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.

Nonlinear Effects on Local Mechanics of Freak Waves

2015 ◽  
Author(s):  
Wataru Fujimoto ◽  
Takuji Waseda
Keyword(s):  
Limit State ◽  
Nonlinear Effects ◽  
Offshore Structures ◽  
Freak Waves ◽  
Freak Wave ◽  
Wave Kinematics ◽  
Longitudinal Asymmetry ◽  
Two Factors ◽  
Structural Impacts ◽  
Particle Velocities

The local properties of freak waves, such as geometry and particle velocities, are still to be investigated and are essential in the limit state design of ships or offshore structures. We have focused on two factors for this research. The first is nonlinearity higher than 3rd order since local steepness around freak waves will be large. The 4th order nonlinearity deforms a perturbed regular wave like a crescent and also causes a longitudinal asymmetry that means that the shape of the wave is asymmetrical in the propagation direction. The second is higher wavenumber components that will increase particle velocities. We tried to research the effects of these two factors on freak waves with Higher Order Spectral Method. Consequently, a crescent shape and longitudinal asymmetry in freak wave shape were found. In addition, higher wavenumber components increased the maximum horizontal velocity of freak waves significantly. These results show that the 4th order nonlinearity and higher wavenumber components are important for local freak wave kinematics, as well as for determining structural impacts, the motion of floating objects, and wave breaking.

scholarly journals Localized Coherence of Freak Waves

2016 ◽  
Author(s):  
Arnida L. Latifah ◽  
E. van Groesen
Keyword(s):  
Time Signal ◽  
Wave Group ◽  
Freak Waves ◽  
Freak Wave ◽  
Irregular Wave ◽  
Thunder Storm ◽  
Local Coherence ◽  
Wavelet Transform Analysis ◽  
Storm Condition ◽  
Energy Convergence

Abstract. This paper investigates in detail a possible mechanism of energy convergence leading to freak waves. We give examples of a freak wave as a (weak) pseudo-maximal wave to illustrate the importance of phase coherence. Given a time signal at a certain position, we identify parts of the time signal with successive high amplitudes, so-called group events, that may lead to a freak wave using wavelet transform analysis. The local coherence of the critical group event is measured by its time spreading of the most energetic waves. Four types of signals have been investigated; dispersive focussing, normal sea condition, thunder storm condition, and an experimental irregular wave. In all cases presented in this paper, it is shown that a high correlation exists between the local coherence and the appearance of a freak wave. This makes it plausible that freak waves can be developed by local interactions of waves in a wave group and that the effect of waves that are not in the immediate vicinity is minimal. This indicates that a local coherence mechanism within a wave group can be one mechanism that leads to the appearance of a freak wave.

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

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.

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.

Freak Wave Events Within the Second Order Wave Model

2004 ◽  
Author(s):  
Elzbieta M. Bitner-Gregersen ◽  
O̸istein Hagen
Keyword(s):  
Wave Model ◽  
Wave Theory ◽  
Rogue Waves ◽  
Offshore Structures ◽  
Second Order ◽  
Short Term ◽  
Freak Waves ◽  
Freak Wave ◽  
Offshore Industry

Recently significant interest has been paid to abnormal waves, often called rogue waves or freak waves. These waves represent operational risks to ship and offshore structures, and are likely to be responsible for a number of accidents. As shown by several authors, in ‘the second order world’ the freak waves are pretty rare events. The present study focuses on statistical properties of freak waves. The analyses are based on second order time domain simulations, short term distributions for crest statistics obtained from the literature, and long term field data. Time series of wave elevations are generated using the Pierson-Moskowitz, JONSWAP and two-peak Torsethaugen frequency spectrum for long-crested seas and deep water. Effects of combined seas (swell and wind sea) on wave statistics are discussed. Assuming 2nd order wave theory, the short term and long term probability of occurrence of a freak wave is estimated. The difference between a “freak wave” and a “dangerous wave” is pointed out. Finally, 100 year and 10000 year crest events obtained by analysis procedures used in the offshore industry are discussed in relation to freak waves.

Reproduction of Freak Waves Using Variational Data Assimilation and Observation

2018 ◽  
Author(s):  
Wataru Fujimoto ◽  
Takuji Waseda
Keyword(s):  
Data Assimilation ◽  
Variational Method ◽  
Wave Field ◽  
Wave Spectrum ◽  
Offshore Structures ◽  
Estimation Accuracy ◽  
Wave Impact ◽  
Freak Waves ◽  
Freak Wave ◽  
Squared Error

This study proposes ideas to reproduce freak waves from observational data. The reproduced data will apply to investigations on freak wave impact to offshore structures. Four-dimensional variational method (4DVAR) was used for the freak wave reproduction. Under a dynamical constraint, 4DVAR minimizes the squared error between observation and model prediction by adjusting the initial condition iteratively. This study utilizes the Higher Order Spectral Method (HOSM) to predict the nonlinear wave evolution, which is essential for freak wave generation. Information on wave spectrum estimated beforehand by a wave model is also employed to stabilize the reproduction. To increase convergence speed with fewer efforts of coding, a type of ensemble-based variational method (a4dVar) was adopted. The a4dVar performs perturbed ensemble simulations to evaluate the gradient of the squared error and is easy to parallelize and implement. This paper conducted twin experiments of HOSM+a4dVar data assimilation. HOSM model generated the true state of the uni-directional wave field, and the spatiotemporal wave field was reconstructed from time series of one virtual wave gauge located in the model. It is assumed that the virtual wave gauge detected a freak wave. The estimation accuracy of linear estimation and HOSM estimation were compared.

scholarly journals Localized coherence of freak waves

2016 ◽  
Vol 23 (5) ◽  
pp. 341-359 ◽  
Author(s):  
Arnida L. Latifah ◽  
E. van Groesen
Keyword(s):  
Wavelet Transform ◽  
Critical Group ◽  
Time Signal ◽  
Wave Group ◽  
Freak Waves ◽  
Freak Wave ◽  
Irregular Wave ◽  
Local Coherence ◽  
Wavelet Transform Analysis ◽  
Energy Convergence

Abstract. This paper investigates in detail a possible mechanism of energy convergence leading to freak waves. We give examples of a freak wave as a (weak) pseudo-maximal wave to illustrate the importance of phase coherence. Given a time signal at a certain position, we identify parts of the time signal with successive high amplitudes, so-called group events, that may lead to a freak wave using wavelet transform analysis. The local coherence of the critical group event is measured by its time spreading of the most energetic waves. Four types of signals have been investigated: dispersive focusing, normal sea condition, thunderstorm condition and an experimental irregular wave. In all cases presented in this paper, it is shown that a high correlation exists between the local coherence and the appearance of a freak wave. This makes it plausible that freak waves can be developed by local interactions of waves in a wave group and that the effect of waves that are not in the immediate vicinity is minimal. This indicates that a local coherence mechanism within a wave group can be one mechanism that leads to the appearance of a freak wave.

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