Saturation of rogue wave amplification over steep shoals

Mendes, Saulo; Kasparian, Jérôme

doi:10.1103/physreve.106.065101

Cited by 8 publications

(7 citation statements)

References 58 publications

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“…When solving for second-order irregular waves, we assume that the shoal is linear , the length of the shoal is relatively short and we deal with small amplitude waves only (). These assumptions greatly simplify the problem, but are also representative of real ocean bathymetry(Mendes & Kasparian 2022). Furthermore, we have recently demonstrated that as the slope magnitude increases the rogue wave occurrence follows suit.…”

Section: Theoretical Considerationsmentioning

confidence: 99%

“…Furthermore, we have recently demonstrated that as the slope magnitude increases the rogue wave occurrence follows suit. However, if we assume a small effect of reflection due to a small surf similarity parameter among spectral components (Battjes 1974), the increase in rogue wave occurrence saturates for slopes larger than or equal to (Mendes & Kasparian 2022). The evolution of the exceedance probability in (2.2) can be generalized to any arbitrary incoming statistics (Mendes et al.…”

Section: Theoretical Considerationsmentioning

confidence: 99%

“…(2020) provided experimental data with the broadest set of conditions and widest range of relative water depths. As reviewed in Mendes & Kasparian (2022), three complementary theoretical models for the wave statistics have emerged, albeit they tend to focus on either the surface elevation (Moore et al. 2020), the crest height (Li et al.…”

Section: Introductionmentioning

confidence: 99%

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

Mendes

Kasparian

2023

J. Fluid Mech.

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Bathymetric changes have been experimentally shown to affect the occurrence of rogue waves. We recently derived a non-homogeneous correction to the spectral analysis, allowing us to describe the evolution of the rogue wave probability over a shoal. Here, we extend this work to the evolution of the excess kurtosis of the surface elevation, that plays a central role in estimating rare event probabilities. Furthermore, we provide an upper bound to the excess kurtosis. In intermediate and deep water regimes, a shoal does not affect wave steepness nor bandwidth significantly, so that the vertical asymmetry between crests and troughs, the excess kurtosis and the exceedance probability of wave height stay rather constant. In contrast, in shallower water, a sharp increase in wave steepness increases the vertical asymmetry, resulting in a growth of both the tail of the exceedance probability and the excess kurtosis.

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Section: Theoretical Considerationsmentioning

confidence: 99%

Section: Theoretical Considerationsmentioning

confidence: 99%

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

Mendes

Kasparian

2023

J. Fluid Mech.

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“…Dashed vertical lines mark the shoaling and de-shoaling zones (see figure 1). Solid curves include the slope effect [26].…”

Section: Kurtosis Evolution Over a Shoalmentioning

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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“…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 .…”

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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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Saturation of rogue wave amplification over steep shoals

Cited by 8 publications

References 58 publications

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

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

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

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

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