Bound-waves due to sea and swell trigger the generation of freak-waves

Andrade, David; Stiassnie, Michael

doi:10.1007/s40722-020-00179-3

Cited by 4 publications

(6 citation statements)

References 14 publications

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“…which is exactly equation (3). Moreover, the condition ( 50) is equivalent to circular symmetry, i.e.…”

mentioning

confidence: 88%

“…where h A , h B , r n 0 A , r n 0 B are defined in terms of the data of the problem in eq. ( 46) 3 . In that case, inhomogeneities are expected to grow in time.…”

Section: The Alber Equation For Crossing Seasmentioning

confidence: 99%

“…The most well-known stochastic models for ocean waves include the CSY equation [18,3,4], Hasselmann's equation [26] and the Alber equation [2] that we will focus on here. For a recent review of various stochastic models one can see [48].…”

Section: Introductionmentioning

confidence: 99%

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Modelling of ocean waves with the Alber equation: application to non-parametric spectra and generalization to crossing seas

Athanassoulis,

Gramstad

2021

Preprint

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We study the Alber equation, a phase-averaged second-moment model for the statistics of a wavefield, derived under a narrowbandedness assumption. More specifically, we use the Alber equation and its associated instability condition to quantify how close a given non-parametric spectrum is to being modulationally unstable, and apply this to a dataset of 100 non-parametric spectra provided by the Norwegian Meteorological Institute. The vast majority of realistic spectra turn out to be stable, but the "proximity to instability" metric is seen to correlate strongly with their steepness and Benjamin-Feir Index (BFI). Moreover, upon comparing with phase-resolved broadband Monte Carlo simulations, the kurtosis and probability of extreme waves for each sea state wavefield are also seen to correlate well with its "proximity to instability". Finally, in order to extend this approach to crossing seas, we derive a generalized Alber equation starting from a system of nonlinear Schrödinger equations modelling crossing seas. We also derive the associated 2-dimensional instability condition.

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“…which is exactly equation (3). Moreover, the condition ( 50) is equivalent to circular symmetry, i.e.…”

mentioning

confidence: 88%

“…where h A , h B , r n 0 A , r n 0 B are defined in terms of the data of the problem in eq. ( 46) 3 . In that case, inhomogeneities are expected to grow in time.…”

Section: The Alber Equation For Crossing Seasmentioning

confidence: 99%

See 1 more Smart Citation

Modelling of ocean waves with the Alber equation: application to non-parametric spectra and generalization to crossing seas

Athanassoulis,

Gramstad

2021

Preprint

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“…Ribal et al (2013); Gramstad (2017); Athanassoulis and Gramstad (2021)). The source of such initial correlations is not yet fully understood, despite some preliminary results of Regev et al (2008) and Andrade and Stiassnie (2020a). Obstacles, such as walls, offer a natural way to correlate different wave components, thus naturally requiring the use of inhomogeneous evolution equations for the study of the resulting wave fields.…”

Section: Introductionmentioning

confidence: 99%

Freak waves caused by reflection

Andrade

Stuhlmeier

Stiassnie

2021

Coastal Engineering

Self Cite

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“…The most well known stochastic models for ocean waves include the CSY equation [19][20][21], Hasselmann's equation [22] and the Alber equation [23], which we will focus on here. For a recent review of various stochastic models, one can see [24].…”

Section: Introductionmentioning

confidence: 99%

Modelling of Ocean Waves with the Alber Equation: Application to Non-Parametric Spectra and Generalisation to Crossing Seas

Athanassoulis

Gramstad

2021

Fluids

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The Alber equation is a phase-averaged second-moment model used to study the statistics of a sea state, which has recently been attracting renewed attention. We extend it in two ways: firstly, we derive a generalized Alber system starting from a system of nonlinear Schrödinger equations, which contains the classical Alber equation as a special case but can also describe crossing seas, i.e., two wavesystems with different wavenumbers crossing. (These can be two completely independent wavenumbers, i.e., in general different directions and different moduli.) We also derive the associated two-dimensional scalar instability condition. This is the first time that a modulation instability condition applicable to crossing seas has been systematically derived for general spectra. Secondly, we use the classical Alber equation and its associated instability condition to quantify how close a given nonparametric spectrum is to being modulationally unstable. We apply this to a dataset of 100 nonparametric spectra provided by the Norwegian Meteorological Institute and find that the vast majority of realistic spectra turn out to be stable, but three extreme sea states are found to be unstable (out of 20 sea states chosen for their severity). Moreover, we introduce a novel “proximity to instability” (PTI) metric, inspired by the stability analysis. This is seen to correlate strongly with the steepness and Benjamin–Feir Index (BFI) for the sea states in our dataset (>85% Spearman rank correlation). Furthermore, upon comparing with phase-resolved broadband Monte Carlo simulations, the kurtosis and probability of rogue waves for each sea state are also seen to correlate well with the PTI (>85% Spearman rank correlation).

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Bound-waves due to sea and swell trigger the generation of freak-waves

Cited by 4 publications

References 14 publications

Modelling of ocean waves with the Alber equation: application to non-parametric spectra and generalization to crossing seas

Modelling of ocean waves with the Alber equation: application to non-parametric spectra and generalization to crossing seas

Freak waves caused by reflection

Modelling of Ocean Waves with the Alber Equation: Application to Non-Parametric Spectra and Generalisation to Crossing Seas

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