A series of directly numerical simulations of potential Euler equation have been performed using high-order spectral (HOS) method, to investigate the nonlinear wave statistics and the probability of rogue wave occurrence in crossing sea states. Several typical crossing sea states in deep water with different wave steepness are chosen for the computations. The ensemble statistical properties for those crossing waves are measured, including the temporal evolution of directional and omnidirectional wave spectra, exceedance probability of wave crest amplitude, as well as the kurtosis and skewness of free surface elevations. Particular attention is paid to the correlation between kurtosis and rogue wave occurrence. Our numerical results suggest that the global wave steepness plays a significant role in the statistical properties of crossing seas. Results also show the dependence of rogue wave occurrence probability on the kurtosis of free surface elevations.

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