arXiv 0904.28532009-04-18physics.flu-dynphysics.ao-ph

弱穿越海况下两种不同类型的无赖波

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

V. P. Ruban

备注：: revtex4, 4 pages, 10 figures
DOI：: 10.1103/PhysRevE.79.065304

摘要：

使用长峰水波的完全非线性模型[V. P. Ruban，Phys. Rev. E { \bf 71}，055303（R）（2005）]，数值模拟了在具有两个谱极大值的海况中巨浪的形成，所述谱极大值以傅立叶平面中的近波矢量${\bf k}_0\pmΔ{\bf k}/2$为中心。取决于矢量${\bf k}_0$和$Δ{\bf k}$之间的角度$θ$，其确定干涉条纹在物理平面中的典型取向，产生具有不同空间结构的异常波。如果是$θ\lesssim\arctan(1/\sqrt {2})$，那么典型的巨浪是由基本上二维（2D）的脊组成的相对较长的片段，由宽的谷分隔，由交替的斜波峰和波谷组成。在接近垂直的${\bf k}_0$和$Δ{\bf k}$处，干涉极小值发展为类似于非线性薛定谔方程的暗孤子的相干结构，二维畸形波看起来很像一维畸形波的一部分，在横向上由两个这样的暗孤子束缚。

英文摘要：

Formation of giant waves in sea states with two spectral maxima, centered at close wave vectors ${\bf k}_0\pmΔ{\bf k}/2$ 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 $θ$ between the vectors ${\bf k}_0$ and $Δ{\bf k}$, which determines a typical orientation of interference stripes in the physical plane, rogue waves arise having different spatial structure. If $θ\lesssim\arctan(1/\sqrt {2})$, 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 $Δ{\bf k}$, 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.

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