Two different kinds of rogue waves in weakly crossing sea states

Formation of giant waves in sea states with two spectral maxima centered at close wave vectors k_{0}+/-Deltak/2 in the Fourier plane is numerically simulated using the fully nonlinear model for long-crested water waves [V. P. Ruban, Phys. Rev. E 71, 055303(R) (2005)]. Depending on an angle theta between the vectors k_{0} and Deltak , which determines a typical orientation of interference stripes in the physical plane, rogue waves arise having different spatial structure. If theta less, < or = arctan(1/sqrt[2]) , then typical giant waves are relatively long fragments of essentially two-dimensional (2D) ridges, separated by wide valleys and consisting of alternating oblique crests and troughs. At nearly perpendicular k_{0} and Deltak , the interference minima develop to coherent structures similar to the dark solitons of the nonlinear Schrodinger equation, and a 2D freak wave looks much as a piece of a one-dimensional freak wave bounded in the transversal direction by two such dark solitons.