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

TL;DR

This study numerically investigates two types of rogue waves in weakly-crossing sea states with dual spectral maxima, revealing how their structure depends on the orientation of wave vectors and identifying conditions for different rogue wave formations.

Contribution

It introduces a numerical simulation of rogue wave formation in sea states with two spectral maxima, highlighting the influence of wave vector orientation on wave structure.

Findings

Rogue waves can form as long 2D ridges or as structures similar to 1D freak waves.

The wave structure depends on the angle between wave vectors, with specific formations at different angles.

Dark soliton-like structures are involved in the formation of certain rogue waves.

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.