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 Five-Wave Resonances in Deep Water Gravity Waves: Integrability, Numerical Simulations and Experiments

Fluids ◽  
2021 ◽  
Vol 6 (6) ◽  
pp. 205
Author(s):  
Dan Lucas ◽  
Marc Perlin ◽  
Dian-Yong Liu ◽  
Shane Walsh ◽  
Rossen Ivanov ◽  
...  
Keyword(s):  
Normal Form ◽  
Numerical Simulations ◽  
Gravity Waves ◽  
Deep Water ◽  
Plane Waves ◽  
Surface Elevation ◽  
Wave Interactions ◽  
Frequency Space ◽  
Target Mode ◽  
The Hilbert Transform

In this work we consider the problem of finding the simplest arrangement of resonant deep-water gravity waves in one-dimensional propagation, from three perspectives: Theoretical, numerical and experimental. Theoretically this requires using a normal-form Hamiltonian that focuses on 5-wave resonances. The simplest arrangement is based on a triad of wavevectors K1+K2=K3 (satisfying specific ratios) along with their negatives, corresponding to a scenario of encountering wavepackets, amenable to experiments and numerical simulations. The normal-form equations for these encountering waves in resonance are shown to be non-integrable, but they admit an integrable reduction in a symmetric configuration. Numerical simulations of the governing equations in natural variables using pseudospectral methods require the inclusion of up to 6-wave interactions, which imposes a strong dealiasing cut-off in order to properly resolve the evolving waves. We study the resonance numerically by looking at a target mode in the base triad and showing that the energy transfer to this mode is more efficient when the system is close to satisfying the resonant conditions. We first look at encountering plane waves with base frequencies in the range 1.32–2.35 Hz and steepnesses below 0.1, and show that the time evolution of the target mode’s energy is dramatically changed at the resonance. We then look at a scenario that is closer to experiments: Encountering wavepackets in a 400-m long numerical tank, where the interaction time is reduced with respect to the plane-wave case but the resonance is still observed; by mimicking a probe measurement of surface elevation we obtain efficiencies of up to 10% in frequency space after including near-resonant contributions. Finally, we perform preliminary experiments of encountering wavepackets in a 35-m long tank, which seem to show that the resonance exists physically. The measured efficiencies via probe measurements of surface elevation are relatively small, indicating that a finer search is needed along with longer wave flumes with much larger amplitudes and lower frequency waves. A further analysis of phases generated from probe data via the analytic signal approach (using the Hilbert transform) shows a strong triad phase synchronisation at the resonance, thus providing independent experimental evidence of the resonance.

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 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.

scholarly journals APPLYING THE WAVELET TRANSFORM TO STUDY THE FEATURES OF FREAK WAVES

2011 ◽  
Vol 1 (32) ◽  
pp. 69 ◽  
Author(s):  
Li-Chung Wu ◽  
Beng-Chun Lee ◽  
Chia Chuen Kao ◽  
Dong-Jiing Doong ◽  
Chih-Chiang Chang
Keyword(s):  
Wavelet Transform ◽  
Wave Energy ◽  
The Other ◽  
Freak Waves ◽  
Energy Characteristics ◽  
Freak Wave

The issues of freak waves are more and more popular since the late 1980s. This study tries to use the wavelet scalogram of freak wave records to investigate the energy characteristics during the occurrence of the freak waves. Through the analysis of the wave energy and phase, it is found that as freak waves occur, the component waves will lead to constructive superposition due to similar phases. The wavelet scalogram provides the other idea to explain the feature of freak waves.

On the kinetics of Hadamard-type fractional differential systems

2020 ◽  
Vol 23 (2) ◽  
pp. 553-570 ◽  
Author(s):  
Li Ma
Keyword(s):  
Differential Operator ◽  
Numerical Simulations ◽  
Type Inequality ◽  
The Other ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Kinetics Of ◽  
Theoretical Results

AbstractThis paper is devoted to the investigation of the kinetics of Hadamard-type fractional differential systems (HTFDSs) in two aspects. On one hand, the nonexistence of non-trivial periodic solutions for general HTFDSs, which are considered in some functional spaces, is proved and the corresponding eigenfunction of Hadamard-type fractional differential operator is also discussed. On the other hand, by the generalized Gronwall-type inequality, we estimate the bound of the Lyapunov exponents for HTFDSs. In addition, numerical simulations are addressed to verify the obtained theoretical results.

Localized interaction solution and its dynamics of the extended Hirota–Satsuma–Ito equation

2021 ◽  
pp. 2150313
Author(s):  
Jian-Ping Yu ◽  
Wen-Xiu Ma ◽  
Chaudry Masood Khalique ◽  
Yong-Li Sun
Keyword(s):  
Numerical Simulations ◽  
Rogue Wave ◽  
The Other ◽  
Hirota Bilinear Method ◽  
Bilinear Method ◽  
Interaction Solutions ◽  
Physical Phenomena ◽  
Wave Phenomena ◽  
Hirota Bilinear ◽  
Ito Equation

In this research, we will introduce and study the localized interaction solutions and th eir dynamics of the extended Hirota–Satsuma–Ito equation (HSIe), which plays a key role in studying certain complex physical phenomena. By using the Hirota bilinear method, the lump-type solutions will be firstly constructed, which are almost rationally localized in all spatial directions. Then, three kinds of localized interaction solutions will be obtained, respectively. In order to study the dynamic behaviors, numerical simulations are performed. Two interesting physical phenomena are found: one is the fission and fusion phenomena happening during the procedure of their collisions; the other is the rogue wave phenomena triggered by the interaction between a lump-type wave and a soliton wave.

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.

Multifidelity Recursive Cokriging for Dynamic Systems' Response Modification

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Luigi Bregant ◽  
Lucia Parussini ◽  
Valentino Pediroda
Keyword(s):  
Numerical Model ◽  
Numerical Simulations ◽  
Dynamic Systems ◽  
System Optimization ◽  
The Other ◽  
Experimental Measurements ◽  
Reciprocal Influence ◽  
Tests And Measurements ◽  
Invaluable Tool ◽  
Mixed Approach

In order to perform the accurate tuning of a machine and improve its performance to the requested tasks, the knowledge of the reciprocal influence among the system's parameters is of paramount importance to achieve the sought result with minimum effort and time. Numerical simulations are an invaluable tool to carry out the system optimization, but modeling limitations restrict the capabilities of this approach. On the other side, real tests and measurements are lengthy, expensive, and not always feasible. This is the reason why a mixed approach is presented in this work. The combination, through recursive cokriging, of low-fidelity, yet extensive, numerical model results, together with a limited number of highly accurate experimental measurements, allows to understand the dynamics of the machine in an extended and accurate way. The results of a controllable experiment are presented and the advantages and drawbacks of the proposed approach are also discussed.

The Stick Motion of a Harmonically Excited, Friction-Induced Oscillator on a Sinusoidally Traveling Surface

2006 ◽  
Author(s):  
Albert C. J. Luo ◽  
Brandon C. Gegg ◽  
Steve S. Suh
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Dry Friction ◽  
The Other ◽  
Linear Oscillator ◽  
Analytical Prediction ◽  
Nonlinear Friction ◽  
Friction Forces

In this paper, the methodology is presented through investigation of a periodically, forced linear oscillator with dry friction, resting on a traveling surface varying with time. The switching conditions for stick motions in non-smooth dynamical systems are obtained. From defined generic mappings, the corresponding criteria for the stick motions are presented through the force product conditions. The analytical prediction of the onset and vanishing of the stick motions is illustrated. Finally, numerical simulations of stick motions are carried out to verify the analytical prediction. The achieved force criteria can be applied to the other dynamical systems with nonlinear friction forces possessing a CO - discontinuity.

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