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The issue of accounting of the wave breaking phenomenon in direct numericalsimulations of oceanic waves is discussed. It is emphasized that this problemis crucial for the deterministic description of waves, and also for thedynamical calculation of extreme wave statistical characteristics, such asrogue wave height probability, asymmetry, etc. The conditions for reproduciblesimulations of irregular steep waves within the High Order Spectral Method forthe potential Euler equations are identified. Such non-dissipative simulationsare considered as the reference when comparing with the simulations which usetwo kinds of wave breaking regularization. It is shown that the perturbationscaused by the wave breaking attenuation may be noticeable within 20 min of thewave evolution.

Account of occasional wave breaking in numerical simulations of irregular water waves in the focus of the rogue wave problem