Numerous numerical and experimental investigations show that rogue waves present much larger probabilities of occurrence than predicted by 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 long-crested and narrow-banded wave trains are checked using the HOS-NST model. The JONSWAP wave spectra with random phases are selected as the initial state of the incoming wave trains. Different values of spectral parameters are chosen to reproduce different random sea states with different BFI. Numerical results are compared with classical experimental study and show good agreements. Statistical properties of rogue waves are recounted again within the analysis of EDF of wave heights and wave crests. Spectral changes are examined and the monotonic increases with BFI are stressed. However, no bifurcations are observed for BFI near 1. For large BFI, quasi-resonance interactions dominate the wave nonlinearities, and the resulted dynamic excess kurtosis involves initially monotonic enhancement along with space, peaking at around 20-30 wavelengths, but stays at stably high-level values. The quasi-steady-state of dynamic excess kurtosis after full interaction of wave nonlinearities in time and space demonstrates a continuous emergence of rogue waves much more frequent than normality. The changes of excess kurtosis along x are complicated where BFI near 1 and the occurrence of rogue waves might be enhanced even for BFI slightly inferior to 1.

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