New solutions of the C.S.Y. equation reveal increases in freak wave occurrence

Andrade, David; Stiassnie, Michael

doi:10.1016/j.wavemoti.2020.102581

Cited by 8 publications

(5 citation statements)

References 7 publications

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“…Considering the variance for depths of ℎ = 3.6 m and ℎ = 10 m one observes a long warm up period, of about 300 peak periods for ℎ = 3.6 m and 200 peak periods for ℎ = 10 m. This period is characterized by a steady increase in the maximum oscillations of the variance, as if the oscillations were modulated by a slowly increasing monotonic envelope. Solutions of the CSY equation typically exhibit a warm up period, which has previously been observed in the evolution of degenerate quartets by Stuhlmeier and Stiassnie (2019) and in systems involving many modes studied by Andrade and Stiassnie (2020b) and Andrade and Stiassnie (2020a). It is also reminiscent of the time-evolution of resonant amplitudes for standing waves reported in Bryant and Stiassnie (1994).…”

Section: Attacking Wavesmentioning

confidence: 69%

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Freak waves caused by reflection

Andrade

Stuhlmeier

Stiassnie

2021

Coastal Engineering

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Section: Attacking Wavesmentioning

confidence: 69%

“…In Regev et al (2008) this last step is formally different, as the integration over time is replaced by an integral with respect to the probability density function of . However, as noted by Andrade and Stiassnie (2020b), both approaches are equivalent.…”

Section: Casementioning

confidence: 97%

Freak waves caused by reflection

Andrade

Stuhlmeier

Stiassnie

2021

Coastal Engineering

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“…Equation (6.3) was derived by Andrade & Stiassnie (2020) and was shown to be equivalent to the original equation derived by Regev et al. (2008).…”

Section: Probability Of Freak-wave Occurrencementioning

confidence: 85%

On the Alber equation for shoaling water waves

2021

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The problem of unidirectional shoaling of a water-wave field with a narrow energy spectrum is treated by using a new Alber equation. The stability of the linear stationary solution to small non-stationary disturbances is analysed; and numerical solutions for its subsequent long-distance evolution are presented. The results quantify the physics which causes the gradual decay in the probability of freak-wave occurrence, when moving from deep to shallow coastal waters.

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“…Given that now we have a version of the Alber equation (and the corresponding stability condition) applicable to crossing seas, the natural next step is to investigate crossing sea situations and see how well a generalized version of the PTI metric would correlate, e.g., with Monte Carlo estimates of the probability of rogue waves appearing there, as well as directional generalisations of the BFI [55,56]. Another option for this kind of analysis would be by working with the stability condition for the broadband Crawford-Saffman-Yuen equation (CSY) [19,21].…”

Section: Discussionmentioning

confidence: 99%

“…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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New solutions of the C.S.Y. equation reveal increases in freak wave occurrence

Cited by 8 publications

References 7 publications

Freak waves caused by reflection

Freak waves caused by reflection

On the Alber equation for shoaling water waves

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

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