Generalized Boccotti distribution for nonlinear wave heights

Alkhalidi, Mohamad; Tayfun, M. Aziz

doi:10.1016/j.oceaneng.2013.09.014

Cited by 30 publications

(19 citation statements)

References 29 publications

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“…In the following, we will not dwell on wave heights4344 as our main focus will be the statistics of crest heights in oceanic rogue sea states.…”

Section: Return Period Of a Wave Whose Crest Height Exceeds A Given Tmentioning

confidence: 99%

“…We point out that the Tayfun distribution represents an exact result for large second order wave crest heights and it depends solely on the steepness parameter defined as μ = λ 3 /3 9 . In the following, we will not dwell on wave heights 43 44 as our main focus will be the statistics of crest heights in oceanic rogue sea states.…”

Section: Return Period Of a Wave Whose Crest Height Exceeds A Given Tmentioning

confidence: 99%

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Real world ocean rogue waves explained without the modulational instability

Fedele

Brennan

León

et al. 2016

Sci Rep

215

180

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Since the 1990s, the modulational instability has commonly been used to explain the occurrence of rogue waves that appear from nowhere in the open ocean. However, the importance of this instability in the context of ocean waves is not well established. This mechanism has been successfully studied in laboratory experiments and in mathematical studies, but there is no consensus on what actually takes place in the ocean. In this work, we question the oceanic relevance of this paradigm. In particular, we analyze several sets of field data in various European locations with various tools, and find that the main generation mechanism for rogue waves is the constructive interference of elementary waves enhanced by second-order bound nonlinearities and not the modulational instability. This implies that rogue waves are likely to be rare occurrences of weakly nonlinear random seas.

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“…In the following, we will not dwell on wave heights4344 as our main focus will be the statistics of crest heights in oceanic rogue sea states.…”

Section: Return Period Of a Wave Whose Crest Height Exceeds A Given Tmentioning

confidence: 99%

Section: Return Period Of a Wave Whose Crest Height Exceeds A Given Tmentioning

confidence: 99%

Real world ocean rogue waves explained without the modulational instability

Fedele

Brennan

León

et al. 2016

Sci Rep

215

180

View full text Add to dashboard Cite

show abstract

“…The relationship between the fourth-order moment of free surface elevation and the third-order nonlinearity is studied in [51]. The effects resulting from third-order nonlinearity on the statistics of wave height distribution have been taken into consideration by using Edgeworth's form of a Gram-Charlier series [51][52][53][54][55]; this family of wave height distributions is sometimes referred to as modified Edgeworth Rayleigh distribution (MER). They do not seem to be of specific attraction in describing the statistics of coastal wave heights because the corresponding PDF of MER is not always positive (which is not realistic).…”

Section: Gram-charlier Type Model (Gbd)mentioning

confidence: 99%

“…A recent model of this family proposed in [55] is a generalised Boccotti distribution (labelled as GBD) in the form of MER, taking third-order nonlinearity and finite spectral width into consideration. Recall the Boccotti's distribution [56]:…”

Section: Gram-charlier Type Model (Gbd)mentioning

confidence: 99%

Statistics of Extreme Waves in Coastal Waters: Large Scale Experiments and Advanced Numerical Simulations

Zhang

Benoît

Kimmoun

et al. 2019

Fluids

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The formation mechanism of extreme waves in the coastal areas is still an open contemporary problem in fluid mechanics and ocean engineering. Previous studies have shown that the transition of water depth from a deeper to a shallower zone increases the occurrence probability of large waves. Indeed, more efforts are required to improve the understanding of extreme wave statistics variations in such conditions. To achieve this goal, large scale experiments of unidirectional irregular waves propagating over a variable bottom profile considering different transition water depths were performed. The validation of two highly nonlinear numerical models was performed for one representative case. The collected data were examined and interpreted by using spectral or bispectral analysis as well as statistical analysis. The higher probability of occurrence of large waves was confirmed by the statistical distributions built from the measured free surface elevation time series as well as by the local maximum values of skewness and kurtosis around the end of the slope. Strong second-order nonlinear effects were highlighted as waves propagate into the shallower region. A significant amount of wave energy was transmitted to low-frequency modes. Based on the experimental data, we conclude that the formation of extreme waves is mainly related to the second-order effect, which is also responsible for the generation of long waves. It is shown that higher-order nonlinearities are negligible in these sets of experiments. Several existing models for wave height distributions were compared and analysed. It appears that the generalised Boccotti’s distribution can predict the exceedance of large wave heights with good confidence.

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“…Much research has been performed on the statistical distribution of nonlinear random waves with regard to the shapes of wave components (Longuet-Higgins, 1963;Tayfun, 1980;Huang et al, 1983;Hou et al, 2006;Alkhalidi and Tayfun, 2013;Izadparast and Niedzwecki, 2013). However, the effect of a realistic wind-wave spectral bandwidth on the probability distribution of wave heights has been rarely studied.…”

Section: Introductionmentioning

confidence: 99%

Effect of wave spectrum width on the probability density distribution of wind-wave heights

Liu

Hou

et al. 2014

Chin. J. Ocean. Limnol.

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The probability distribution of wave heights under the assumption of narrowband linear wave theory follows the Rayleigh distribution and the statistical relationships between some characteristic wave heights, derived from this distribution, are widely used for the treatment of realistic wind waves. However, the bandwidth of wave frequency infl uences the probability distribution of wave heights. In this paper, a wave-spectrum-width parameter B was introduced into the JONSWAP spectrum. This facilitated the construction of a wind-wave spectrum and the reconstruction of wind-wave time series for various growth stages, based on which the probability density distributions of the wind-wave heights were studied statistically. The distribution curves deviated slightly from the theoretical Rayleigh distribution with increasing B . The probability that a wave height exceeded a certain value was clearly smaller than the theoretical value for B ≥0.3, and the difference between them increased with the threshold value. The relation between the H s / σ ratio and B was investigated statistically, which revealed that the H s / σ ratio deviated from 4.005 and declined with B . When B reached 0.698 1, the H s / σ ratio was 3.825, which is about 95.5% of its original value. This indicates an overestimation in the prediction of H s from H s =4.005 σ , and provides a potential method for improving the accuracy of the H s remote sensing retrieval algorithm, critical for extremely large waves under severe sea states.

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Generalized Boccotti distribution for nonlinear wave heights

Cited by 30 publications

References 29 publications

Real world ocean rogue waves explained without the modulational instability

Real world ocean rogue waves explained without the modulational instability

Statistics of Extreme Waves in Coastal Waters: Large Scale Experiments and Advanced Numerical Simulations

Effect of wave spectrum width on the probability density distribution of wind-wave heights

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