Wave crest and trough distributions in a broad-banded directional wave field

Toffoli, Alessandro; Bitner‐Gregersen, Elzbieta M.; Onorato, Miguel; Babanin, Alexander V.

doi:10.1016/j.oceaneng.2008.08.010

Cited by 65 publications

(52 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Some previous investigations (Hagen, 2002;Onorato et al, 2006;Cherneva et al, 2009;Toffoli et al, 2008aToffoli et al, , b, 2010aToffoli et al, , b, 2011 suggest that the noticeably increasing frequency of occurrence of unusually large waves is accompanied by an increment on the coefficient of kurtosis λ 40 , which has been related with the Benjamin-Feir index for narrowband long-crested waves at long times (Janssen, 2003).…”

Section: Theorymentioning

confidence: 94%

Modeling extreme wave heights from laboratory experiments with the nonlinear Schrödinger equation

Zhang¹,

Soares²,

Cherneva³

et al. 2014

Nat. Hazards Earth Syst. Sci.

Self Cite

View full text Add to dashboard Cite

Abstract. Spatial variation of nonlinear wave groups with different initial envelope shapes is theoretically studied first, confirming that the simplest nonlinear theoretical model is capable of describing the evolution of propagating wave packets in deep water. Moreover, three groups of laboratory experiments run in the wave basin of CEHIPAR (Canal de Experiencias Hidrodinámicas de El Pardo, known also as El Pardo Model Basin) was founded in 1928 by the Spanish Navy. are systematically compared with the numerical simulations of the nonlinear Schrödinger equation. Although a little overestimation is detected, especially in the set of experiments characterized by higher initial wave steepness, the numerical simulation still displays a high degree of agreement with the laboratory experiments. Therefore, the nonlinear Schrödinger equation catches the essential characteristics of the extreme waves and provides an important physical insight into their generation. The modulation instability, resulting from the quasi-resonant four-wave interaction in a unidirectional sea state, can be indicated by the coefficient of kurtosis, which shows an appreciable correlation with the extreme wave height and hence is used in the modified Edgeworth-Rayleigh distribution. Finally, some statistical properties on the maximum wave heights in different sea states have been related with the initial Benjamin-Feir index.

show abstract

Section: Theorymentioning

confidence: 94%

Modeling extreme wave heights from laboratory experiments with the nonlinear Schrödinger equation

Zhang¹,

Soares²,

Cherneva³

et al. 2014

Nat. Hazards Earth Syst. Sci.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Mori and Yasuda (2002), Ducrozet et al (2007), Toffoli et al (2008a) and Toffoli et al (2008b). Note that other numerical methods have also been proposed by Annenkov and Shrira (2001), Clamond and Grue (2001), and Zakharov et al (2002).…”

Section: The Modelmentioning

confidence: 99%

“…Toffoli et al: Third-order nonlinearity in water of finite depth deep water third-order nonlinearity is substantially reduced when non-collinear wave components (short crested or directional wave fields) are considered (Onorato et al, 2002). In particular, experimental and numerical studies revealed that short crested waves deviate from Gaussian statistics only due to bound wave contributions despite third-order nonlinear evolution (see, e.g., Socquet-Juglard et al, 2005;Gramstad and Trulsen, 2007;Waseda, 2006;Toffoli et al, 2008a).…”

mentioning

confidence: 99%

The effect of third-order nonlinearity on statistical properties of random directional waves in finite depth

Toffoli

Benoît

Onorato

et al. 2009

Nonlin. Processes Geophys.

Self Cite

View full text Add to dashboard Cite

Abstract. It is well established that third-order nonlinearity produces a strong deviation from Gaussian statistics in water of infinite depth, provided the wave field is long crested, narrow banded and sufficiently steep. A reduction of thirdorder effects is however expected when the wave energy is distributed on a wide range of directions. In water of arbitrary depth, on the other hand, third-order effects tend to be suppressed by finite depth effects if waves are long crested. Numerical simulations of the truncated potential Euler equations are here used to address the combined effect of directionality and finite depth on the statistical properties of surface gravity waves; only relative water depth kh greater than 0.8 are here considered. Results show that random directional wave fields in intermediate water depths, kh=O(1), weakly deviate from Gaussian statistics independently of the degree of directional spreading of the wave energy.

show abstract

“…At the moment the in situ directional measurements of ocean waves are limited. Nowadays, numerical simulations of the Euler equations in two horizontal dimensions are feasible (see, for example, [30] or [31]); therefore, we are planning in the near future to perform a detailed comparison between experimental and numerical results.…”

mentioning

confidence: 99%

Statistical Properties of Directional Ocean Waves: The Role of the Modulational Instability in the Formation of Extreme Events

et al. 2009

Self Cite

View full text Add to dashboard Cite

We discuss two independent, large scale experiments performed in two wave basins of different dimensions in which the statistics of the surface wave elevation are addressed. Both facilities are equipped with a wave maker capable of generating waves with prescribed frequency and directional properties. The experimental results show that the probability of the formation of large amplitude waves strongly depends on the directional properties of the waves. Sea states characterized by long-crested and steep waves are more likely to be populated by freak waves with respect to those characterized by a large directional spreading. DOI: 10.1103/PhysRevLett.102.114502 PACS numbers: 47.35.Bb, 47.55.NÀ An important task in the study of surface gravity waves is the determination of the probability density function of the surface wave elevation. The knowledge of the probability of the occurrence of large amplitude waves is essential for different engineering purposes such as the prediction of wave forces and structural responses or the design of offshore structures. A deep comprehension of the physical mechanisms of the generation of such waves is also a first step towards the development of an operational methodology for the probabilistic forecast of freak waves. It is well known that surface gravity waves obey nonlinear equations and, to date, a universal tool suitable for deriving the probability distribution function of a nonlinear system has not yet been developed. Fortunately, water waves are on average weakly nonlinear [1,2] and solutions can be generally written as power series, where the small parameter, in the case of deep water waves, is the wave steepness ". Strong departure from Gaussian statistics of the surface elevation can be observed if third order nonlinearities are considered. At such order it has been shown numerically [3] and theoretically [4] that, for long-crested waves, a generalization of the Benjamin-Feir instability [5] (or modulational instability [2]) for random spectra can take place [6]. This instability, that corresponds to a quasiresonant four-wave interaction in Fourier space, results in the formation of large amplitude waves (or rogue waves) [7] which affect the statistical properties of the surface elevation (see, for example, [8]). This is particularly true if the ratio between the wave steepness and the spectral bandwidth, known as the Benjamin-Feir Index (BFI), is large [4]. We mention that rogue waves have also been recently observed in optical systems [9] and in acoustic turbulence in He II [10] where giant waves are observed during an inverse cascade process.We emphasize that in many different fields of physics (plasmas [11,12], nonlinear optics [13,14], chargedparticle beam dynamics [15,16]) the modulational instability plays an important role; under suitable physical conditions a nonlinear Schrödinger equation can be derived and the modulational instability can be analyzed directly with this equation [2]. A major question which has to be addressed (and is the subject of the pre...

show abstract

Wave crest and trough distributions in a broad-banded directional wave field

Cited by 65 publications

References 40 publications

Modeling extreme wave heights from laboratory experiments with the nonlinear Schrödinger equation

Modeling extreme wave heights from laboratory experiments with the nonlinear Schrödinger equation

The effect of third-order nonlinearity on statistical properties of random directional waves in finite depth

Statistical Properties of Directional Ocean Waves: The Role of the Modulational Instability in the Formation of Extreme Events

Contact Info

Product

Resources

About