Formation of giant waves in sea states with two spectral maxima, centered atclose wave vectors ${\bf k}_0\pm\Delta {\bf k}/2$ in the Fourier plane, isnumerically simulated using the fully nonlinear model for long-crested waterwaves [V. P. Ruban, Phys. Rev. E {\bf 71}, 055303(R) (2005)]. Depending on anangle $\theta$ between the vectors ${\bf k}_0$ and $\Delta {\bf k}$, whichdetermines a typical orientation of interference stripes in the physical plane,rogue waves arise having different spatial structure. If $\theta\lesssim\arctan(1/\sqrt {2})$, then typical giant waves are relatively longfragments of essentially two-dimensional (2D) ridges, separated by wide valleysand consisting of alternating oblique crests and troughs. At nearlyperpendicular ${\bf k}_0$ and $\Delta {\bf k}$, the interference minima developto coherent structures similar to the dark solitons of the nonlinearShroedinger equation, and a 2D freak wave looks much as a piece of a 1D freakwave, bounded in the transversal direction by two such dark solitons.
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