On the statistical properties of surface elevation, velocities and accelerations in multi-directional irregular water waves

Klahn, Mathias; Madsen, Peter Hauge; Fuhrman, David R.

doi:10.1017/jfm.2020.968

Cited by 9 publications

(29 citation statements)

References 31 publications

(97 reference statements)

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“…They are reported in figure 3(b) based on the typical experimental values S = K − 3 = 0.2 from table 1. As observed in Klahn, Madsen & Fuhrman (2021), they both underestimate large positive values and fail to capture large negative ones (for which the p.d.f. is either undefined, as for the second-order Gram-Charlier approximation, or largely above the experimental data, as for the third-order approximation).…”

Section: Probability Density Functions (Pdfs)mentioning

confidence: 78%

“…where (Fedele & Tayfun 2009). Previous studies have only tested this result in the linear limit in which η C = 0 (Soquet-Juglard Klahn et al 2021). The normalized elevation η(t)/η(0) computed from (6.1) with both η C = 0 and η C = 1.25H s is reported in figure 6, along with experimental and numerical values for crests such that η C > 1.25H S .…”

Section: Shape Of Large Crestsmentioning

confidence: 93%

“…Similar to surface elevation, the p.d.f. of η C has been empirically found to fit the tails of multidirectional wave fields as well (Soquet-Juglard et al 2005;Denissenko et al 2007;Klahn et al 2021). Both experimental and numerical p.d.f.s are reported in figure 4 along with the theoretical Rayleigh distribution (f R (ξ ) = ξ exp(−ξ 2 /2), capturing linear waves) and the Tayfun distributions with the steepness parameter tuned to describe a skewness of 0.24.…”

Section: Probability Density Functions (Pdfs)mentioning

confidence: 97%

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Statistics of rogue waves in isotropic wave fields

et al. 2022

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We investigate the statistics of rogue waves occurring in the inverse cascade of surface gravity wave turbulence. In such statistically homogeneous, stationary and isotropic wave fields, low-frequency waves are generated by nonlinear interactions rather than directly forced by a wave maker. This provides a laboratory realization of arguably the simplest nonlinear sea state, in which long-time acquisitions are performed and compared with theoretical models. The analysis of thousands of rogue waves reveals that some of their properties crucially depend on four-wave resonant interactions, large crests being for instance more likely than predicted by second-order models.

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Section: Probability Density Functions (Pdfs)mentioning

confidence: 78%

Section: Shape Of Large Crestsmentioning

confidence: 93%

Section: Probability Density Functions (Pdfs)mentioning

confidence: 97%

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Statistics of rogue waves in isotropic wave fields

et al. 2022

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“…Drawing on the fact that irregular wave fields in some sense tend to become more nonlinear when the directional spread decreases (e.g. Onorato et al [13] and Toffoli et al [14]) this result could to some degree have been anticipated from the results Klahn et al [26], who have recently shown that the variance of the Eulerian velocity at the surface decreases with nonlinearity (see e.g. their table 3).…”

Section: (B) Variance Of the Eulerian Velocitymentioning

confidence: 91%

Mean and variance of the Eulerian and Lagrangian horizontal velocities induced by nonlinear multi-directional irregular water waves

2021

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In this paper, we study the mean and variance of the Eulerian and Lagrangian fluid velocities as a function of depth below the surface of directionally spread irregular wave fields given by JONSWAP spectra in deep water. We focus on the behaviour of these quantities in the bulk of the water, and using second-order potential flow theory we derive new simple asymptotic approximations for their decay in the limit of large depth below the surface. Specifically, we show that when the depth is greater than about 1.5 peak wavelengths, the variance of the Eulerian velocity decays in proportion to exp ⁡ ( − ( 135 4 ) 1 / 3 ( − k p z ) 2 / 3 ) , and the mean Lagrangian velocity decays in proportion to 1 ( − k p z ) 1 / 6 exp ⁡ ( − ( 135 4 ) 1 / 3 ( − k p z ) 2 / 3 ) . Here, k p is the peak wave number and z is the vertical coordinate measured positively upwards from the still water level. We test the accuracy of the second-order formulation against new fully nonlinear simulations of both short crested and long crested irregular wave fields and find a good match, even when the simulations are known to be affected substantially by third-order effects. To our knowledge, this marks the first fully nonlinear investigation of the Eulerian and Lagrangian velocities below the surface in irregular wave fields.

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“…(2021 b ), it was observed that strongly non-Gaussian statistics for both surface elevation and horizontal velocity fields are triggered by abrupt depth changes. Recent studies by Klahn, Madsen & Fuhrman (2021 a , b ) consider statistical properties of surface elevation, velocity field, acceleration and forces on a vertical column in deep water that show the deviation from Gaussian statistics as the wave steepness increases.…”

Section: Introductionmentioning

confidence: 99%

Extreme wave statistics of surface elevation and velocity field of gravity waves over a two-dimensional bathymetry

2022

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This paper presents the effects of two-dimensional bathymetry on the evolution of skewness and kurtosis of the surface elevation and velocity field in long-crested irregular waves propagating over a circular shoal and a submerged bar with a semicircular step. For a circular shoal, we show that the surface elevation has a local maximum of skewness and kurtosis on top of the shoal. We find that the skewness of the horizontal velocity field has similar behaviour to the surface elevation, but the kurtosis of the horizontal velocity field has two local maxima at different locations on the lee side of the shoal. For a semicircular step, which acts similar to a converging lens, we find that refraction contributes to the statistical properties of the surface elevation and horizontal velocity field to deviate from Gaussian statistics.

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On the statistical properties of surface elevation, velocities and accelerations in multi-directional irregular water waves

Abstract: Abstract

Cited by 9 publications

References 31 publications

Statistics of rogue waves in isotropic wave fields

Statistics of rogue waves in isotropic wave fields

Mean and variance of the Eulerian and Lagrangian horizontal velocities induced by nonlinear multi-directional irregular water waves

Extreme wave statistics of surface elevation and velocity field of gravity waves over a two-dimensional bathymetry

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