Numerous numerical and experimental investigations show that rogue waves present a much larger probability of occurrence than expected from the linear random wave model, i.e., Gaussian distributed waves. The deviation from normal statistical events excites a continuous concern about rogue-wave research. In this study, rogue waves under random wave seas are addressed within the framework of the horizontal 1-D fully nonlinear Euler equations. The JONSWAP wave spectra with a different set of random phases are selected as the initial state of the recurrences of incoming wave trains. Different values of spectrum parameters (i.e., enhancement factor γ and significant wave height Hs) for JONSWAP spectra are chosen in order to reproduce different random sea states with different BFI values. The results of the numerical method using in this study are compared with classical experimental studies of rogue waves and show good agreements. Nonlinear wave interactions and the evolution of simulated waves are investigated in order to study the emergence of rogue waves. Statistics analysis is applied to the simulating results to find the deviations with normal distributions. Numerical results reveal that the initial unstable waves need some space to evolve, i.e., around 20 wavelengths, and will keep in an energetic state for the formation of rogue waves.

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