Showing papers on "Rogue wave published in 2009"
TL;DR: In this article, a hierarchy of rational solutions of the nonlinear Schrodinger equation (NLSE) with increasing order and with progressively increasing amplitude is presented. And the authors apply the WANDT title to two objects: rogue waves in the ocean and rational solution of the NLSE.
1,036 citations
TL;DR: This work can elucidate the appearance of rogue waves in the deep ocean and can be applied to the observation of rogue light pulse waves in optical fibers.
Abstract: We present a method for finding the hierarchy of rational solutions of the self-focusing nonlinear Schrodinger equation and present explicit forms for these solutions from first to fourth order. We also explain their relation to the highest amplitude part of a field that starts with a plane wave perturbed by random small amplitude radiation waves. Our work can elucidate the appearance of rogue waves in the deep ocean and can be applied to the observation of rogue light pulse waves in optical fibers.
845 citations
TL;DR: In this article, the authors discuss the early history of the field of modulation instability in modern theory of nonlinear waves, and demonstrate how scientific demand resulted in independent and almost simultaneous publications by many different authors on modulation instability, a phenomenon resulting in a variety of non-linear processes such as envelope solitons, envelope shocks, freak waves, etc.
663 citations
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TL;DR: In this article, the existence of rogue waves in Bose-Einstein condensates either loaded into a parabolic trap or embedded in an optical lattice was shown to be possible.
Abstract: We predict the existence of rogue waves in Bose-Einstein condensates either loaded into a parabolic trap or embedded in an optical lattice. In the latter case, rogue waves can be observed in condensates with positive scattering length. They are immensely enhanced by the lattice. Local atomic density may increase up to tens times. We provide the initial conditions necessary for the experimental observation of the phenomenon. Numerical simulations illustrate the process of creation of rogue waves.
561 citations
Book•
12 Jan 2009
TL;DR: In this paper, the authors present deterministic and statistical approaches for studying the behavior of Rogue Waves in Waters of Infinite and Finite Depths and Shallow-Water Rogue Waves, respectively.
Abstract: Observation of Rogue Waves.- Deterministic and Statistical Approaches for Studying Rogue Waves.- Quasi-Linear Wave Focusing.- Rogue Waves in Waters of Infinite and Finite Depths.- Shallow-Water Rogue Waves.- Conclusion.
550 citations
TL;DR: In this article, a plane wave is modulated by relatively weak random waves, and it is shown that the peaks with highest amplitude of the resulting wave composition can be described in terms of exact solutions of the focusing nonlinear Schrrodinger equation in the form of the collision of Akhmediev breathers.
507 citations
TL;DR: In this article, the authors reported the financial rogue waves analytically in the nonlinear option pricing model due to Ivancevic, which is nonlinear wave alternative of the Black-Scholes model.
Abstract: The financial rogue waves are reported analytically in the nonlinear option pricing model due to Ivancevic, which is nonlinear wave alternative of the Black-Scholes model. These solutions may be used to describe the possible physical mechanisms for rogue wave phenomenon in financial markets and related fields.
310 citations
TL;DR: In this article, the authors propose initial conditions that facilitate the excitation of rogue waves, which is useful both in attempts to avoid them by seafarers and in generating highly energetic pulses in optical fibers.
Abstract: We propose initial conditions that could facilitate the excitation of rogue waves. Understanding the initial conditions that foster rogue waves could be useful both in attempts to avoid them by seafarers and in generating highly energetic pulses in optical fibers.
255 citations
TL;DR: The appearance of rogue waves is well known in oceanographic, optics, and cold-matter systems as mentioned in this paper, and there is even a possibility for the existence of atmospheric rogue waves.
Abstract: The appearance of rogue waves is well known in oceanographics, optics, and cold matter systems. Here we show a possibility for the existence of atmospheric rogue waves.
205 citations
TL;DR: In this article, the effect of various perturbations on the fundamental rational solution of the nonlinear Schrodinger equation (NLSE) was studied, and it was shown that the rational solution remains rational and localized in each direction, thus representing a modified rogue wave.
184 citations
TL;DR: In this paper, the wave climate off the Swedish west coast is discussed based on 8 years of wave data from 13 sites, nearshore and offshore, in the Skagerrak and Kattegat.
TL;DR: The intensity histograms obtained from spectrally filtering the supercontinuum exhibit the L-shaped characteristics typical of extreme-value phenomena on both the long-wa wavelength and short-wavelength edges of the spectrum owing to cross-phase modulation and soliton-dispersive wave coupling.
Abstract: We experimentally study the characteristics of optical rogue waves in supercontinuum generation in the femtosecond regime. Specifically, the intensity histograms obtained from spectrally filtering the supercontinuum exhibit the L-shaped characteristics typical of extreme-value phenomena on both the long-wavelength and short-wavelength edges of the spectrum owing to cross-phase modulation and soliton-dispersive wave coupling. Furthermore, the form of the histogram on the long-wavelength edge varies from L-shaped to quasi-Gaussian as wavelengths closer to the pump are included in the filtered measurements. Our observations are in agreement with numerical simulations.
TL;DR: In an array of nonlinear waveguides, a giant compression of the input beam can be achieved by exciting a rogue wave by determining the required input profile of the electric field.
Abstract: In an array of nonlinear waveguides, a giant compression of the input beam can be achieved by exciting a rogue wave Input field almost homogeneously distributed over hundreds of waveguides concentrates practically all the energy into a single waveguide at the output plane of the structure We determine the required input profile of the electric field to achieve this We illustrate the phenomenon by modeling the array by direct numerical simulations of the discrete nonlinear Schrodinger equation
TL;DR: In this article, a hindcast wave simulation, as realistically as possible, using an improved third-generation wave model driven by wind and current reanalysis products, was conducted to determine the sea state at the time of the incident.
Abstract: [1] On 23 June 2008, a fishing boat with 20 crewmembers onboard sank in reportedly moderate sea-state conditions in the Kuroshio Extension region east of Japan To determine the sea state at the time of the incident, we conducted a hindcast wave simulation, as realistically as possible, using an improved third-generation wave model driven by wind and current reanalysis products Our results indicated that at the time of the accident, the wave steepness increased and the spectral peakedness narrowed, creating a sea state favorable for freak wave occurrence due to quasi-resonance Detailed analyses of the spectral evolution revealed that nonlinear coupling of swell and windsea waves was the key to generating the narrow spectrum Under the influence of rising wind speed, the swell system grew exponentially at the expense of the windsea energy, and the bimodal crossing sea state transformed into a freakish unimodal sea
TL;DR: In this article, the authors experimentally observed optical rogue wave statistics during high power femtosecond pulse filamentation in air and characterized wavelength-dependent intensity fluctuations across 300 nm broadband filament spectra generated by pulses with several times the critical power for filamentation.
Abstract: We experimentally observed optical rogue wave statistics during high power femtosecond pulse filamentation in air. We characterized wavelength-dependent intensity fluctuations across 300 nm broadband filament spectra generated by pulses with several times the critical power for filamentation. We show how the statistics vary from a near-Gaussian distribution in the vicinity of the pump to a long tailed “L-shaped” distribution at the short wavelength and long wavelength edges. The results are interpreted in terms of pump noise transfer via self-phase modulation.
TL;DR: In this article, the rogue wave energy statistics were shown to follow a strongly non-Gaussian L-shaped value probability distribution, and experimental results were in good agreement with numerical simulations.
Abstract: Characterisation of optical rogue wave fluctuations in supercontinuum generation is reported using a gigahertz-bandwidth detection setup to directly measure the pulse energy statistics. The rogue wave energy statistics are shown to follow a strongly non-Gaussian L-shaped value probability distribution, and experimental results are in good agreement with numerical simulations.
TL;DR: In this paper, the truncated potential Euler equations are used to address the combined effect of directionality and finite depth on the statistical properties of surface gravity waves; only relative water depth greater than 0.8 is considered.
Abstract: . It is well established that third-order nonlinearity produces a strong deviation from Gaussian statistics in water of infinite depth, provided the wave field is long crested, narrow banded and sufficiently steep. A reduction of third-order effects is however expected when the wave energy is distributed on a wide range of directions. In water of arbitrary depth, on the other hand, third-order effects tend to be suppressed by finite depth effects if waves are long crested. Numerical simulations of the truncated potential Euler equations are here used to address the combined effect of directionality and finite depth on the statistical properties of surface gravity waves; only relative water depth kh greater than 0.8 are here considered. Results show that random directional wave fields in intermediate water depths, kh=O(1), weakly deviate from Gaussian statistics independently of the degree of directional spreading of the wave energy.
Abstract: 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 Schrodinger 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.
TL;DR: In this paper, the long-term evolution of random wind waves is studied by direct numerical simulation within the framework of the Zakharov equation, where the emphasis is on kurtosis as a single characteristics of field departure from Gaussianity.
Abstract: [1] Long-term evolution of random wind waves is studied by direct numerical simulation within the framework of the Zakharov equation. The emphasis is on kurtosis as a single characteristics of field departure from Gaussianity. For generic wave fields generated by a steady or changing wind, kurtosis is found to be almost entirely due to bound harmonics. This observation enables one to predict the departure of evolving wave fields from Gaussianity, capitalizing on the already existing capability of wave spectra forecasting. Kurtosis rapidly adjusts to a sharp increase of wind and slowly decreases after a drop of wind. Typically kurtosis is in the range 0.1-0.3, which implies a tangible increase of freak wave probability compared to the Rayleigh distribution. Evolution of narrow-banded fields is qualitatively different from the generic case of wind waves: statistics is essentially non-Gaussian, which confirms that in this special case the standard kinetic equation paradigm is inapplicable.
TL;DR: In this paper, the statistical properties of supercontinuum spectra generated in photonic crystal fiber with two zero dispersion wavelengths were studied for picosecond pulse excitation, with the detailed form of the probability distribution depending strongly on input pulse energy.
Abstract: Stochastic numerical simulations are used to study the statistical properties of supercontinuum spectra generated in photonic crystal fibre with two zero dispersion wavelengths. For picosecond pulse excitation, we examine how the statistical properties of solitons generated on the long wavelength edge of the supercontinuum (``optical rogue waves") are modified by energy transfer to dispersive waves across the second zero dispersion wavelength. The soliton statistics (characterized in terms of peak power, wavelength and pulse duration) are shown to be strongly modified by the mechanism of dispersive wave generation, with the detailed form of the probability distribution depending strongly on input pulse energy.
TL;DR: In this paper, the underlying nonlinear dynamics of ultra-broadband optical wavelength converters based on fourth-order scalar modulation instability was numerically studied, and the spontaneous emergence of solitons and trapped radiation waves during the frequency conversion process was demonstrated.
Abstract: We numerically study the underlying nonlinear dynamics of ultra-broadband optical wavelength converters based on fourth-order scalar modulation instability. Specifically, we demonstrate the spontaneous emergence of solitons and trapped radiation waves during the frequency conversion process, leading to significant blue and red spectral expansions. Furthermore, we provide a statistical analysis of both Stokes and anti-Stokes bands, showing their intensity histogram evolution as a function of the propagation toward the L-shape signature typical of rogue events.
TL;DR: A characteristic peak in the extreme event probability appears that is attributed to the onset of interaction of the discrete solitons of the AL equation and the accompanied transition from the local to the global stochasticity monitored through the positive Lyapunov exponent of a nonlinear map.
Abstract: We perform statistical analysis on discrete nonlinear waves generated through modulational instability in the context of the Salerno model that interpolates between the intregable Ablowitz-Ladik (AL) equation and the nonintegrable discrete nonlinear Schr\"odinger equation. We focus on extreme events in the form of discrete rogue or freak waves that may arise as a result of rapid coalescence of discrete breathers or other nonlinear interaction processes. We find power law dependence in the wave amplitude distribution accompanied by an enhanced probability for freak events close to the integrable limit of the equation. A characteristic peak in the extreme event probability appears that is attributed to the onset of interaction of the discrete solitons of the AL equation and the accompanied transition from the local to the global stochasticity monitored through the positive Lyapunov exponent of a nonlinear map.
TL;DR: In this article, a σ-coordinate non-hydrostatic model, combined with the embedded Boussinesq-type-like equations, a reference velocity, and an adapted top-layer control, is developed to study the evolution of deep-water waves.
Abstract: A σ-coordinate non-hydrostatic model, combined with the embedded Boussinesq-type-like equations, a reference velocity, and an adapted top-layer control, is developed to study the evolution of deep-water waves. The advantage of using the Boussinesq-type-like equations with the reference velocity is to provide an analytical-based non-hydrostatic pressure distribution at the top-layer and to optimize wave dispersion property. The σ-based non-hydrostatic model naturally tackles the so-called overshooting issue in the case of non-linear steep waves. Efficiency and accuracy of this non-hydrostatic model in terms of wave dispersion and nonlinearity are critically examined. Overall results show that the newly developed model using a few layers is capable of resolving the evolution of non-linear deep-water wave groups. Copyright © 2009 John Wiley & Sons, Ltd.
TL;DR: In this paper, the authors assess the adequacy for describing bimodal sea states of different nonlinear probability distributions that have been developed for single sea states based on data collected at an offshore test basin, and the results are discussed with respect to three classes of sea states that reflect the relative contribution of swell and wind sea energy.
TL;DR: In this paper, the authors studied the evolution of random directional gravity waves in deep water and provided new insight into the nature of the spectral evolution of the ocean waves and the relative significance of resonant and quasi-resonant wave interaction.
Abstract: Recent experimental study of the evolution of random directional gravity waves in deep water provides new insight into the nature of the spectral evolution of the ocean waves and the relative significance of resonant and quasi-resonant wave interaction. When the directional angle containing half the total energy is broader than ∼20°, the spectrum evolves following the energy transfer that can be described by the four-wave resonant interaction alone. In contrast, in the case of a directionally confined spectrum, the effect of quasi-resonant wave–wave interaction becomes important, and the wave system becomes unstable. When the temporal change of the spectral shape due to quasi resonance becomes irreversible owing to energetic breaking dissipation, the spectrum rapidly downshifts. Under such extreme conditions, the likelihood of a freak wave is high.
TL;DR: In this article, an optimization approach for the experimental generation of wave sequences with predefined characteristics is applied. And the extreme sea state obtained with this method is measured at different locations in the tank, in a range from 2163 m (full scale) ahead of to 1470 m behind the target position.
Abstract: In the past years the existence of freak waves has been affirmed by observations, registrations, and severe accidents. Many publications investigated the occurrence of extreme waves, their characteristics and their impact on offshore structures, but their formation process is still under discussion. One of the famous real world registrations is the so called "New Year wave," recorded in the North Sea at the Draupner jacket platform on January 1st, 1995. Since there is only a single point registration available, it is not possible to draw conclusions on the spatial development in front of and behind the point of registration, which is indispensable for a complete understanding of this phenomenon. This paper presents the spatial development of the New Year wave generated in a model basin. To transfer the recorded New Year wave into the wave tank, an optimization approach for the experimental generation of wave sequences with predefined characteristics is applied. The extreme sea state obtained with this method is measured at different locations in the tank, in a range from 2163 m (full scale) ahead of to 1470 m behind the target position—520 registrations altogether. The focus lies on the detailed description of a possible evolution of the New Year wave over a large area and time interval. It is observed that the extreme wave at the target position develops mainly from a wave group of three smaller waves. The group velocity, wave propagation, and the energy flux of this wave group are analyzed, in particular.
TL;DR: In this article, the scaling behavior of freak wave formation in a model of two interacting waves, described by two coupled non-linear Schrodinger equations, is analyzed, and it is shown that there are two different dynamical scaling behaviors above and below a critical angle θc of the direction of the interacting waves.
Abstract: Large-amplitude water waves on deep water have long been known in the seafaring community, and are the cause of great concern for, e.g., oil platform constructions. The concept of such freak waves is nowadays, thanks to satellite and radar measurements, well established within the scientific community. There are a number of important models and approaches for the theoretical description of such waves. By analyzing the scaling behavior of freak wave formation in a model of two interacting waves, described by two coupled non-linear Schrodinger equations, we show that there are two different dynamical scaling behaviors above and below a critical angle θc of the direction of the interacting waves, below which all wave systems evolve and display statistics similar to a wave system of non-interacting waves. The results equally apply to other systems described by the non-linear Schrodinger equations, and should be of interest when designing optical wave guides.
01 Jan 2009
TL;DR: In this article, four wave models for the generation of freak wave events were proposed based on the modification of the Longuet-Higgins model, based on different energy distribution techniques in the four models.
Abstract: Four focusing models for generation of freak waves are presented. An extreme wave focusing model is presented on the basis of the enhanced High-Order Spectral (HOS) method and the importance of the nonlinear wave-wave interaction is evaluated by comparison of the calculated results with experimental and theoretical data. Based on the modification of the Longuet-Higgins model, four wave models for generation of freak waves (a. extreme wave model + random wave model; b. extreme wave model + regular wave model; c. phase interval modulation wave focusing model; d. number modulation wave focusing model with the same phase) are proposed. By use of different energy distribution techniques in the four models, freak wave events are obtained with different Hmax/Hs in finite space and time.
TL;DR: In this paper, the effects of freak waves on a mobile jack-up drilling platform stationed in exposed waters of the North Sea were analyzed based on the use of advanced computational fluid dynamics techniques.
Abstract: This paper analyzed the effects of freak waves on a mobile jack-up drilling platform stationed in exposed waters of the North Sea. Under freak wave conditions, highly nonlinear effects, such as wave run-up on platform legs and impact-related wave loads on the hull, had to be considered. Traditional methods based on the Morison formula needed to be critically examined to accurately predict these loads. Our analysis was based on the use of advanced computational fluid dynamics techniques. The code used here solves the Reynolds-averaged Navier-Stokes equations and relies on the interface-capturing technique of the volume-of-fluid type. It computed the two-phase flow of water and air to describe the physics associated with complex free-surface shapes with breaking waves and air trapping, hydrodynamic phenomena that had to be considered to yield reliable predictions. Lastly, the finite element method was used to apply the wave-induced loads onto a comprehensive finite element structural model of the platform, yielding deformations and stresses.
TL;DR: In this paper, the effects of the water depth on wave kinematics, wave forces, and wave-structure interaction were examined in order to clarify how it affects wave dynamics and where the deep water assumption holds.