scholarly journals PROPERTIES OF FREAK WAVES INDUCED BY TWO KINDS OF NONLINEAR MECHANISMS

2012 ◽  
Vol 1 (33) ◽  
pp. 73
Author(s):  
Aifeng Tao ◽  
Jinhai Zheng ◽  
Botao Chen ◽  
Hui Li ◽  
Ji Peng
Keyword(s):  
Modulation Instability ◽  
Stokes Wave ◽  
Wave Spectra ◽  
Wave Group ◽  
Wave Interactions ◽  
Freak Waves ◽  
Kinematic Characteristics ◽  
Long Time ◽  
Wave Trains ◽  
Different Time Scales

We investigate the dynamic and kinematic characteristics of freak waves using a direct phase-resolved nonlinear numerical method. The focus is on the understanding of the effects of different nonlinear wave-wave interactions on freak waves development and characteristics in the evolution process of modulated Stokes wave trains. Long time simulations of modulated Stokes wave trains, with different parameters, are obtained. Based on these simulations, we find that there are different kinds of freak waves in different time scales due to two kinds of different nonlinear mechanisms. One is the modulation instability and another related to the wave group interaction. Both the dynamic and kinematic characteristics of the different kinds of freak waves are distinct. Occurrence of freak waves (especially of large height) is usually correlated with broadband wave spectra.

scholarly journals Nonlinear Evolution Equations for Broader Bandwidth Wave Packets in Crossing Sea States

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
S. Debsarma ◽  
S. Senapati ◽  
K. P. Das
Keyword(s):  
Growth Rate ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Modulational Instability ◽  
Wave Packets ◽  
Nonlinear Evolution Equations ◽  
Wave Spectra ◽  
Surface Gravity Wave ◽  
Freak Waves ◽  
Wave Trains

Two coupled nonlinear equations are derived describing the evolution of two broader bandwidth surface gravity wave packets propagating in two different directions in deep water. The equations, being derived for broader bandwidth wave packets, are applicable to more realistic ocean wave spectra in crossing sea states. The two coupled evolution equations derived here have been used to investigate the instability of two uniform wave trains propagating in two different directions. We have shown in figures the behaviour of the growth rate of instability of these uniform wave trains for unidirectional as well as for bidirectional perturbations. The figures drawn here confirm the fact that modulational instability in crossing sea states with broader bandwidth wave packets can lead to the formation of freak waves.

scholarly journals The Effects on Water Particle Velocity of Wave Peaks Induced by Nonlinearity under Different Time Scales

2021 ◽  
Vol 9 (7) ◽  
pp. 748
Author(s):  
Aifeng Tao ◽  
Shuya Xie ◽  
Di Wu ◽  
Jun Fan ◽  
Yini Yang
Keyword(s):  
Particle Velocity ◽  
Modulation Instability ◽  
Wave Train ◽  
Quadratic Function ◽  
Offshore Structures ◽  
Stokes Wave ◽  
Wave Load ◽  
Freak Waves ◽  
Water Particle ◽  
Generation Mechanisms

The water particle velocity of the wave peaks is closely related to the wave load borne by offshore structures. It is of great value for marine disaster prevention to study the water particle velocity of nonlinear extreme waves represented by Freak waves. This study applies the High-order Spectral Method (HOS) numerical model to analyze the characteristics and influencing factors of the water particle velocity of Freak wave peak with two different generation mechanisms under the initial condition of a weakly modulated Stokes wave train. Our results show that the water particle velocity of the wave peak increases linearly with wave height and initial wave steepness in the evolution stage of modulation instability. While in the later stage, the relationship becomes exponential. Under the condition of similar wave heights, the deformation degrees of Freak waves with different generation mechanisms are distinct, the deformation degree of modulation instability stage is smaller than that of the later stage. The water particle velocity of the wave peaks increases with the deformation degrees. Furthermore, the correlation between wave peak height and water particle velocity is a quadratic function. This provides a theoretical basis for further understanding of nonlinear waves and the prediction of marine disasters.

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 Hydrological response to different time scales of climatological drought: an evaluation of the Standardized Precipitation Index in a mountainous Mediterranean basin

2005 ◽  
Vol 9 (5) ◽  
pp. 523-533 ◽  
Author(s):  
S. M. Vicente-Serrano ◽  
J. I. López-Moreno
Keyword(s):  
Time Scales ◽  
Hydrological Cycle ◽  
Standardized Precipitation Index ◽  
Precipitation Index ◽  
Drought Indices ◽  
Long Time ◽  
The Standardized Precipitation Index ◽  
Hydrological Droughts ◽  
Different Time Scales

Abstract. At present, the Standardized Precipitation Index (SPI) is the most widely used drought index to provide good estimations about the intensity, magnitude and spatial extent of droughts. The main advantage of the SPI in comparison with other indices is the fact that the SPI enables both determination of drought conditions at different time scales and monitoring of different drought types. It is widely accepted that SPI time scales affect different sub-systems in the hydrological cycle due to the fact that the response of the different water usable sources to precipitation shortages can be very different. The long time scales of SPI are related to hydrological droughts (river flows and reservoir storages). Nevertheless, few analyses empirically verify these statements or the usefulness of the SPI time scales to monitor drought. In this paper, the SPI at different time scales is compared with surface hydrological variables in a big closed basin located in the central Spanish Pyrenees. We provide evidence about the way in which the longer (>12 months) SPI time scales may not be useful for drought quantification in this area. In general, the surface flows respond to short SPI time scales whereas the reservoir storages respond to longer time scales (7–10 months). Nevertheless, important seasonal differences can be identified in the SPI-usable water sources relationships. This suggests that it is necessary to test the drought indices and time scales in relation to their usefulness for monitoring different drought types under different environmental conditions and water demand situations.

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.

ANALYTICAL SOLUTIONS OF COUPLED NONLINEAR SCHRODINGER EQUATIONS FOR TWO NON LINEARLY INTERACTING STOKES WAVE TRAINS OVER INFINITE DEPTH

2021 ◽  
Vol 10 (3) ◽  
pp. 1137-1144
Author(s):  
S. Manna ◽  
A.K. Dhar
Keyword(s):  
Analytical Solutions ◽  
Nonlinear Schrödinger Equations ◽  
Stokes Wave ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Coupled Nonlinear Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Wave Trains ◽  
Coupled Nonlinear Schrodinger Equations

An attempt to find the exact analytical solutions of the two coupled nonlinear Schrodinger equations of 3rd order occurring from the oblique interaction of two capillary gravity wave trains in the case of crossing sea states in deep water is the main premise of the present paper. The solutions obtained here are due to the nonlinear interaction of two Stokes wave trains in one spatial dimension. Graphs have been plotted to investigate the influence of capillarity on the amplitudes of such wave trains. From 3D figures it has been observed that the capillarity has diminishing influence on the amplitudes of the either wave packet.

scholarly journals On the existence of steady-state resonant waves in experiments

2014 ◽  
Vol 763 ◽  
pp. 1-23 ◽  
Author(s):  
Z. Liu ◽  
D. L. Xu ◽  
J. Li ◽  
T. Peng ◽  
A. Alsaedi ◽  
...  
Keyword(s):  
Experimental Investigation ◽  
Steady State ◽  
Multiple Solutions ◽  
Wave Spectra ◽  
Ocean Engineering ◽  
System Error ◽  
Exact Resonance ◽  
Wave Trains ◽  
Theoretical Results ◽  
Resonant Waves

AbstractThis paper describes an experimental investigation of steady-state resonant waves. Several co-propagating short-crested wave trains are generated in a basin at the State Key Laboratory of Ocean Engineering (SKLOE) in Shanghai, and the wavefields are measured and analysed both along and normal to the direction of propagation. These steady-state resonant waves are first calculated theoretically under the exact resonance criterion with sufficiently high nonlinearity, and then are generated in the basin by means of the main wave components that contain at least 95 % of the wave energy. The steady-state wave spectra are quantitatively observed within the inherent system error of the basin and identified by means of a contrasting experiment. Both symmetrical and anti-symmetrical steady-state resonant waves are observed and the experimental and theoretical results show excellent agreement. These results offer the first experimental evidence of the existence of steady-state resonant waves with multiple solutions.

The Consistence Between the Stokes Wave Theory and General Wave Theory

2009 ◽  
Vol 25 (3) ◽  
pp. N17-N20 ◽  
Author(s):  
C.-M. Liu ◽  
H.-H. Hwung ◽  
R.-Y. Yang
Keyword(s):  
Wave Theory ◽  
The Self ◽  
The Other ◽  
Stokes Wave ◽  
First Order ◽  
General Wave ◽  
Wave Trains ◽  
Mathematical Equivalence ◽  
Nonlinear Solutions

AbstractThe consistence between the Stokes wave theory and general wave theory is examined in this study. As well known, the nonlinear terms of Stokes wave are generated by the self-interaction of first-order wave. On the other side, using the general wave theory one can also obtain the nonlinear solutions according to the interaction of n waves with the same amplitude, frequency and phase. It is found that the inconsistence between these two wave trains arises due to the subharmonic effects included in general wave theory but not considered in the Stokes theory. In conclusion, these two theories are substantially different unless the Bernoulli constants are properly chosen for mathematical equivalence.

Influence of Wave Group Characteristics on the Motion of a Semisubmersible in Freak Waves

2014 ◽  
Author(s):  
Yanfei Deng ◽  
Jianmin Yang ◽  
Longfei Xiao
Keyword(s):  
Time Lag ◽  
Ocean Waves ◽  
Offshore Structures ◽  
Hydrodynamic Performance ◽  
Wave Crest ◽  
Time Lags ◽  
Wave Group ◽  
Freak Waves ◽  
Motion Responses ◽  
Group Characteristics

In the last few decades, the hydrodynamic performance of offshore structures has been widely studied to ensure their safety as well as to achieve an economical design. However, an increasing number of reported accidents due to rough ocean waves call for in-depth investigations on the loads and motions of offshore structures, particularly the effect of freak waves. The aim of this paper is to determine the sea conditions that may cause the maximum motion responses of offshore structures, which have a significant effect on the loads of mooring systems because of their tight relationship. As a preliminary step, the response amplitude operators (RAOs) of a semisubmersible platform of 500 meters operating depth are obtained with the frequency-domain analysis method. Subsequently, a series of predetermined extreme wave sequences with different wave group characteristics, such as the maximum crest amplitude and the time lag between successive high waves, are adopted to calculate the hydrodynamic performance of the semisubmersible with mooring systems in time-domain. The paper shows that the maximum motion responses not only depend on the largest wave crest amplitude but also the time lags between successive giant waves. This paper will provide an important reference for future designs which could consider the most dangerous wave environment.

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