  The issue of accounting of the wave breaking phenomenon in direct numerical
simulations of oceanic waves is discussed. It is emphasized that this problem
is crucial for the deterministic description of waves, and also for the
dynamical calculation of extreme wave statistical characteristics, such as
rogue wave height probability, asymmetry, etc. The conditions for reproducible
simulations of irregular steep waves within the High Order Spectral Method for
the potential Euler equations are identified. Such non-dissipative simulations
are considered as the reference when comparing with the simulations which use
two kinds of wave breaking regularization. It is shown that the perturbations
caused by the wave breaking attenuation may be noticeable within 20 min of the
wave evolution.
