Showing papers on "Rogue wave published in 2011"
TL;DR: This work presents the first experimental results with observations of the Peregrine soliton in a water wave tank, and proposes a new approach to modeling deep water waves using the nonlinear Schrödinger equation.
Abstract: The conventional definition of rogue waves in the ocean is that their heights, from crest to trough, are more than about twice the significant wave height, which is the average wave height of the largest one-third of nearby waves. When modeling deep water waves using the nonlinear Schr\"odinger equation, the most likely candidate satisfying this criterion is the so-called Peregrine solution. It is localized in both space and time, thus describing a unique wave event. Until now, experiments specifically designed for observation of breather states in the evolution of deep water waves have never been made in this double limit. In the present work, we present the first experimental results with observations of the Peregrine soliton in a water wave tank.
950 citations
TL;DR: In this paper, the authors derived general high-order rogue waves in the nonlinear Schroedinger equation by bilinear method and showed that these general rogue waves can exhibit other solution dynamics such as arrays of fundamental rogue waves arising at different times and spatial positions.
Abstract: General high-order rogue waves in the nonlinear Schroedinger equation are derived by the bilinear method. These rogue waves are given in terms of determinants whose matrix elements have simple algebraic expressions. It is shown that the general N-th order rogue waves contain N-1 free irreducible complex parameters. In addition, the specific rogue waves obtained by Akhmediev et al. (Phys. Rev. E 80, 026601 (2009)) correspond to special choices of these free parameters, and they have the highest peak amplitudes among all rogue waves of the same order. If other values of these free parameters are taken, however, these general rogue waves can exhibit other solution dynamics such as arrays of fundamental rogue waves arising at different times and spatial positions and forming interesting patterns.
258 citations
TL;DR: In this article, the authors analytically propose vector financial rogue waves of the coupled nonlinear volatility and option pricing model without an embedded w-learning, and exhibit their dynamical behaviors for chosen different parameters.
250 citations
TL;DR: In this paper, explicit rogue wave solutions, breather solitons, and rogue-bright-dark solutions for the coupled non-linear Schrodinger equations by the Darboux transformation were constructed.
Abstract: We construct explicit rogue wave solutions, breather solitons, and rogue-bright-dark solutions for the coupled non-linear Schrodinger equations by the Darboux transformation.
219 citations
TL;DR: In this article, it was shown that the electrostatic surface plasma rogue waves can be excited and propagate along a plasma-vacuum interface due to the nonlinear coupling between high-frequency surface plasmons and low-frequency ion oscillations.
Abstract: It is shown that the electrostatic surface plasma rogue waves can be excited and propagate along a plasma-vacuum interface due to the nonlinear coupling between high-frequency surface plasmons and low-frequency ion oscillations. The nonlinear pulse propagation condition and its behavior are discussed. The nonlinear structures may be useful for controlling and maximizing plasmonic energy along the plasma surface.
210 citations
TL;DR: Simulations of a simple rate equation model show good qualitative agreement with the experiments and provide a framework for understanding the observed extreme amplitude events as the result of a deterministic nonlinear process.
Abstract: Experimental observations of rare giant pulses or rogue waves were done in the output intensity of an optically injected semiconductor laser. The long-tailed probability distribution function of the pulse amplitude displays clear non-Gaussian features that confirm the rogue wave character of the intensity pulsations. Simulations of a simple rate equation model show good qualitative agreement with the experiments and provide a framework for understanding the observed extreme amplitude events as the result of a deterministic nonlinear process.
210 citations
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TL;DR: In this article, the authors consider the family of 2nd order rogue wave rational solutions of the nonlinear Schrodinger equation with two free parameters and show that the three components of the triplet are located on an equilateral triangle, thus maintaining a certain symmetry in the solution.
200 citations
TL;DR: This analysis reveals the existence of rogue wave clusters with a high level of symmetry in the (x,t) plane that arise naturally when the shifts in the Darboux scheme are taken to be eigenvalue dependent.
Abstract: Using the Darboux transformation technique and numerical simulations, we study the hierarchy of rational solutions of the nonlinear Schrodinger equation that can be considered as higher order rogue waves in this model. This analysis reveals the existence of rogue wave clusters with a high level of symmetry in the (x,t) plane. These structures arise naturally when the shifts in the Darboux scheme are taken to be eigenvalue dependent. We have found single-shell structures where a central higher order rogue wave is surrounded by a ring of first order peaks on the (x,t) plane.
189 citations
TL;DR: Clear evidence of rogue waves in a multistable system is revealed by experiments with an erbium-doped fiber laser driven by harmonic pump modulation and the results of numerical simulations are in good agreement with experiments.
Abstract: Clear evidence of rogue waves in a multistable system is revealed by experiments with an erbium-doped fiber laser driven by harmonic pump modulation. The mechanism for the rogue wave formation lies in the interplay of stochastic processes with multistable deterministic dynamics. Low-frequency noise applied to a diode pump current induces rare jumps to coexisting subharmonic states with high-amplitude pulses perceived as rogue waves. The probability of these events depends on the noise filtered frequency and grows up when the noise amplitude increases. The probability distribution of spike amplitudes confirms the rogue wave character of the observed phenomenon. The results of numerical simulations are in good agreement with experiments.
175 citations
TL;DR: This work studies numerically rogue waves in dissipative systems, taking as an example a unidirectional fiber laser in a nonstationary regime of operation and finding that the probability of producing extreme pulses in this setup is higher than in any other system considered so far.
Abstract: We study numerically rogue waves in dissipative systems, taking as an example a unidirectional fiber laser in a nonstationary regime of operation. The choice of specific set of parameters allows the laser to generate a chaotic sequence of pulses with a random distribution of peak amplitudes. The probability density function for the intensity maxima has an elevated tail at higher intensities. We have found that the probability of producing extreme pulses in this setup is higher than in any other system considered so far.
158 citations
TL;DR: In this paper, a multi-parametric family of quasi-rational solutions to the focusing NLS equation is presented, presenting a profile of multiple rogue waves, and these solutions have also been used by us to construct a large family of smooth, real localized rational solutions of the KP-I equation quite different from the multi-lumps solutions first constructed in Bordag et al. (1977).
Abstract: . We construct a multi-parametric family of quasi-rational solutions to the focusing NLS equation, presenting a profile of multiple rogue waves. These solutions have also been used by us to construct a large family of smooth, real localized rational solutions of the KP-I equation quite different from the multi-lumps solutions first constructed in Bordag et al. (1977). The physical relevance of both equations is very large. From the point of view of geosciences,the focusing NLS equation is relevant to the description of surface waves in deep water, and the KP-I equation occurs in the description of capillary gravitational waves on a liquid surface, but also when one considers magneto-acoustic waves in plasma (Zhdanov, 1984) etc. In addition, there are plenty of equations of physical importance, having their origin in fiber optics, hydrodynamics, plasma physics and many other areas, which are gauge equivalent to the NLS equation or to the KP-I equation. Therefore our results can be easily extended to a large number of systems of physical interest to be discussed in separate publications.
TL;DR: It is shown that rogue waves can be triggered naturally when a stable wave train enters a region of an opposing current flow, and the maximum amplitude of the rogue wave depends on the ratio between the current velocity U(0) and the wave group velocity c(g).
Abstract: We show that rogue waves can be triggered naturally when a stable wave train enters a region of an opposing current flow. We demonstrate that the maximum amplitude of the rogue wave depends on the ratio between the current velocity U(0) and the wave group velocity c(g). We also reveal that an opposing current can force the development of rogue waves in random wave fields, resulting in a substantial change of the statistical properties of the surface elevation. The present results can be directly adopted in any field of physics in which the focusing nonlinear Schrodinger equation with nonconstant coefficient is applicable. In particular, nonlinear optics laboratory experiments are natural candidates for verifying experimentally our results.
TL;DR: In this paper, the nonlinear Langmuir rogue wave dynamics associated with collisionless electron-positron (e-p) plasmas are investigated. But the results of the system are limited to the case of collisionless e-p plasma.
Abstract: Progress in understanding the nonlinear Langmuir rogue waves which accompany collisionless electron-positron (e-p) plasmas is presented. The nonlinearity of the system results from the nonlinear coupling between small, but finite, amplitude Langmuir waves and quasistationary density perturbations in an e-p plasma. The nonlinear Schrodinger equation is derived for the Langmuir waves’ electric field envelope, accounting for small, but finite, amplitude quasistationary plasma slow motion describing the Langmuir waves’ ponderomotive force. Numerical calculations reveal that the rogue structures strongly depend on the electron/positron density and temperature, as well as the group velocity of the envelope wave. The present study might be helpful to understand the excitation of nonlinear rogue pulses in astrophysical environments, such as in active galactic nuclei, in pulsar magnetospheres, in neutron stars, etc.
TL;DR: In this article, the evidence of rogue wave existence all over the world during last five years (2006-2010) has been collected based mainly on mass media sources and only events associated with damage and human loss are included.
Abstract: . The evidence of rogue wave existence all over the world during last five years (2006–2010) has been collected based mainly on mass media sources. Only events associated with damage and human loss are included. The waves occurred not only in deep and shallow zones of the World Ocean, but also at the coast, where they were manifested as either sudden flooding of the coast or high splashes over steep banks or sea walls. From the total number of 131 reported events, 78 were identified as evidence of rogue waves (which are expected to be at least twice larger than the significant wave height). The background significant wave height was estimated from the satellite wave data. The rogue waves at the coast, where the significant wave height is unknown or meaningless, were selected based on their unexpectedness and hazardous character. The statistics built on the selected 78 events suggests that extreme waves cause more damage in shallow waters and at the coast than in the deep sea and can be used for hazard assessment of the rogue wave phenomenon.
TL;DR: It is shown that optical rogue waves originate from two key ingredients: granularity, or a minimal size of the light speckles at the fiber exit, and inhomogeneity, that is,Speckles clustering into separate domains with different average intensities characterize also rogue waves in nonlinear systems.
Abstract: In the presence of many waves, giant events can occur with a probability higher than expected for random dynamics. By studying linear light propagation in a glass fiber, we show that optical rogue waves originate from two key ingredients: granularity, or a minimal size of the light speckles at the fiber exit, and inhomogeneity, that is, speckles clustering into separate domains with different average intensities. These two features characterize also rogue waves in nonlinear systems; thus, nonlinearity just plays the role of bringing forth the two ingredients of granularity and inhomogeneity.
TL;DR: In this paper, the generation of nonlinear ion-acoustic waves in a plasma having nonextensive electrons and positrons has been studied, where the reductive perturbation method is used to obtain a Korteweg-de Vries equation describing the system.
Abstract: Generation of nonlinear ion-acoustic waves in a plasma having nonextensive electrons and positrons has been studied. Two wave modes existing in such plasma are considered, namely solitary and rogue waves. The reductive perturbation method is used to obtain a Korteweg-de Vries equation describing the system. The latter admits solitary wave pulses, while the dynamics of the modulationally unstable wave packets described by the Korteweg-de Vries equation gives rise to the formation of rogue excitation that is described by a nonlinear Schrodinger equation. The dependence of both solitary and rogue waves profiles on the nonextensive parameter, positron-to-ion concentration ratio, electron-to-positron temperature ratio, and ion-to-electron temperature ratio are investigated numerically. The results from this work are expected to contribute to the in-depth understanding of the nonlinear excitations that may appear in nonextensive astrophysical plasma environments, such as galactic clusters, interstellar medium, etc.
TL;DR: In this paper, the authors investigate the formation of a matter rogue wave in Bose-Einstein condensates with attractive interatomic interaction analytically and numerically and show that the formation is mainly due to the accumulation of energy and atoms toward its central part; and the decay rate of atoms in unstable matter rogue waves can be effectively controlled by modulating the trapping frequency of external potential.
Abstract: We investigate the matter rogue wave in Bose-Einstein condensates with attractive interatomic interaction analytically and numerically. Our results show that the formation of rogue wave is mainly due to the accumulation of energy and atoms toward to its central part; and the decay rate of atoms in unstable matter rogue wave can be effectively controlled by modulating the trapping frequency of external potential. The numerical simulation demonstrate that even a small periodic perturbation with small modulation frequency can induce the generation of a near-ideal matter rogue wave. We also give an experimental protocol to observe this phenomenon in Bose-Einstein condensates.
TL;DR: In this article, an experimental and numerical investigation on the statistical properties of the surface elevation in crossing sea conditions was performed in a very large wave basin (70 m × 50 m × 3 m) and numerical results were obtained using a higher order method for solving the Euler equations.
Abstract: [1] We present an experimental and numerical investigation on the statistical properties of the surface elevation in crossing sea conditions. Experiments are performed in a very large wave basin (70 m × 50 m × 3 m) and numerical results are obtained using a higher order method for solving the Euler equations. Both experimental and numerical results indicate that the number of extreme events depends on the angle between the two interacting systems. This outcome is supported by recent theoretical investigations which have highlighted that the instability of wave packets may be triggered by the nonlinear interactions between coexisting, non-collinear wave systems.
TL;DR: In this paper, the authors investigated the directionality of the Draupner wave and concluded it might have resulted from two wave-groups crossing, whose mean wave directions were separated by about 90° or more.
Abstract: The ‘New Year Wave’ was recorded at the Draupner platform in the North Sea and is a rare high-quality measurement of a ‘freak’ or ‘rogue’ wave. The wave has been the subject of much interest and numerous studies. Despite this, the event has still not been satisfactorily explained. One piece of information that was not directly measured at the platform, but which is vital to understanding the nonlinear dynamics is the wave’s directional spreading. This paper investigates the directionality of the Draupner wave and concludes it might have resulted from two wave-groups crossing, whose mean wave directions were separated by about 90° or more. This result has been deduced from a set-up of the low-frequency second-order difference waves under the giant wave, which can be explained only if two wave systems are propagating at such an angle. To check whether second-order theory is satisfactory for such a highly nonlinear event, we have run numerical simulations using a fully nonlinear potential flow solver, which confirm the conclusion deduced from the second-order theory. This is backed up by a hindcast from European Centre for Medium-Range Weather Forecasts that shows swell waves propagating at approximately 80° to the wind sea. Other evidence that supports our conclusion are the measured forces on the structure, the magnitude of the second-order sum waves and some other instances of freak waves occurring in crossing sea states.
TL;DR: In this article, the authors investigate the formation of the matter rogue wave in Bose-Einstein condensates with attractive interatomic interaction analytically and numerically and show that the formation is mainly due to the accumulation of energy and atoms toward to its central part; the decay rate of the atomic number can be effectively controlled by modulating the trapping frequency of external potential.
Abstract: We investigate the matter rogue wave in Bose-Einstein Condensates with attractive interatomic interaction analytically and numerically. Our results show that the formation of rogue wave is mainly due to the accumulation of energy and atoms toward to its central part; Rogue wave is unstable and the decay rate of the atomic number can be effectively controlled by modulating the trapping frequency of external potential. The numerical simulation demonstrate that even a small periodic perturbation with small modulation frequency can induce the generation of a near-ideal matter rogue wave. We also give an experimental protocol to observe this phenomenon in Bose-Einstein Condensates.
TL;DR: In this article, the formation of rogue waves in nonlinear hyperbolic systems with an application to nonlinear shallow-water waves is studied in the framework of nonlinear hypersphere.
Abstract: The formation of rogue waves is studied in the framework of nonlinear hyperbolic systems with an application to nonlinear shallow-water waves. It is shown that the nonlinearity in the random Riemann (travelling) wave, which manifests in the steeping of the face-front of the wave, does not lead to extreme wave formation. At the same time, the strongly nonlinear Riemann wave cannot be described by the Gaussian statistics for all components of the wave field. It is shown that rogue waves can appear in nonlinear hyperbolic systems only in the result of nonlinear wave–wave or/and wave–bottom interaction. Two special cases of wave interaction with a vertical wall (interaction of two Riemann waves propagating in opposite directions) and wave transformation in the basin of variable depth are studied in detail. Open problems of the rogue wave occurrence in nonlinear hyperbolic systems are discussed.
TL;DR: Modulation instability of the discrete constant-background wave of the Ablowitz-Ladik (A-L) equation is studied to derive exact solutions of the A-L equation which are nonlinear continuations of MI at longer times, which can be considered as a complete resolution of the Fermi-Pasta-Ulam paradox.
Abstract: We study modulation instability (MI) of the discrete constant-background wave of the Ablowitz-Ladik (A-L) equation. We derive exact solutions of the A-L equation which are nonlinear continuations of MI at longer times. These periodic solutions comprise a family of two-parameter solutions with an arbitrary background field and a frequency of initial perturbation. The solutions are recurrent, since they return the field state to the original constant background solution after the process of nonlinear evolution has passed. These solutions can be considered as a complete resolution of the Fermi-Pasta-Ulam paradox for the A-L system. One remarkable consequence of the recurrent evolution is the nonlinear phase shift gained by the constant background wave after the process. A particular case of this family is the rational solution of the first-order or fundamental rogue wave.
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TL;DR: In this paper, the authors give an overview on the problem of rogue or freak wave formation in the ocean, which is a sporadic occurrence of unexpectedly high waves on the sea surface These waves cause serious danger for sailing and sea use.
Abstract: In this essay we give an overview on the problem of rogue or freak wave formation in the ocean The matter of the phenomenon is a sporadic occurrence of unexpectedly high waves on the sea surface These waves cause serious danger for sailing and sea use A number of huge wave accidents resulted in damages, ship losses and people injuries and deaths are known Now marine researchers do believe that these waves belong to a specific kind of sea waves, not taken into account by conventional models for sea wind waves This paper addresses to the nature of the rogue wave problem from the general viewpoint based on the wave process ideas We start introducing some primitive elements of sea wave physics with the purpose to pave the way for the further discussion We discuss linear physical mechanisms which are responsible for high wave formation, at first Then, we proceed with description of different sea conditions, starting from the open deep sea, and approaching the sea cost Nonlinear effects which are able to cause rogue waves are emphasised In conclusion we briefly discuss the generality of the physical mechanisms suggested for the rogue wave explanation; they are valid for rogue wave phenomena in other media such as solid matters, superconductors, plasmas and nonlinear optics
TL;DR: In this paper, the transformation of a random wave field in shallow water of variable depth is analyzed within the framework of the variable-coefficient Korteweg-de Vries equation.
Abstract: . The transformation of a random wave field in shallow water of variable depth is analyzed within the framework of the variable-coefficient Korteweg-de Vries equation. The characteristic wave height varies with depth according to Green's law, and this follows rigorously from the theoretical model. The skewness and kurtosis are computed, and it is shown that they increase when the depth decreases, and simultaneously the wave state deviates from the Gaussian. The probability of large-amplitude (rogue) waves increases within the transition zone. The characteristics of this process depend on the wave steepness, which is characterized in terms of the Ursell parameter. The results obtained show that the number of rogue waves may deviate significantly from the value expected for a flat bottom of a given depth. If the random wave field is represented as a soliton gas, the probabilities of soliton amplitudes increase to a high-amplitude range and the number of large-amplitude (rogue) solitons increases when the water shallows.
TL;DR: It was found that limited effort has been put on developing statistical models for waves incorporating spatial and long-term temporal variability and it is suggested that model improvements could be achieved by adopting approaches from other application areas.
Abstract: This paper presents a literature survey on time-dependent statistical modelling of extreme waves and sea states. The focus is twofold: on statistical modelling of extreme waves and space- and time-dependent statistical modelling. The first part will consist of a literature review of statistical modelling of extreme waves and wave parameters, most notably on the modelling of extreme significant wave height. The second part will focus on statistical modelling of time- and space-dependent variables in a more general sense, and will focus on the methodology and models used also in other relevant application areas. It was found that limited effort has been put on developing statistical models for waves incorporating spatial and long-term temporal variability and it is suggested that model improvements could be achieved by adopting approaches from other application areas. In particular, Bayesian hierarchical space–time models were identified as promising tools for spatio-temporal modelling of extreme waves. Finally, a review of projections of future extreme wave climate is presented.
TL;DR: In this article, the authors present a theoretical analysis of rare events of high-intensity fluctuations (optical freak waves) that occur in fiber communication links using bit-overlapping transmission.
Abstract: Large broadening of short optical pulses due to fiber dispersion leads to a strong overlap in information data streams resulting in statistical deviations of the local power from its average. We present a theoretical analysis of rare events of high-intensity fluctuations---optical freak waves---that occur in fiber communication links using bit-overlapping transmission. Although the nature of the large fluctuations examined here is completely linear, as compared to commonly studied freak waves generated by nonlinear effects, the considered deviations inherit from rogue waves the key features of practical interest---random appearance of localized high-intensity pulses. We use the term ``rogue wave'' in an unusual context mostly to attract attention to both the possibility of purely linear statistical generation of huge amplitude waves and to the fact that in optics the occurrence of such pulses might be observable even with the standard Gaussian or even rarer-than-Gaussian statistics, without imposing the condition of an increased probability of extreme value events.
TL;DR: In this paper, a trapezoidal embankment was overtopped by three distinct types of waves: wave groups of compact form, wave groups embedded in a background wave field and a solitary wave.
Abstract: Prediction of individual wave overtopping events is important in assessing danger to life and property, but data are sparse and hydrodynamic understanding is lacking. Laboratory-scale waves of three distinct types were generated at the Coastal Research Facility to model extreme waves overtopping a trapezoidal embankment. These comprised wave groups of compact form, wave groups embedded in a background wave field, and a solitary wave. The inshore wave propagation was measured and the time variation of overtopping rate estimated. The total volume overtopped was measured directly. The experiments provide well-defined data without uncertainty due to the effect of reflection on the incident wave train. The dependence of overtopping on a range of wave shapes is thus determined and the influence of wave–wave interactions on overtopping assessed. It was found that extreme overtopping may arise from focused waves with deep troughs rather than large crests. Furthermore, overtopping waves can be generated from small...
TL;DR: In this article, the existence of rogue wave events in the highly incoherent state of the system and compare them with the recently identified hierarchy of rational soliton solutions is investigated. But the authors do not consider the nonlinearity of the Schrodinger optical model.
TL;DR: In this article, the authors used the in-house Computational Fluid Dynamics (CFD) flow code AMAZON-SC as a numerical wave tank (NWT) to study wave loading on a wave energy converter (WEC) device in heave motion.
Abstract: . In this paper, we use the in-house Computational Fluid Dynamics (CFD) flow code AMAZON-SC as a numerical wave tank (NWT) to study wave loading on a wave energy converter (WEC) device in heave motion. This is a surface-capturing method for two fluid flows that treats the free surface as contact surface in the density field that is captured automatically without special provision. A time-accurate artificial compressibility method and high resolution Godunov-type scheme are employed in both fluid regions (air/water). The Cartesian cut cell method can provide a boundary-fitted mesh for a complex geometry with no requirement to re-mesh globally or even locally for moving geometry, requiring only changes to cut cell data at the body contour. Extreme wave boundary conditions are prescribed in an empty NWT and compared with physical experiments prior to calculations of extreme waves acting on a floating Bobber-type device. The validation work also includes the wave force on a fixed cylinder compared with theoretical and experimental data under regular waves. Results include free surface elevations, vertical displacement of the float, induced vertical velocity and heave force for a typical Bobber geometry with a hemispherical base under extreme wave conditions.