It is well established that the modulational instability enhances the probability of occurrence for extreme events if waves are long crested. Recent studies, however, have shown that the coexistence of directional wave components can substantially reduce its effects. Here, direct numerical simulations of the Euler equations are used to investigate whether the modulational instability may produce significant deviations from second-order statistical properties of surface gravity waves when short crestness (i.e., directionality) is accounted for. The case of a broad-banded directional wave field (i.e. wind sea) is investigated. Results will show that the distribution proposed by Forristall [1] provides a good estimate of the simulated crest height also at low probability levels.

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