Wave Statistics in Non-Linear Random Sea

Machado, Ulla B.; Rychlik, Igor

doi:10.1023/b:extr.0000025663.45811.9b

Cited by 16 publications

(11 citation statements)

References 18 publications

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“…Most of the models for individual waves are based on Gaussian approaches, but other types of stochastic wave models have also been proposed to account for observed asymmetries (e.g. adding random correction terms to a Gaussian model (Machado and Rychlik 2003) or based on Lagrangian models (Lindgren 2006;Aberg and Lindgren 2008)). Asymptotic models for the distribution of maxima for Gaussian processes for a certain period of time exist, and under certain assumptions, the maximum values are asymptotically distributed according to the Gumbel distribution.…”

Section: Short-term Stochastic Wave Modelsmentioning

confidence: 99%

Long-term time-dependent stochastic modelling of extreme waves

Vanem

2010

Stoch Environ Res Risk Assess

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This paper presents a literature survey on timedependent statistical modelling of extreme waves and sea states. The focus is twofold: on statistical modelling of extreme waves and space-and time-dependent statistical modelling. The first part will consist of a literature review of statistical modelling of extreme waves and wave parameters, most notably on the modelling of extreme significant wave height. The second part will focus on statistical modelling of time-and space-dependent variables in a more general sense, and will focus on the methodology and models used also in other relevant application areas. It was found that limited effort has been put on developing statistical models for waves incorporating spatial and long-term temporal variability and it is suggested that model improvements could be achieved by adopting approaches from other application areas. In particular, Bayesian hierarchical space-time models were identified as promising tools for spatio-temporal modelling of extreme waves. Finally, a review of projections of future extreme wave climate is presented.

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Section: Short-term Stochastic Wave Modelsmentioning

confidence: 99%

Long-term time-dependent stochastic modelling of extreme waves

Vanem

2010

Stoch Environ Res Risk Assess

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“…The first one is the statistical description of the nonlinear wave field based on the Gaussian distribution of the sea surface in the linear approximation (central limit theorem due to the large number of independent spectral components). It should be mentioned that distribution of extremes in general is a hard mathematical task even for a Gaussian sea (Machado andRychlik 2003, Baxevani andRychlik 2006) with the exception of the narrow-band wind wave process, when the extremes are distributed by the Rayleigh law (Kharif et al 2009). It is known that nonlinearity leads to the correlation of the spectral components and non-Gaussianity of the wave field (Dysthe et al 2008).…”

Section: Introductionmentioning

confidence: 99%

Rogue waves in nonlinear hyperbolic systems (shallow-water framework)

Didenkulova

Pelinovsky

2011

Nonlinearity

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The formation of rogue waves is studied in the framework of nonlinear hyperbolic systems with an application to nonlinear shallow-water waves. It is shown that the nonlinearity in the random Riemann (travelling) wave, which manifests in the steeping of the face-front of the wave, does not lead to extreme wave formation. At the same time, the strongly nonlinear Riemann wave cannot be described by the Gaussian statistics for all components of the wave field. It is shown that rogue waves can appear in nonlinear hyperbolic systems only in the result of nonlinear wave-wave or/and wave-bottom interaction. Two special cases of wave interaction with a vertical wall (interaction of two Riemann waves propagating in opposite directions) and wave transformation in the basin of variable depth are studied in detail. Open problems of the rogue wave occurrence in nonlinear hyperbolic systems are discussed.

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“…the covariances r ww u0 (τ, u) and r wx u0 (τ, u) are respectively given by (14) and (15), and the variance σ u (w) 2 is given by (12 (0, u)), u ∈ R, as described in Section 3.1. The space wave model is always uniquely defined, in contrast to the time wave model, for which multiple solutions can exist.…”

Section: G Lindgren Where Y (T K + τ ) = (Y (T K + τ 1 ) (Ymentioning

confidence: 99%

“…This physically based model also allows a theoretical statistical description, at least for waves with second-order interaction; for examples, see [14] and [15].…”

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confidence: 99%

Slepian models for the stochastic shape of individual Lagrange sea waves

Lindgren

2006

Adv. Appl. Probab.

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Gaussian wave models have been successfully used since the early 1950s to describe the development of random sea waves, particularly as input to dynamic simulation of the safety of ships and offshore structures. A drawback of the Gaussian model is that it produces stochastically symmetric waves, which is an unrealistic feature and can lead to unconservative safety estimates. The Gaussian model describes the height of the sea surface at each point as a function of time and space. The Lagrange wave model describes the horizontal and vertical movements of individual water particles as functions of time and original location. This model is physically based, and a stochastic version has recently been advocated as a realistic model for asymmetric water waves. Since the stochastic Lagrange model treats both the vertical and the horizontal movements as Gaussian processes, it can be analysed using methods from the Gaussian theory. In this paper we present an analysis of the stochastic properties of the first-order stochastic Lagrange waves model, both as functions of time and as functions of space. A Slepian model for the description of the random shape of individual waves is also presented and analysed.

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Wave Statistics in Non-Linear Random Sea

Cited by 16 publications

References 18 publications

Long-term time-dependent stochastic modelling of extreme waves

Long-term time-dependent stochastic modelling of extreme waves

Rogue waves in nonlinear hyperbolic systems (shallow-water framework)

Slepian models for the stochastic shape of individual Lagrange sea waves

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