exact solution techniques.Hydraulic EngineeringCivil Engineering and Geoscience