Modulational instability and wave amplification in finite water depth

被引:24
作者
Fernandez, L. [1 ]
Onorato, M. [2 ,3 ]
Monbaliu, J. [1 ]
Toffoli, A. [4 ]
机构
[1] Katholieke Univ Leuven, Dept Civil Engn, B-3001 Heverlee, Belgium
[2] Univ Turin, Dipartimento Fis, I-10125 Turin, Italy
[3] Ist Nazl Fis Nucl, Sez Torino, I-10125 Turin, Italy
[4] Swinburne Univ Technol, Ctr Ocean Engn Sci & Technol, Hawthorn, Vic 3122, Australia
关键词
SURFACE GRAVITY-WAVES; DIRECT NUMERICAL SIMULATIONS; RANDOM DIRECTIONAL WAVES; ROGUE WAVES; DEEP-WATER; EVOLUTION; DYNAMICS; EQUATION; BREAKING; TRAINS;
D O I
10.5194/nhess-14-705-2014
中图分类号
P [天文学、地球科学];
学科分类号
07 ;
摘要
The modulational instability of a uniform wave train to side band perturbations is one of the most plausible mechanisms for the generation of rogue waves in deep water. In a condition of finite water depth, however, the interaction with the sea floor generates a wave-induced current that subtracts energy from the wave field and consequently attenuates the instability mechanism. As a result, a plane wave remains stable under the influence of collinear side bands for relative depths kh <= 1.36 (where k is the wavenumber of the plane wave and h is the water depth), but it can still destabilise due to oblique perturbations. Using direct numerical simulations of the Euler equations, it is here demonstrated that oblique side bands are capable of triggering modulational instability and eventually leading to the formation of rogue waves also for kh <= 1.36. Results, nonetheless, indicate that modulational instability cannot sustain a substantial wave growth for kh < 0.8.
引用
收藏
页码:705 / 711
页数:7
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