Two different kinds of rogue waves in weakly-crossing sea states

Abstract

Formation of giant waves in sea states with two spectral maxima, centered at close wave vectors ${\bf k}_0\pm\Delta {\bf k}/2$ in the Fourier plane, is numerically simulated using the fully nonlinear model for long-crested water waves [V. P. Ruban, Phys. Rev. E {\bf 71}, 055303(R) (2005)]. Depending on an angle $\theta$ between the vectors ${\bf k}_0$ and $\Delta {\bf k}$, which determines 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 long fragments of essentially two-dimensional (2D) ridges, separated by wide valleys and consisting of alternating oblique crests and troughs. At nearly perpendicular ${\bf k}_0$ and $\Delta {\bf k}$, the interference minima develop to coherent structures similar to the dark solitons of the nonlinear Shroedinger equation, and a 2D freak wave looks much as a piece of a 1D freak wave, bounded in the transversal direction by two such dark solitons.