The effects of wind and nonlinear damping on rogue waves and permanent downshift

Schober, C. M.; Strawn, M.

doi:10.1016/j.physd.2015.09.010

Cited by 11 publications

(10 citation statements)

References 29 publications

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“…We report here briefly the evolution of the most important quantities (norm, momentum, spectral mean) in the damped-forced model, in order to better compare to the approximated results reported in the text, Eqs. (6c) and (7). From Eq.…”

Section: Appendix B: Evolution Of Momentsmentioning

confidence: 99%

“…Naturally, the first step is to include in one dimensional propagation equations the two main forcing and damping mechanisms, viscosity and wind. The former is an unavoidable limit in laboratory facilities, the impact of which on propagation is non-trivial [4][5][6][7][8][9]; the latter [10,11] has attracted much interest in theoretical and experimental efforts, particularly in recent years [12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear stage of Benjamin-Feir instability in forced/damped deep-water waves

et al. 2018

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We study a three-wave truncation of a recently proposed damped/forced high-order nonlinear Schrödinger equation (DF-HONLS) for deep-water gravity waves under the effect of wind and viscosity. The evolution of the norm (wave-action) and spectral mean of the full model are well captured by the reduced dynamics. Three regimes are found for the wind-viscosity balance: we classify them according to the attractor in the phase-plane of the truncated system and to the shift of the spectral mean. A downshift can coexist with both net forcing or damping, i.e. attraction to period-1 or period-2 solutions. Upshift is associated to stronger winds, i.e. to a net forcing where the attractor is always a period-1 solution. The applicability of our classification to experiments in long wave-tanks is verified.

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Section: Appendix B: Evolution Of Momentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear stage of Benjamin-Feir instability in forced/damped deep-water waves

et al. 2018

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“…For example, the spectral downshift observed in BFI [15] can be often explained in the HONLS framework. However, in the last decades much effort has been devoted to discuss the properties of this model and to include other effects, such as viscosity or wind [16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Recurrence in the high-order nonlinear Schrödinger equation: A low-dimensional analysis

2017

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We study a three-wave truncation of the high-order nonlinear Schrödinger equation for deepwater waves (HONLS, also named Dysthe equation). We validate the model by comparing it to numerical simulation, we distinguish the impact of the different fourth-order terms and classify the solutions according to their topology. This allows us to properly define the temporary spectral upshift occurring in the nonlinear stage of Benjamin-Feir instability and provides a tool for studying further generalizations of this model.

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“…Even so, frequency downshifting is not captured by either the linear damped NLS or Dysthe equations since momentum and energy decay at the same rate, thus preserving the spectral center. However, the nonlinear damped higher order NLS (Equation ( 1)) exhibits permanent downshifting [23]) and, in a comparative study, it was shown to be one of the most accurate models for predicting the downshifting observed in a set of laboratory experiments [7].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear damped spatially periodic breathers and the emergence of soliton-like rogue waves

Schober,

Islas

2022

Preprint

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The spatially periodic breather solutions (SPBs) of the nonlinear Schrödinger equation, prominent in modeling rogue waves, are unstable. In this paper we numerically investigate the effects of nonlinear dissipation and higher order nonlinearities on the routes to stability of the SPBs in the framework of the nonlinear damped higher order nonlinear Schrödinger (NLD-HONLS) equation. The initial data used in the experiments are generated by evaluating exact SPB solutions at time T 0 . The number of instabilities of the background Stokes wave and the damping strength are varied. The Floquet spectral theory of the NLS equation is used to interpret and provide a characterization of the perturbed dynamics in terms of nearby solutions of the NLS equation. Significantly, as T 0 is varied, tiny bands of complex spectrum are observed to pinch off in the Floquet decomposition of the NLD-HONLS data, reflecting the breakup of the SPB into a waveform that is close to either a one or two "soliton-like" structure. For wide ranges of T 0 , i.e. for solutions initialized in the early to middle stage of the development of the MI, all rogue waves are observed to occur when the spectrum is close to a one or two soliton-like state. When the solutions are initialized as the MI is saturating, rogue waves also can occur after the spectrum has left a soliton-like state. Other novel features arise due to nonlinear damping: enhanced asymmetry, two timescales in the evolution of the spectrum and a delay in the growth of instabilities due to frequency downshifting.

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The effects of wind and nonlinear damping on rogue waves and permanent downshift

Abstract: openAccessArticle: Falsecover date: 2015-12-01pii: S0167-2789(15)00177-3Harvest Date: 2016-01-06 13:08:11issueName:Page Range: 81-81href scidir: http://www.sciencedirect.com/science/article/pii/S0167278915001773pubType

Cited by 11 publications

References 29 publications

Nonlinear stage of Benjamin-Feir instability in forced/damped deep-water waves

Nonlinear stage of Benjamin-Feir instability in forced/damped deep-water waves

Recurrence in the high-order nonlinear Schrödinger equation: A low-dimensional analysis

Nonlinear damped spatially periodic breathers and the emergence of soliton-like rogue waves

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