Ocean wave spectrum properties as derived from quasi-exact computations of nonlinear wave-wave interactions

The estimation of nonlinear wave‐wave interactions is one of the central problems in the development of operational and research models for ocean wave prediction. In this paper, we present results obtained with a numerical model based on a quasi‐exact computation of the nonlinear wave‐wave interactions called the Gaussian quadrature method (GQM) that gives both precise and computationally efficient calculations of the four‐wave interactions. Two situations are presented: a purely nonlinear evolution of the spectrum and a duration‐limited case. Properties of the directional wave spectrum obtained using GQM and the Discrete Interaction Approximation Method (DIM) are compared. Different expressions for the wind input and dissipation terms are considered. Our results are consistent with theoretical predictions. In particular, they reproduce the self‐similar evolution of the spectrum. The bimodality of the directional distribution of the spectrum at frequencies lower and greater than the peak frequency is shown to be a strong feature of the sea states, which is consistent with high‐resolution field measurements. Results show that nonlinear interactions constitute the key mechanism responsible for bimodality, but forcing terms also have a quantitative effect on the directional distribution of the spectrum. The influence of wind and dissipation parameterizations on the high‐frequency shape of the spectrum is also highlighted. The imposition of a parametric high‐frequency tail has a significant effect not only on the high‐frequency shape of the spectrum but also on the energy level and peak period and on the global directional distribution.