1. Introduction 2. Observation techniques 3. Description of ocean waves 4. Statistics 5. Linear wave theory (oceanic waters) 6. Waves in oceanic waters 7. Linear wave theory (coastal waters) 8. Waves in coastal waters 9. The SWAN wave model Appendices References Index.

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Waves in Oceanic and Coastal Waters

Earlier models of random wave transformation are reviewed in the first section. Then the transformation of waves, including dissipation due to breaking and bottom friction, is described by an energy flux balance model. The wave height pdf of all waves (broken and unbroken) is shown by the field data to be well described by the Rayleigh distribution everywhere. The observed distributions of breaking and broken wave heights are fitted to simple analytical forms, and breaking wave dissipation is calculated by using a periodic bore formulation. The energy flux equation is integrated to yield local values of Hrms as a function of offshore wave conditions. Both analytical and numerical models are developed. In the last section the models are compared with results from random wave experiments in the laboratory and from an extensive set of field measurements.

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Transformation of wave height distribution

http://personalpages.to.infn.it/~onorato/publications_files/2013_Onorato_etal_PhysRep.pdf

Rogue waves and their generating mechanisms in different physical contexts

Oceanic rogue waves are surface gravity waves whose wave heights are much larger than expected for the sea state. The common operational definition requires them to be at least twice as large as the significant wave height. In most circumstances, the properties of rogue waves and their probability of occurrence appear to be consistent with second-order random-wave theory. There are exceptions, although it is unclear whether these represent measurement errors or statistical flukes, or are caused by physical mechanisms not covered by the model. A clear deviation from second-order theory occurs in numerical simulations and wave-tank experiments, in which a higher frequency of occurrence of rogue waves is found in long-crested waves owing to a nonlinear instability.

Oceanic Rogue Waves

iii Foreword This is a tutorial for how to use the MATLAB toolbox WAFO for analysis and simulation of random waves and random fatigue. The toolbox consists of a number of MATLAB m-files together with executable routines from FORTRAN or C++ source, and it requires only a standard MATLAB setup, with no additional toolboxes. A main and unique feature of WAFO is the module of routines for computation of the exact statistical distributions of wave and cycle characteristics in a Gaussian wave or load process. The routines are described in a series of examples on wave data from sea surface measurements and other load sequences. There are also sections for fatigue analysis and for general extreme value analysis. Although the main applications at hand are from marine and reliability engineering, the routines are useful for many other applications of Gaussian and related stochastic processes. The routines are based on algorithms for extreme value and crossing analysis, developed over many years by the authors as well as many results available in the literature. References are given to the source of the algorithms whenever it is possible. These references are given in the MATLAB-code for all the routines and they are also listed in the last section of this tutorial. If the references are not used explicitly in the tutorial; it means that it is referred to in one of the MATLAB m-files. Besides the dedicated wave and fatigue analysis routines the toolbox contains many statistical simulation and estimation routines for general use, and it can therefore be used as a toolbox for statistical work. These routines are listed, but not explicitly explained in this tutorial. The present toolbox represents a considerable development of two earlier toolboxes, the FAT and WAT toolboxes, for fatigue and wave analysis, respectively. These toolboxes were both Version 1; therefore WAFO has been named Version 2. The routines in the tutorial are tested on WAFO-version 2.5, which was made available in beta-version in January 2009 and in a stable version in February 2011. The persons that take actively part in creating this tutorial are (in alphabetical order): Per v vi Many other people have contributed to our understanding of the problems dealt with in this text, first of all Professor Ross Leadbetter at the University of North Carolina at Chapel Hill and Professor Krzysztof Podgórski, Mathematical Statistics, Lund University. We would also like to particularly thank Michel …

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WAFO - A Matlab Toolbox For Analysis of Random Waves And Loads

Probabilistic description of nonlinear waves with a narrow-band spectrum is simplified to a form in which each realization of the surface displacement becomes an amplitude-modulated Stokes wave with a mean frequency and random phase. Under appropriate conditions this simplification provides a convenient yet rigorous means of describing nonlinear effects on sea surface properties in a semiclosed or closed form. In particular, it is shown that surface displacements are non-Gaussian and skewed, as was previously predicted by the Gram-Charlier approximation; that wave heights are Rayleigh distributed, just as in the linear case; and that crests are non-Rayleigh.

Narrow-band nonlinear sea waves

Wave-height distributions and nonlinear effects

We present a second-order stochastic model of weakly nonlinear waves and develop theoretical expressions for the expected shape of large surface displacements. The model also leads to an exact theoretical expression for the statistical distribution of large wave crests in a form that generalizes the Tayfun distribution (Tayfun, J. Geophys. Res., vol. 85, 1980, p. 1548). The generalized distribution depends on a steepness parameter given by μ = λ3/3, where λ3 represents the skewness coefficient of surface displacements. It converges to the Tayfun distribution in narrowband waves, where both distributions describe the crests of all waves well. In broadband waves, the generalized distribution represents the crests of large waves just as well whereas the Tayfun distribution appears as an upper bound and tends to overestimate them. However, the theoretical nature of the generalized distribution presents practical difficulties in oceanic applications. We circumvent these by adopting an appropriate approximation for the steepness parameter. Comparisons with wind-wave measurements from the North Sea suggest that this approximation allows both distributions to assume an identical form with which we can describe the distribution of large wave crests fairly accurately. The same comparisons also show that third-order nonlinear effects do not appear to have any discernable effect on the statistics of large surface displacements or wave crests.

On nonlinear wave groups and crest statistics

The description of linear random waves in the form of an amplitude-modulated carrier wave is known as narrow-band representation. Herewith, the theoretical basis of such a representation is examined in terms of integral properties of surface spectra and criteria governing the statistical and kinematic characteristics of the carrier wave. These considerations are then extended systematically to derive two narrow-band type representations for nonlinear waves. The nature of these representations and their statistical properties are discussed and compared with other models such as those proposed earlier by Tayfun (1980) and Huang et al. (1983).

On narrow‐band representation of ocean waves: 1. Theory

The statistical distribution of zero-crossing wave heights is considered within the context of a previous theory proposed by the writer some years ago. The underlying model, definitions, and assumptions are reexamined systematically to develop asymptotic approximations to the probability density, exceedance probability, and statistical moments of wave heights larger than the mean wave height. The asymptotic results have closed forms, and thus are easier to use in practical applications than the original theory, which requires numerical integration. Comparisons to empirical data are given to show that the present asymptotic theory produces the observed statistics of large wave heights faithfully to within 1%. Further, comparisons with other relevant theories also reveal that if one remains true to the theoretical definitions, then the present theory is the most accurate in predicting the exceedance distribution of large wave heights. Finally, the asymptotic theory is coupled with the statistics of wave periods to derive a theoretical expression for the joint distribution of large wave heights and associated periods. The predictive utility of this last result remains to be explored.

M. Aziz Tayfun

Papers

Narrow-band nonlinear sea waves

Wave-height distributions and nonlinear effects

On nonlinear wave groups and crest statistics

On narrow‐band representation of ocean waves: 1. Theory

Distribution of Large Wave Heights