scholarly journals ON THE PROBABILITY DISTRIBUTION OF FREAK WAVES IN FINITE WATER DEPTH

2012 ◽  
Vol 1 (33) ◽  
pp. 13
Author(s):  
Kyungmo Ahn ◽  
Sun-Kyung Kim ◽  
Se-Hyun Cheon
Keyword(s):  
Probability Distribution ◽  
Wave Height ◽  
Distribution Functions ◽  
Occurrence Probability ◽  
Extreme Waves ◽  
Wave Interactions ◽  
Freak Waves ◽  
Freak Wave ◽  
Wave Data ◽  
Finite Water Depth

This paper presents the occurrence probability of freak waves based on the analysis of extensive wave data collected during ARSLOE project. It is suggested to use the probability distribution of extreme waves heights as a possible means of defining the freak wave criteria instead of conventional definition which is the wave height greater than the twice of the significant wave height. Analysis of wave data provided such finding as 1) threshold tolerance of 0.2 m is recommended for the discrimination of the false wave height due to noise, 2) no supportive evidence on the linear relationship between the occurrence probability of freak waves and the kurtosis of surface elevation 3) nonlinear wave-wave interactions is not thh primary cause of the generation of freak waves 4) the occurrence of freak waves does not depend on the wave period 5) probability density function of extreme waves can be used to predict the occurrence probability of freak waves. Three different distribution functions of extreme wave height by Rayleigh, Ahn, and Mori were compared for the analysis of freak waves.

Non-Gaussian Extreme Waves in the Central North Sea

1997 ◽  
Vol 119 (3) ◽  
pp. 146-150 ◽  
Author(s):  
J. Skourup ◽  
N.-E. O. Hansen ◽  
K. K. Andreasen
Keyword(s):  
Wave Height ◽  
North Sea ◽  
Upper Bound ◽  
Wave Crest ◽  
Extreme Waves ◽  
Freak Waves ◽  
Freak Wave ◽  
Wave Trains ◽  
Central North Sea ◽  
Crest Height

The area of the Central North Sea is notorious for the occurrence of very high waves in certain wave trains. The short-term distribution of these wave trains includes waves which are far steeper than predicted by the Rayleigh distribution. Such waves are often termed “extreme waves” or “freak waves.” An analysis of the extreme statistical properties of these waves has been made. The analysis is based on more than 12 yr of wave records from the Mærsk Olie og Gas AS operated Gorm Field which is located in the Danish sector of the Central North Sea. From the wave recordings more than 400 freak wave candidates were found. The ratio between the extreme crest height and the significant wave height (20-min value) has been found to be about 1.8, and the ratio between extreme crest height and extreme wave height has been found to be 0.69. The latter ratio is clearly outside the range of Gaussian waves, and it is higher than the maximum value for steep nonlinear long-crested waves, thus indicating that freak waves are not of a permanent form, and probably of short-crested nature. The extreme statistical distribution is represented by a Weibull distribution with an upper bound, where the upper bound is the value for a depth-limited breaking wave. Based on the measured data, a procedure for determining the freak wave crest height with a given return period is proposed. A sensitivity analysis of the extreme value of the crest height is also made.

scholarly journals Probability Distribution Functions of Freak Waves: Nonlinear Versus Linear Model

2016 ◽  
Vol 137 (2) ◽  
pp. 189-198 ◽  
Author(s):  
Alexander I. Dyachenko ◽  
Dmitriy I. Kachulin ◽  
Vladimir E. Zakharov
Keyword(s):  
Probability Distribution ◽  
Linear Model ◽  
Distribution Functions ◽  
Freak Waves ◽  
Probability Distribution Functions

Freak wave statistics on collinear currents

2009 ◽  
Vol 637 ◽  
pp. 267-284 ◽  
Author(s):  
KARINA B. HJELMERVIK ◽  
KARSTEN TRULSEN
Keyword(s):  
Wave Height ◽  
Significant Wave Height ◽  
Constant Current ◽  
Local Criterion ◽  
Freak Waves ◽  
Freak Wave ◽  
Significant Wave ◽  
Wave Statistics ◽  
Global Criterion ◽  
Wave Distribution

Linear refraction of waves on inhomogeneous current is known to provoke extreme waves. We investigate the effect of nonlinearity on this phenomenon, with respect to the variation of significant wave height, kurtosis and occurrence of freak waves. Monte Carlo simulations are performed employing a modified nonlinear Schrödinger equation that includes the effects of a prescribed non-potential current. We recommend that freak waves should be defined by a local criterion according to the wave distribution at each location of constant current, not by a global criterion that is either averaged over, or insensitive to, inhomogeneities of the current. Nonlinearity can reduce the modulation of significant wave height. Depending on the configuration of current and waves, the kurtosis and probability of freak waves can either grow or decrease when the wave height increases due to linear refraction. At the centre of an opposing current jet where waves are known to become large, we find that freak waves should be more rare than in the open ocean away from currents. The largest amount of freak waves on an opposing current jet is found at the jet sides where the significant wave height is small.

scholarly journals 3-D HOS simulations of extreme waves in open seas

2007 ◽  
Vol 7 (1) ◽  
pp. 109-122 ◽  
Author(s):  
G. Ducrozet ◽  
F. Bonnefoy ◽  
D. Le Touzé ◽  
P. Ferrant
Keyword(s):  
Wave Spectrum ◽  
Original Study ◽  
Test Cases ◽  
Extreme Waves ◽  
Extreme Wave ◽  
Freak Waves ◽  
Freak Wave ◽  
Directional Spectrum ◽  
Long Time ◽  
Directional Wave

Abstract. In the present paper we propose a method for studying extreme-wave appearance based on the Higher-Order Spectral (HOS) technique proposed by West et al. (1987) and Dommermuth and Yue (1987). The enhanced HOS model we use is presented and validated on test cases. Investigations of freak-wave events appearing within long-time evolutions of 2-D and 3-D wavefields in open seas are then realized, and the results are discussed. Such events are obtained in our periodic-domain HOS model by using different kinds of configurations: either i) we impose an initial 3-D directional spectrum with the phases adjusted so as to form a focused forced event after a while, or ii) we let 2-D and 3-D wavefields defined by a directional wave spectrum evolve up to the natural appearance of freak waves. Finally, we investigate the influence of directionality on extreme wave events with an original study of the 3-D shape of the detected freak waves.

The Relationship Between the Shape of Freak Waves and Nonlinear Wave Interactions

2016 ◽  
Author(s):  
Wataru Fujimoto ◽  
Takuji Waseda
Keyword(s):  
Limit State ◽  
Offshore Structures ◽  
Class I ◽  
Finite Width ◽  
Wave Interactions ◽  
Freak Waves ◽  
Freak Wave ◽  
Irregular Wave ◽  
The Relationship ◽  
Different Order

The local shapes of freak waves are essential to estimate responses of ships or offshore structures by freak waves for limit state design or maritime accident survey. It is known that freak waves deform like a crescent and their trough depth become asymmetric in directional and irregular wave fields. Meanwhile, Class I & II instabilities also affect wave shape. We discussed how those instabilities affect the geometry of freak waves, using Higher Order Spectrum Method (HOSM) which is a fast simulator of water wave. This paper investigated the relationship between Class I & II instabilities and the nonlinear order of HOSM to separate the effects of the different order nonlinear instabilities on freak waves. This investigation and freak wave simulations by HOSM clarified that four-wave Class I instability with finite width wave spectra affected both the crescent deformation and the asymmetry. The results showed that Class II instability effects to the freak wave shapes were not significant.

scholarly journals On Kurtosis and Occurrence Probability of Freak Waves

2006 ◽  
Vol 36 (7) ◽  
pp. 1471-1483 ◽  
Author(s):  
Nobuhito Mori ◽  
Peter A. E. M. Janssen
Keyword(s):  
Time Series ◽  
Field Data ◽  
Wave Theory ◽  
Fixed Number ◽  
Occurrence Probability ◽  
Freak Waves ◽  
Freak Wave ◽  
Amplification Ratio ◽  
Gaussian Theory ◽  
Non Gaussian

Abstract Based on a weakly non-Gaussian theory, the occurrence probability of freak waves is formulated in terms of the number of waves in a time series and the surface elevation kurtosis. Finite kurtosis gives rise to a significant enhancement of freak wave generation in comparison with the linear narrowbanded wave theory. For a fixed number of waves, the estimated amplification ratio of freak wave occurrence due to the deviation from the Gaussian theory is 50%–300%. The results of the theory are compared with laboratory and field data.

scholarly journals FREAK WAVE AND WEATHER CONDITION

2011 ◽  
Vol 1 (32) ◽  
pp. 70
Author(s):  
Nobuhito Mori ◽  
Hajime Mase ◽  
Tomohiro Yasuda
Keyword(s):  
Numerical Simulations ◽  
Weather Condition ◽  
The Other ◽  
Surface Elevation ◽  
Fourth Quadrant ◽  
Wave Interactions ◽  
Freak Waves ◽  
Freak Wave

The kurtosis of the surface elevation, Benjamin-Feir Index (BFI) and directional spread are measures of nonlinear four-wave interactions and freak waves. The dependence of kurtosis, BFI and directional spread under typhoon conditions are examined by numerical simulations. The BFI is significantly large in the fourth quadrant of the typhoon while the directional spread is small in the fourth quadrant. It was found that the potentially possible area of freak wave occurrence is the fourth quadrant of the typhoon rather than the other quadrants.

scholarly journals Dynamic analysis of a tension leg platform under extreme waves

2013 ◽  
Vol 10 (1) ◽  
pp. 59-68 ◽  
Author(s):  
Srinivasan Chandrasekaran ◽  
Koshti Yuvraj
Keyword(s):  
Wave Structure ◽  
Wave Model ◽  
Offshore Structures ◽  
Extreme Waves ◽  
Sea State ◽  
Freak Waves ◽  
Freak Wave ◽  
Offshore Installations ◽  
Wave Directionality ◽  
Type Response

Recent observations of the sea state that result in the undesirable events confirm the presence of extreme waves like freak waves, which is capable of causing irreparable damages to offshore installations and (or) create inoperable conditions to the crew on board. Knowledge on the extreme wave environment and the related wave-structure interaction are required for safer design of deep-water offshore structures. In the current study, typical long crested extreme waves namely:  i) New Year wave at offshore Norway; and ii) Freak wave at North Sea are simulated using the combined wave model. Dynamic response of the Tension Leg Platforms (TLP) under these extreme waves is carried out for different wave approach angles. Based on the analytical studies cared out, it is seen that the TLPs are sensitive to the wave directionality when encountered by such extreme waves; ringing type response is developed in TLPs which could result in tether pull out.DOI: http://dx.doi.org/10.3329/jname.v10i1.14518

Plain Interpretation of Freak Waves Phenomenon

2018 ◽  
Author(s):  
Dmitry Chalikov ◽  
Alexander V. Babanin
Keyword(s):  
Nonlinear Models ◽  
Modulational Instability ◽  
Wave Interactions ◽  
Freak Waves ◽  
Freak Wave ◽  
One Dimensional ◽  
Linear Waves ◽  
Instability Theory ◽  
Wave Trains ◽  
Integral Probability

An extremely large (‘freak’) wave is a typical though quite a rare phenomenon observed in the sea. Special theories (for example, the modulational instability theory) were developed to explain the mechanics and appearance of freak waves as a result of nonlinear wave-wave interactions. This paper demonstrates that freak wave appearance can be also explained by superposition of linear modes with a realistic spectrum. The integral probability of trough-to-crest waves is calculated by two methods: the first one is based on the results of a numerical simulation of wave field evolution, performed with one-dimensional and two-dimensional nonlinear models. The second method is based on the calculation of the same probability over ensembles of wave fields, constructed as a superposition of linear waves with random phases and a spectrum similar to that used in nonlinear simulations. It is shown that the integral probabilities for nonlinear and linear cases are of the same order of values. One-dimensional model was used for performing thousands of exact short-term simulations of evolution of two superposed wave trains with different steepness and wavenumbers to investigate the effect of wave crests merging. The nonlinear sharpening of merging crests is demonstrated. It is suggested that such effect may be responsible for appearance of typical sharp crests of surface waves, as well as for the wave breaking.

EXCITATION OF FREAK WAVE BY NATURAL OSCILLATIONS OF THE WATER BODY

2021 ◽  
pp. 106-114
Author(s):  
P. V. Anakhov
Keyword(s):  
Spatial Structure ◽  
Linear Theory ◽  
Water Body ◽  
Standing Waves ◽  
Dam Break ◽  
Extreme Waves ◽  
Natural Oscillations ◽  
Freak Waves ◽  
Freak Wave ◽  
Fixed Period

In linear theory the formation of extreme waves their existence is interpreted as a local superposition of surface monochromatic waves. Natural water areas are resonators that have their own set of natural oscillations – standing waves of stable spatial structure and fixed period. In the spectra of waves of many water bodies of World Ocean observed double high waves, this is explained by the tidal-seiche resonance. During a storm, the energy of natural oscillations increases ten times the background energy, during a tsunami it can increase up to three orders of magnitude. Examples of the effects of natural oscillations on the coast are given, and it is reported about the increased probability of the occurrence on the coast freak waves. Additionally, it is noted that natural oscillations in water mass are a normal state for any body of water at any time of its existence. The corresponding indices of the water fluctuations of the water basins are given. The events of extreme waves during the accidents at DniproHES (Zaporizhia) on August 18, 1941, and the Kurenivsky dam (Kyiv) on March 13, 1961, are presented. The excitement of the freak wave can be interpreted as enhancing the natural oscillations of the water basin, represented by standing waves of stable spatial structure, fixed period and high probability of waves in the water body. This does not contradict the linear theory of the resonant formation of abnormally high waves. The purpose of the article is to investigate possible sources of the excitement of freak waves, the results are proposed to be implemented in the development of countermeasures to the destructive process. However, the waves carry out both destructive and creative work. A task is presented, which involves the development of measures to stimulate extreme waves. This will increase electricity generation. Affiliation of dam-break waves to freak waves can be doubtful. However, they formally correspond to the classical condition of double exceeding the significant wave height. Most water basins are integral anthropogenic sites. The variability of both natural and anthropogenic environments forces the overriding of systematization and definition. It is proposed to attribute extreme waves of dam-break waves to freak waves.

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