The Rayleigh-Haring-Tayfun distribution of wave heights in deep water

Mendes, Saulo; Scotti, Alberto

doi:10.1016/j.apor.2021.102739

Cited by 11 publications

(8 citation statements)

References 69 publications

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“…If the null hypothesis H 0,3 is rejected, with the above mentioned tests, the null hypothesis H 0,4 : X is a Gaussian process (5) is rejected against the alternative H a,4 : X is not a Gaussian process.…”

Section: Tests For Gaussianitymentioning

confidence: 99%

“…Much attention in the literature is dedicated to the study of the sea surface height [1-3], a function of the sea surface elevation which is generally obtained by making use of the zero-up or down crossing methodology. The sea surface height is relevant because of design and analysis of off-shore structures [4] and ships [5] and, therefore, the literature is large in terms of studying its distribution [6][7][8][9][10]. The sea surface height has been modeled, for instance, as a Battjes-Groenendijk distribution [18], • a Mendez distribution [19], or • a LoWiSh II distribution [20].…”

Section: Introductionmentioning

confidence: 99%

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On the Non-Gaussianity of Sea Surface Elevations

Nieto-Reyes

2022

JMSE

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The sea surface elevations are generally stated as non-Gaussian processes in the current literature, being considered Gaussian for short periods of relatively low wave heights. The objective here is to study the evolution of the distribution of the sea surface elevation from Gaussian to non-Gaussian as the period of time in which the associated time series is recorded increases. To do this, an empirical study based on the measurements of the buoys in the US coast downloaded at a casual day is performed. This study results in rejecting the null hypothesis of Gaussianity in below 25% of the cases for short periods of time and in over 95% of the cases for long periods of time. The analysis pursued relates to a recent one by the author in which the heights of sea waves are proved to be non-Gaussian. It is similar in that the Gaussianity of the process is studied as a whole and not just of its one-dimensional marginal, as it is common in the literature. It differs, however, in that the analysis of the sea surface elevations is harder from a statistical point of view, as the one-dimensional marginals can be Gaussian, which is observed throughout the study and in that a longitudinal study is performed here.

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Section: Tests For Gaussianitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Non-Gaussianity of Sea Surface Elevations

Nieto-Reyes

2022

JMSE

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“…On the other hand, no standard distribution reproduces observations over a wide range of depths and sea states [12,13]. For sea states in equilibrium (without shoaling), it may be possible to describe both deep and shallow regimes with second-order models of enhanced empirical parameter space (steepness, bandwidth, depth) [14,15], albeit such methods lack first principles of the physical problem. For seas out of equilibrium, experiments in shallower regimes have shown that inhomogeneities in the wave field due to shoaling contribute to rogue wave formation and amplification [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Saturation of rogue wave amplification over steep shoals

Mendes

Kasparian

2022

Phys. Rev. E

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Shoaling surface gravity waves induce rogue wave formation. Though commonly reduced to water waves passing over a step, nonequilibrium physics allows finite slopes to be considered in this problem. Using nonhomogeneous spectral analysis of a spatially varying energy density ratio, we describe the dependence of the amplification as a function of the slope steepness. Increasing the slope increases the amplification of rogue wave probability until this amplification saturates at steep slopes. In contrast, the increase of the down slope of a subsequent de-shoal zone leads to a monotonic decrease in the rogue wave probability, thus featuring a strong asymmetry between shoaling and de-shoaling zones. Due to the saturation of the rogue wave amplification at steep slopes, our model is applicable beyond its range of validity up to a step, thus elucidating why previous models based on a step could describe the physics of steep finite slopes. We also explain why the rogue wave probability increases over a shoal while it is lower in shallower water.

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“…Much attention in the literature is dedicated to the study of the sea surface height (Forristall, 1978;Azaïs, León and Ortega, 2005;Karmpadakis, Swan and Christou, 2020), a function of the sea surface elevation which is generally obtained by making use of the zero-up or down crossing methodology. The sea surface height is relevant because of design and analysis of off-shore structures (Haver, 1987) and ships (Mendes and Scotti, 2021) and, therefore, the literature is large in terms of studying its distribution Tayfun (1990); Mori, Liu and Yasuda (2002); Stansell (2004Stansell ( , 2005; Casas- Prat and Holthuijsen (2010). The sea surface height has been modeled, for instance, as…”

Section: Introductionmentioning

confidence: 99%

On the Non-Gaussianity of Sea Surface Elevations

Nieto-Reyes¹

2022

Preprint

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The sea surface elevations are generally stated as Gaussian processes in the literature. To show the inaccuracy of this statement, an empirical study of the buoys in the US coast at a random day is performed, which results in rejecting the null hypothesis of Gaussianity in over 80% of the cases. The analysis pursued relates to a recent one by the author in which the heights of sea waves are proved to be non-Gaussian. It is similar in that the Gaussianity of the process is studied as a whole and not just of its one-dimensional marginal, as it is common in the literature. It differs, however, in that the analysis of the sea surface elevations is harder from a statistical point of view, as the one-dimensional marginals are commonly Gaussian, which is observed throughout the study.

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The Rayleigh-Haring-Tayfun distribution of wave heights in deep water

Cited by 11 publications

References 69 publications

On the Non-Gaussianity of Sea Surface Elevations

On the Non-Gaussianity of Sea Surface Elevations

Saturation of rogue wave amplification over steep shoals

On the Non-Gaussianity of Sea Surface Elevations

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