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

Osborne, A. R.; Onorato, Miguel; Serio, M.

doi:10.1016/s0375-9601(00)00575-2

Cited by 352 publications

(276 citation statements)

References 13 publications

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“…More satisfactorily, equation (2.2), as we see below, admits an exact two-dimensional generalization of the PB with the desirable properties of a realistic surface RW. It is promising that many characteristic properties, such as directional preference, MI, appearance of higher amplitude, etc., observed theoretically and experimentally in connection with the formation of RWs in two-dimensional models [10,11,17,18], which remained as numerical approximations, are confirmed through analytic result in our model based on integrable equation (2.2).…”

Section: Proposed Integrable Two-dimensional Nonlinear Schrödinger Eqsupporting

confidence: 84%

“…In two-dimensional water basin experiments as well as in the related simulations the amplitude and the modular inclination of the RWs were found to be higher [10,13,17,18] than those predicted and observed in one dimension [14,17].…”

Section: Introductionmentioning

confidence: 58%

“…This elusive freak wave caught the imagination of the broad scientific community quite recently [8][9][10][11][12][13][14][15], triggering off an upsurge in theoretical [7,[16][17][18] and experimental [5,[8][9][10][11][12][13][14][15] studies of this unique phenomenon. For identifying such extreme waves, the suggested signature of these rare events is a deviation of the probability distribution function (PDF) of the wave amplitude from its usual random Gaussian distribution (GD), by having a long-tail, indicating that the appearance of high-intensity pulses more often has much higher probability than that predicted by the GD [19].…”

Section: Introductionmentioning

confidence: 99%

“…However such modifications of the NLS equation (1.1) make the system non-integrable, allowing only numerical solutions. The most popular one-dimensional RW model is a unique analytic rational solution of the original NLS equation (1.1) [24], given by the Peregrine breather (PB) [12,14,17] or its higher order versions [25][26][27] and the trigonometric variants [28,29]. However, as the RW is an aperiodic event with a single appearance, the trigonometric breather solutions, owing to their periodic nature, are not very suitable for a direct description of the RW.…”

Section: Introductionmentioning

confidence: 99%

“…where q(x, y, t) is a slowly varying envelop and d 1 and d 2 represent linear dispersion coefficients [18] of the deep-water gravity wave, was proposed in connection with RWs [17,18]. Note however that the two-dimensional NLS equation (1.6) is not an integrable system and gives only approximate numerical solutions with no stable soliton.…”

Section: Introductionmentioning

confidence: 99%

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Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents

2014

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Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The twodimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves.

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Section: Proposed Integrable Two-dimensional Nonlinear Schrödinger Eqsupporting

confidence: 84%

Section: Introductionmentioning

confidence: 58%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents

2014

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Crossing sea state and rogue wave probability during the Prestige accident

et al. 2015

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We discuss the crossing sea state and the probability of rogue waves during the accident of the tanker Prestige on 13 November 2002. We present newly computed hindcast spectra for every hour during that day at nearby locations, showing the development of a bimodal sea state with two wave systems crossing at nearly right angle. We employ four different nonlinear models capable of computing the phase‐resolved sea surface from the hindcast spectra, allowing us to estimate statistics for the occurrence of rogue waves. At the location and moment of the accident, the models give expected values for the kurtosis κ = 3.0119 ± 0.0078. The models coincide that the maximum crest elevation was about 5–6% larger than the expected maximum crest elevation in a Gaussian sea at the moment of the accident. We also conclude that the possible nonlinear interaction between the two crossing wave systems practically did not modify neither the kurtosis nor the largest crest elevation.

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Observation of hole Peregrine soliton in a multicomponent plasma with critical density of negative ions

Sharma

Bailung

2013

JGR Space Physics

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[1] The evolution of hole Peregrine soliton (appearing as a deep trough between two crests) from ion-acoustic perturbations excited in a multicomponent plasma with critical density of negative ions has been observed. The observed soliton is described by the rational solution of the cubic nonlinear Schrödinger equation, which can appear as an isolated high peak or a deep hole depending on the phase of the underlying carrier wave relative to the envelope. The measured amplitude of the hole Peregrine soliton (depth from crest to trough) is found to be more than twice the background wave height. The experimental observations are compared with the theoretical results obtained from the solution of the cubic nonlinear Schrödinger equation. The frequency spectrum of the Peregrine soliton is analyzed and found to be triangular in shape.Citation: Sharma, S. K., and H. Bailung (2013), Observation of hole Peregrine soliton in a multicomponent plasma with critical density of negative ions,

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

Cited by 352 publications

References 13 publications

Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents

Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents

Crossing sea state and rogue wave probability during the Prestige accident

Observation of hole Peregrine soliton in a multicomponent plasma with critical density of negative ions

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