Numerical investigation of third-order resonant interactions between two gravity wave trains in deep water

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Jian-Jian Xie ◽  
Yuxiang Ma ◽  
Guohai Dong ◽  
Marc Perlin
Keyword(s):  
Numerical Investigation ◽  
Gravity Wave ◽  
Deep Water ◽  
Third Order ◽  
Resonant Interactions ◽  
Wave Trains

The nonlinear dynamics of rogue waves and holes in deep-water gravity wave trains

2000 ◽  
Vol 275 (5-6) ◽  
pp. 386-393 ◽  
Author(s):  
Alfred R Osborne ◽  
Miguel Onorato ◽  
Marina Serio
Keyword(s):  
Nonlinear Dynamics ◽  
Gravity Wave ◽  
Deep Water ◽  
Rogue Waves ◽  
Wave Trains

scholarly journals Emergence of Solitons from Irregular Waves in Deep Water

2021 ◽  
Vol 9 (12) ◽  
pp. 1369
Author(s):  
Weida Xia ◽  
Yuxiang Ma ◽  
Guohai Dong ◽  
Jie Zhang ◽  
Xiaozhou Ma
Keyword(s):  
Deep Water ◽  
Rogue Wave ◽  
Wave Train ◽  
Irregular Waves ◽  
Peak Wavelength ◽  
Long Distance ◽  
Irregular Wave ◽  
Resonant Interactions ◽  
Dispersion Effects ◽  
Wave Trains

Numerical simulations were performed to study the long-distance evolution of irregular waves in deep water. It was observed that some solitons, which are the theoretical solutions of the nonlinear Schrödinger equation, emerged spontaneously as irregular wave trains propagated in deep water. The solitons propagated approximately at a speed of the linear group velocity. All the solitons had a relatively large amplitude and one detected soliton’s height was two times larger than the significant wave height of the wave train, therefore satisfying the rogue wave definition. The numerical results showed that solitons can persist for a long distance, reaching about 65 times the peak wavelength. By analyzing the spatial variations of these solitons in both time and spectral domains, it is found that the third-and higher-order resonant interactions and dispersion effects played significant roles in the formation of solitons.

Oscillatory Third-Order Perturbation Solutions for Sums of Interacting Long-Crested Stokes Waves on Deep Water

1993 ◽  
Vol 37 (04) ◽  
pp. 354-383
Author(s):  
Willard J. Pierson
Keyword(s):  
Free Surface ◽  
Deep Water ◽  
Perturbation Expansion ◽  
The United States ◽  
Order Perturbation ◽  
Naval Academy ◽  
Third Order ◽  
First Order ◽  
Stokes Waves ◽  
Perturbation Solutions

Oscillatory third-order perturbation solutions for sums of interacting long-crested Stokes waves on deep water are obtained. A third-order perturbation expansion of the nonlinear free boundary value problem, defined by the coupled Bernoulli equation and kinematic boundary condition evaluated at the free surface, is solved by replacing the exponential term in the potential function by its series expansion and substituting the equation for the free surface into it. There are second-order changes in the frequencies of the first-order terms at third order. The waves have a Stokes-like form when they are high. The phase speeds are a function of the amplitudes and wave numbers of all of the first-order terms. The solutions are illustrated. A preliminary experiment at the United States Naval Academy is described. Some applications to sea keeping are bow submergence and slamming, capsizing in following seas and bending moments.

Experiments on nonlinear instabilities and evolution of steep gravity-wave trains

1982 ◽  
Vol 124 (-1) ◽  
pp. 45 ◽  
Author(s):  
Ming-Yang Su ◽  
Mark Bergin ◽  
Paul Marler ◽  
Richard Myrick
Keyword(s):  
Gravity Wave ◽  
Wave Trains

scholarly journals Numerical investigation of deep water circulation in the Faroese Channels

2011 ◽  
Vol 58 (7) ◽  
pp. 787-799 ◽  
Author(s):  
Nataliya Stashchuk ◽  
Vasiliy Vlasenko ◽  
Toby J. Sherwin
Keyword(s):  
Numerical Investigation ◽  
Deep Water ◽  
Water Circulation

scholarly journals Third-order stokes wave solutions of the free surface capillary-gravity wave and the interfacial internal wave

2017 ◽  
Vol 31 (6) ◽  
pp. 781-787
Author(s):  
Rui-jun Meng ◽  
Ji-feng Cui ◽  
Xiao-gang Chen ◽  
Bao-le Zhang ◽  
Hong-bo Zhang
Keyword(s):  
Free Surface ◽  
Internal Wave ◽  
Gravity Wave ◽  
Stokes Wave ◽  
Third Order ◽  
Wave Solutions
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