A numerical and experimental study on the nonlinear evolution of long-crested irregular waves

Goullet, Arnaud; Choi, Woo-Young

doi:10.1063/1.3533961

Cited by 47 publications

(33 citation statements)

References 48 publications

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“…The MNLS equation has been shown to reproduce laboratory experiments reasonably well (Lo & Mei 1985;Goullet & Choi 2011). There are even higher order envelope equations, such as the Broadband Modified NLS Equation (BMNLS) (Trulsen & Dysthe 1996) as well as the more recent compact Zakharov equation (Dyachenko & Zakharov (2011)).…”

Section: Extreme Events In Envelope Equationsmentioning

confidence: 99%

Reduced-order precursors of rare events in unidirectional nonlinear water waves

2016

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We consider the problem of short-term prediction of rare, extreme water waves in irregular unidirectional fields, a critical topic for ocean structures and naval operations. One possible mechanism for the occurrence of such rare, unusually-intense waves is nonlinear wave focusing. Recent results have demonstrated that random localizations of energy, induced by the linear dispersive mixing of different harmonics, can grow significantly due to modulation instability. Here we show how the interplay between i) modulation instability properties of localized wave groups and ii) statistical properties of wave groups that follow a given spectrum defines a critical length scale associated with the formation of extreme events. The energy that is locally concentrated over this length scale acts as the 'trigger' of nonlinear focusing for wave groups and the formation of subsequent rare events. We use this property to develop inexpensive, shortterm predictors of large water waves, circumventing the need for solving the governing equations. Specifically, we show that by merely tracking the energy of the wave field over the critical length scale allows for the robust, inexpensive prediction of the location of intense waves with a prediction window of 25 wave periods. We demonstrate our results in numerical experiments of unidirectional water wave fields described by the Modified Nonlinear Schrodinger equation. The presented approach introduces a new paradigm for understanding and predicting intermittent and localized events in dynamical systems characterized by uncertainty and potentially strong nonlinear mechanisms.

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Section: Extreme Events In Envelope Equationsmentioning

confidence: 99%

Reduced-order precursors of rare events in unidirectional nonlinear water waves

2016

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“…That is, there is a considerably smaller set of wave groups that would lead to an extreme event in the MNLSE in comparison to the NLSE. These features are critical for understanding realistic extreme waves, as the MNLSE is significantly more accurate in reproducing experimental results when compared with the NLSE [19,20].We explain this difference in the NLSE and MNLSE focusing analytically by using a single mode, adaptive projection where the length scale of the mode is allowed to vary with time. We close this model by enforcing conservation of the L 2 norm, which follows from the envelope equations.…”

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confidence: 99%

Unsteady evolution of localized unidirectional deep-water wave groups

Cousins

Sapsis

2015

Phys. Rev. E

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We study the evolution of localized wave groups in unidirectional water wave envelope equations [the nonlinear Schrödinger (NLSE) and the modified NLSE (MNLSE)]. These localizations of energy can lead to disastrous extreme responses (rogue waves). We analytically quantify the role of such spatial localization, introducing a technique to reduce the underlying partial differential equation dynamics to a simple ordinary differential equation for the wave packet amplitude. We use this reduced model to show how the scale-invariant symmetries of the NLSE break down when the additional terms in the MNLSE are included, inducing a critical scale for the occurrence of extreme waves. [5,6]. In this work we address the formation of freak or extreme waves on the surface of deep water. These waves have caused considerable damage to ships, oil rigs, and human life [7,8].Extreme waves are rare and available data describing them are limited. Thus, analytical understanding of the physics of their triggering mechanisms is critical. One such mechanism is the Benjamin-Feir modulation instability of a plane wave to small sideband perturbations. This instability, which has been demonstrated experimentally, generates huge coherent structures by soaking up energy from the nearby field [9][10][11][12]. The ocean surface, however, is much more irregular than a simple plane wave. The Benjamin-Feir index (BFI), the ratio of surface amplitude to spectral width, measures the strength of the modulation instability in such irregular fields. For spectra with a large BFI, nonlinear interactions dominate, resulting in more extreme waves than Gaussian statistics would suggest. However, a large BFI does not provide precise spatiotemporal locations where extreme events might occur.In large BFI regimes, spatially localized wave groups of modest amplitude focus, creating the extreme waves. Here we quantify the role of this spatial localization in extreme wave formation. In addition to providing insight into the triggering mechanisms for extreme waves, this analysis will allow the development of different spatiotemporal predictive schemes. Specifically, by understanding which wave groups are likely to trigger an extreme wave, one could identify when and where an extreme wave is likely to occur, in a manner similar to that of Cousins and Sapsis [13] for the Majda-McLaughlinTabak model [14]. By analyzing the evolution of spatially localized fields, the authors found a particular length scale that was highly sensitive for the formation of extreme events. By measuring energy localized at this critical scale, the authors reliably predicted extreme events for meager computational expense. * Corresponding author: sapsis@mit.edu Two commonly used equations to model the envelope of a modulated carrier wave on deep water are the nonlinear Schrödinger equation (NLSE) and the modified NLSE (MNLSE) [15]. The focusing of localized groups is well understood for the NLSE (see the work of Adcock et al. [16,17] and Onorato et al. [18]). In this paper we study the less u...

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“…12 ical NLS framework, with NWT2D simulations as well as with the MNLS. The latter extension of the NLS is known to take into account higher-order dispersion and the mean flow of the wave field (Dysthe 1979;Trulsen and Stansberg 2001;Goullet and Choi 2011). For the sake of brevity, we make the comparison only for the case shown in Fig.…”

Section: Results Of Bem-based Nwt2d Simulationsmentioning

confidence: 99%

“…3 and 4, and that are at play when the wave groups experience a strong nonlinear interaction and significant focusing. These are well-captured in the MNLS approach (Dysthe 1979;Trulsen and Stansberg 2001;Goullet and Choi 2011;Slunyaev et al 2013;Chabchoub 2013;Shemer and Alperovich 2013;Chabchoub and Waseda 2016) or fully nonlinear water wave numerical schemes (Ma 2010). The asymmetry increases when the wave steepness is increased from ak = 0.05 to ak = 0.06.…”

Section: Numerical Simulations and Experimental Set-upmentioning

confidence: 95%

Experiments on higher-order and degenerate Akhmediev breather-type rogue water waves

Chabchoub

Waseda

Kibler

et al. 2017

J. Ocean Eng. Mar. Energy

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A possible mechanism that is responsible for the occurrence of rogue waves in the ocean is the Benjamin-Feir instability or modulation instability. The deterministic framework that describes this latter instability of Stokes waves in deep water is provided by the family of Akhmediev breather (AB) solutions of the nonlinear Schrödinger equation (NLS). It is indeed very convenient to use these exact pulsating envelopes particularly for laboratory experiments, since they allow to generate extreme waves at any location in space at any instant of time. As such, using this framework is more advantageous compared to the classical initialization of the unstable wave dynamics from a three wave system (main wave frequency and one pair of unstable sidebands). In this work, we report an experimental study on higher-order AB hydrodynamics that describe a higher-order stage of modulation instability, namely, starting from five wave systems (main wave frequency and two pairs of unstable sidebands). The corresponding laboratory experiments, that have been conducted in a large water wave facility, confirm the NLS wave dynamics forecast while boundary element method-

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A numerical and experimental study on the nonlinear evolution of long-crested irregular waves

Cited by 47 publications

References 48 publications

Reduced-order precursors of rare events in unidirectional nonlinear water waves

Reduced-order precursors of rare events in unidirectional nonlinear water waves

Unsteady evolution of localized unidirectional deep-water wave groups

Experiments on higher-order and degenerate Akhmediev breather-type rogue water waves

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