Giant waves in weakly crossing sea states

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Abstract
The formation of rogue waves in sea states with two close spectral maxima near the wave vectors k 0 ± Δk/2 in the Fourier plane is studied through numerical simulations using a completely nonlinear model for long-crested surface waves [24]. Depending on the angle θ between the vectors k 0 and Δk, which specifies a typical orientation of the interference stripes in the physical plane, the emerging extreme waves have a different spatial structure. If θ ≲ arctan(1/√2), then typical giant waves are relatively long fragments of essentially two-dimensional ridges separated by wide valleys and composed of alternating oblique crests and troughs. For nearly perpendicular vectors k 0 and Δk, the interference minima develop into coherent structures similar to the dark solitons of the defocusing nonlinear Schroedinger equation and a two-dimensional killer wave looks much like a one-dimensional giant wave bounded in the transverse direction by two such dark solitons.

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