Giant waves in weakly crossing sea states
- PDF / 363,372 Bytes
- 8 Pages / 612 x 792 pts (letter) Page_size
- 23 Downloads / 212 Views
AL, NONLINEAR, AND SOFT MATTER PHYSICS
Giant Waves in Weakly Crossing Sea States V. P. Ruban Landau Institute for Theoretical Physics, ul. Kosygina 2, Moscow, 119334 Russia email: [email protected] Received September 24, 2009
Abstract—The formation of rogue waves in sea states with two close spectral maxima near the wave vectors k0 ± Δk/2 in the Fourier plane is studied through numerical simulations using a completely nonlinear model for longcrested surface waves [24]. Depending on the angle θ between the vectors k0 and Δk, which specifies a typical orientation of the interference stripes in the physical plane, the emerging extreme waves have a dif ferent spatial structure. If θ ⱗ arctan ( 1/ 2 ) , then typical giant waves are relatively long fragments of essen tially twodimensional ridges separated by wide valleys and composed of alternating oblique crests and troughs. For nearly perpendicular vectors k0 and Δk, the interference minima develop into coherent struc tures similar to the dark solitons of the defocusing nonlinear Schroedinger equation and a twodimensional killer wave looks much like a onedimensional giant wave bounded in the transverse direction by two such dark solitons. DOI: 10.1134/S1063776110030155
1. INTRODUCTION The problem of rogue ocean waves (also known as killer or extreme waves) has attracted attention in recent years (see, e.g., the reviews [1, 2], where the various physical mechanisms of the roguewave phe nomenon are discussed and references to many of the available papers on this subject matter are given; for some of the recent achievements in this field, see also [3–17]). An individual wave with a crest height Ymax several times larger than the typical amplitude A0 of the neighboring waves is usually meant by a rogue or extreme wave. With a wavelength λ0 = 2π/k0 in the range 100–250 m and a background amplitude A0 ≈ [0.015…0.020]λ0, the inequality Ymax > 0.06λ0 can be achieved at the maximum elevation of the free surface, which is comparable to the height of the limiting Stokes wave. The profile of a rogue wave differs greatly in shape from a sinusoid and is very steep, suggesting that the phenomenon under consideration is strongly nonlinear. In different circumstances, giant waves are known to be produced by different factors and, accordingly, there are several possible scenarios that explain the formation of such waves. The modula tional Benjamin–Feir–Zakharov instability, which essentially determines the dynamics of fairly long and high wave groups, has been recognized as one of the most important causes for the appearance of killer waves [18–20]. The efficiency of this mechanism is usually characterized by the socalled Benjamin–Feir –2 index (BFI) [4], BFI ~ λ 0 A 0 l 0 , where l0 is a typical group length. The higher this index, the more probable the appearance of killer waves in a given sea state.
Obviously, high values of BFI correspond to spectrally narrow distributions of the wave action, i.e., to fairly coherent waves. In contrast, low values of BFI are characterist
Data Loading...
