Experiments on uni-directional and nonlinear wave group shoaling

Kimmoun, Olivier; Hsu, Hung-Chu; Hoffmann, Norbert; Chabchoub, Amin

doi:10.1007/s10236-021-01485-6

Cited by 17 publications

(12 citation statements)

References 43 publications

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“…The combination of these two effects redistributes the exceedance probability by causing the rise in ζ 2 to exceed the growth of E . Such uneven growth explains why a shoal in intermediate water amplifies rogue wave occurrence as compared to deep water [19,20] while it reduces this occurrence in shallow water [21,22]. The linear term in ζ(x, t) has the leading order in deep water and Γ − 1 10 −2 is small.…”

Section: Theoretical Considerationsmentioning

confidence: 99%

Non-homogeneous approximation for the kurtosis evolution of shoaling rogue waves

Mendes¹,

Kasparian²

2023

Preprint

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Bathymetric changes have been experimentally shown to affect the occurrence of rogue waves. In view of the central role played by the excess kurtosis of the surface elevation in estimating rare event probabilities, we translate the recently determined evolution of the rogue wave probability over a shoal into that of the kurtosis. We provide an effective theory that connects the non-homogeneous correction to the spectral analysis and the evolution of excess kurtosis over the shoal, as well as the kurtosis upper bound. In intermediate water depth the vertical asymmetry between crests and troughs is virtually constant throughout the shoal for a given wave steepness and bandwidth, thus not affecting the exceedance probability. Conversely, a sharp increase in steepness increases the asymmetry for waves in intermediate depth. Thus, both the tail of the exceedance probability and excess kurtosis grow.

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Section: Theoretical Considerationsmentioning

confidence: 99%

Non-homogeneous approximation for the kurtosis evolution of shoaling rogue waves

Mendes¹,

Kasparian²

2023

Preprint

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“…Several numerical studies of the different nonlinear evolution equations have been given, such as the NLS-like equation (Zeng & Trulsen 2012; Kimmoun et al. 2021; Lyu, Mori & Kashima 2021), the Korteweg–De Vries (KdV) equation (Sergeeva, Pelinovsky & Talipova 2011; Majda, Moore & Qi 2019), Boussinesq equations (Gramstad et al. 2013; Kashima, Hirayama & Mori 2014; Zhang et al.…”

Section: Introductionmentioning

confidence: 99%

“…Several numerical studies of the different nonlinear evolution equations have been given, such as the NLS-like equation Kimmoun et al 2021;Lyu, Mori & Kashima 2021), the Korteweg-De Vries (KdV) equation (Sergeeva, Pelinovsky & Talipova 2011;Majda, Moore & Qi 2019), Boussinesq equations (Gramstad et al 2013;Kashima, Hirayama & Mori 2014;Zhang et al 2019) and other nonlinear methods (Viotti & Dias 2014;Zheng et al 2020;Lawrence, Trulsen & Gramstad 2021, etc.). From the research mentioned above, a similar conclusion can be derived, that is, the increase of bottom slope angle will give rise to inhomogeneity of the wavefield and lead to an increase of the kurtosis of surface elevation in very shallow water, which equals to the increase of the exceedance probability of extreme wave height P m (H max ) occurring; here P m represents the cumulative distribution function (CDF) and H represents wave height.…”

Section: Introductionmentioning

confidence: 99%

Freak wave in a two-dimensional directional wavefield with bottom topography change. Part 1. Normal incidence wave

2023

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In the propagation and evolution of sea waves, previous studies pointed out that the occurrence of the freak wave height is significantly related to the quasi-resonant four-wave interaction in the modulated waves. From numerical--experimental study over an uneven bottom, the nonlinear effect caused by the bathymetry change also contributes to the occurrence of extreme events in unidirectional waves. To comprehensively analyse the two-dimensional wavefield, this study develops an evolution model for a directional random wavefield based on the depth-modified nonlinear Schrödinger equation, which considers the nonlinear resonant interactions and the wave shoaling the shallow water. Through Monte Carlo simulation, we discuss the directional effect on the four-wave interaction in the wave train and the maximum wave height distribution from deep to shallow water with a slow varying slope. The numerical result indicates that the directional spreading has a dispersion effect on the freak wave height. In a shallow-water environment, this effect becomes weak, and the bottom topography change is the main influencing factor in the wave evolution.

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“…Although beyond the scope of our work, there Some successful attempts have been to study extreme events in water waves (often called rogue or freak waves) with distributions uniquely determined by the dynamics of the physical system. For instance 18,19 , have shown that water waves departing from linear theory will modify their distribution from a Rayleigh type [20][21][22] to a distribution dependent on the square root of the wave steepness. Similarly 23,24 , have shown that a Rayleigh distribution modified by a polynomial function of the ratio between height and water depth controls extreme events in Hurricane data.…”

mentioning

confidence: 99%

“…In addition, spectrum bandwidth seems to have different types of effects in extreme wave distribution depending on whether they are in deep [25][26][27][28] or shallow water 13 . Furthermore, ocean processes such as shoaling or wave-current systems that drive wave trains out of equilibrium have been experimentally 22,25,[29][30][31][32][33][34][35][36][37] associated with increasing the occurrence of extreme waves by order of magnitude. However, it has been recently found that no established theoretical distribution to date, neither universal as Gumbel nor based on physical principles, can describe extreme wave statistics in a wide range of conditions .…”

mentioning

confidence: 99%

Novel methods for coupled prediction of extreme wind speeds and wave heights

Gaidai

Xing

2023

Sci Rep

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Two novel methods are being outlined that, when combined, can be used for spatiotemporal analysis of wind speeds and wave heights, thus contributing to global climate studies. First, the authors provide a unique reliability approach that is especially suited for multi-dimensional structural and environmental dynamic system responses that have been numerically simulated or observed over a substantial time range, yielding representative ergodic time series. Next, this work introduces a novel deconvolution extrapolation technique applicable to a wide range of environmental and engineering applications. Classical reliability approaches cannot cope with dynamic systems with high dimensionality and responses with complicated cross-correlation. The combined study of wind speed and wave height is notoriously difficult, since they comprise a very complex, multi-dimensional, non-linear environmental system. Additionally, global warming is a significant element influencing ocean waves throughout the years. Furthermore, the environmental system reliability method is crucial for structures working in any particular region of interest and facing actual and often harsh weather conditions. This research demonstrates the effectiveness of our approach by applying it to the concurrent prediction of wind speeds and wave heights from NOAA buoys in the North Pacific. This study aims to evaluate the state-of-the-art approach that extracts essential information about the extreme responses from observed time histories.

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Experiments on uni-directional and nonlinear wave group shoaling

Cited by 17 publications

References 43 publications

Non-homogeneous approximation for the kurtosis evolution of shoaling rogue waves

Non-homogeneous approximation for the kurtosis evolution of shoaling rogue waves

Freak wave in a two-dimensional directional wavefield with bottom topography change. Part 1. Normal incidence wave

Novel methods for coupled prediction of extreme wind speeds and wave heights

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