Simulation of time-invariant three-dimensional Freak waves and their scattering identification based on the JONSWAP spectrum and Donelan direction function

Abstract Investigations into recent maritime accidents have revealed that a significant number are linked to the impact of freak waves, which possess the potential to capsize vessels rapidly due to their immense energy. In order to detect and predict these freak waves with precision, thereby mitigating the risks they pose to maritime infrastructure and human safety, we have delved deeper into the study of such waves. This paper introduces an effective and time-invariant three-dimensional (3D) computational model for freak waves. The model is designed to analyze the scattering properties of these waves and to provide a clearer understanding of the variations in their scattering behavior. First, this paper adopts linear superposition method to simulate a 3D random rough sea surface based on the JONSWAP wave spectrum and Donelan directional distribution function. Moreover, we analyze the effect of different angular frequencies on the simulated sea surface. At the same time, the Monte Carlo method is used to further simulate the capillary waves based on the random sea surface, and this method vastly improves the computational accuracy of the random sea surface. Then, based on the two-wave train superposition wave energy focusing mode, a numerical calculation method of time-invariant 3D freak waves is proposed, and the time-series evolution process of 3D freak waves is simulated. Finally, the backscattering coefficients of the 3D freak wave surface are calculated using the two-scale method, and the electromagnetic scattering characteristics of the freak wave surface under different evolution stages, wind speeds, and radar incidence angles are analyzed. By this method, we conclude that the recognition of freak waves is more accurate under medium-high wind speed and significant incidence angle conditions. Our experimental findings demonstrate that the methodologies presented in this study are capable of enhancing the identification and prediction of freak waves. This advancement is expected to bolster the precision of future freak wave forecasts and holds potential for practical application in the realm of freak wave risk alert systems.