Generation Of Rogue Waves Research Articles

An Empirical Model for Skillful Rogue Wave Forecasts

Abstract One of the leading goals of rogue wave research is to develop a robust rogue wave warning system to mitigate the danger they pose. One such system has been developed by the European Centre for Medium-Range Weather Forecasts (ECMWF), called the freak wave warning system (FWWS), based on nonlinear wave effects. The FWWS predicts maximum expected wave envelope height as a risk parameter for forecasts. Recently, a data-driven alternative has been proposed by Häfner et al., which was distilled from a neural network using wave buoy observations. However, it has yet to be evaluated by a spectral wave model for application to operational wave forecasting. The data-driven, learned model emphasizes bandwidth-controlled linear superposition as the predominant mechanism in crest-to-trough rogue wave generation, while nonlinear effects are a secondary term. The present work evaluates the performance of the empirical model using output from an ECMWF global wave hindcast. We find that the prediction models based on bandwidth effects have the highest log likelihood scores, with the empirical model outperforming all other tested models. In contrast, the expected maximum envelope wave height from the FWWS does not predict the occurrence of rogue waves. These results indicate that the empirical model with wave model input is a skillful predictor and should be considered for operational implementation to improve rogue wave forecasting. Significance Statement Rogue waves are unexpectedly large and unpredictable waves. Encounters with rogue waves can result in damage to marine vessels and offshore infrastructures. Research is devoted to developing systems to predict the risk of rogue wave events. A novel predictive model has been shown to perform well in predicting rogue wave occurrences based on wave buoy observations. This model is a symbolic expression distilled from an artificial neural network that incorporates known rogue wave dynamics and that can be evaluated alongside traditional risk estimates with minor adjustments to operational forecasting systems. This study evaluates the newly proposed empirical model in a forecasting setting. Our work demonstrates the efficacy of the empirical model for operational forecasting purposes.

Modulational instability, generation, and evolution of rogue waves in the generalized fractional nonlinear Schrödinger equations with power-law nonlinearity and rational potentials.

In this paper, we investigate several properties of the modulational instability (MI) and rogue waves (RWs) within the framework of the generalized fractional nonlinear Schrödinger (FNLS) equations with rational potentials. We derive the dispersion relation for a continuous wave (CW), elucidating the relationship between the wavenumber and the instability growth rate of the CW solution in the absence of potentials. This relationship is primarily influenced by the power parameter σ, the Lévy index α, and the nonlinear coefficient g. Our theoretical findings are corroborated by numerical simulations, which demonstrate that MI occurs in the focusing context. Furthermore, we study the RW generations in both cubic and quintic FNLS equations with two types of time-dependent rational potentials, which make both cubic and quintic NLS equations support the exact RW solutions. Specifically, we show that the introduction of these two potentials allows for the excitations of controllable RWs in the defocusing regime. When these two potentials become the time-independent cases such that the stable W-shaped solitons with non-zero backgrounds are generated in these cubic and quintic FNLS equations. Moreover, we consider the excitations of higher-order RWs and investigate the conditions necessary for their generations. Our analysis reveals the intricate interplay between the system parameters and the potential configurations, offering insights into the mechanisms that facilitate the emergence of higher-order RWs. Finally, we find the separated controllable multi-RWs in the defocusing cubic FNLS equation with time-dependent multi-potentials. This comprehensive study not only enhances our understanding of MI and RWs in the fractional nonlinear wave systems, but also paves the way for future research in related nonlinear wave phenomena.

Generation and control of optical rogue waves by super-Gaussian pulses with varying steepness

We investigate the dynamics of optical rogue waves induced by super-Gaussian (SG) pulses in fiber optics. SG pulses with controlled steep leading and trailing edges can produce high-intensity self-focusing when propagating in nonlinear fibers with weak dispersion and strong nonlinearity. We observe the emergence of various rogue waves, including Peregrine breathers, Akhmediev breathers (ABs), and second-order ABs. By adjusting the steepness of the SG pulses, the generation of these rogue waves can be controlled. As the steepness of the SG pulse increases, we find the fundamental-order AB can stably coexist. Simultaneously, we reveal that the period of these ABs can be effectively controlled by adjusting the steepness of the SG pulse. At a certain steepness, the second-order AB with high power can also be observed. We also investigated the propagation of SG pulses with an initial chirp in fiber optics and found that they can also control AB and second-order Peregrine breathers. To our knowledge, our findings present a new approach to generating controllable rogue waves.

Cavity soliton inhibition of extreme events in lasers with injection.

Vortex mediated turbulence can be the key element in the generation of extreme events in spatially extended lasers with optical injection. Here, we study the interplay of vortex mediated turbulence and cavity solitons on the onset of extreme events in semiconductor lasers with injection. We first analyze and characterize these two features separately, spatiotemporal chaotic optical vortices for low values of the injection intensity and cavity solitons above the locking regime. In regimes where vortex mediated turbulence and cavity solitons coexist, localized peaks of light inhibit instead of enhancing the generation of rogue waves by locally regularizing the otherwise chaotic phase of the optical field. Cavity solitons can then be used to manipulate and control extreme events in systems displaying vortex mediated turbulence.

Self-similarity of rogue wave generation in gyrotrons: Beyond the Peregrine breather

Within the framework of numerical simulations, we study the gyrotron dynamics under conditions of a significant excess of the operating current over the starting value, when the generation of electromagnetic pulses with anomalously large amplitudes (“rogue waves”) can be realized. The averaged shape of high-power pulses is shown to be very close to the celebrated Peregrine breather. At the same time, we demonstrate that the relation between peak power and duration of rogue waves is self-similar, but does not reproduce the one characteristic for Peregrine breathers. Remarkably, the discovered self-similar relation corresponds to the exponential nonlinearity of an equivalent Schrödinger-like evolution equation. This interpretation can be used as a theoretical basis for explaining the giant amplitudes of gyrotron rogue waves.

Observations of Rogue Seas in the Southern Ocean.

We report direct observations of surface waves from a stereo camera system along with concurrent measurements of wind speed during an expedition across the Southern Ocean in the austral winter aboard the South African icebreaker S.A. Agulhas II. Records include water surface elevation across a range of wave conditions spanning from early stages of wave growth to full development. We give experimental evidence of rogue seas, i.e., sea states characterized by heavy tails of the probability density function well beyond the expectation based on bound mode theory. These conditions emerge during wave growth, where strong wind forcing and high nonlinearity drive wave dynamics. Quasiresonance wave-wave interactions, which are known to sustain the generation of large amplitude rogue waves, capture this behavior. Wave statistics return to normality as the wind forcing ceases and waves switch to a full developed condition.

Optical Darboux Transformer.

The optical Darboux transformer for solitons is introduced as a photonic device that performs the Darboux transformation directly in the optical domain. This enables two major advances for optical signal processing based on the nonlinear Fourier transform: (i)the multiplexing of solitonic waveforms corresponding to different discrete eigenvalues of the Zakharov-Shabat system, and (ii)the selective filtering of an arbitrary number of individual solitons too. The optical Darboux transformer can be built using existing commercially available photonic technology components and constitutes a universal tool for signal processing, optical communications, optical rogue waves generation, and waveform shaping and control in the nonlinear Fourier domain.

Higher rogue and rogue-soliton interaction solutions of a (2 + 1) dimensional nonlinear model in fluid mechanics

In this study, two new theorems are generalized. We obtained a new paradigm about the second order rogue wave and multiple exponential functions, and a new paradigm about the second order rogue wave and multiple hyperbolic cosine functions. Six sets of interaction solutions of the model are solved by means of symbolic calculation and two new theorems. Meaningful graphs of the propagation processes along time demonstrated the interaction phenomena for these solutions. The energy transfer process can be observed when the second order rogue waves interact with multiple exponential functions or multiple hyperbolic cosine functions. As a conclusion from our paper, the solitons’ energy transfers to the second order rogue wave at beginning, the rogue wave’s energy dissipates and transfers to the solitons along the time moving. It will contribute to the research on the generation of rogue waves.

Simulation of spatial rogue waves in actively Q-switched solid-state laser with transverse mode locking

We report the generation of spatial rogue waves in the actively Q-switched Nd:YAG laser with several transverse modes and negligible nonlinear effects in the cavity. We discuss a basic theoretical model that is able to reproduce the experimental observations of spatial rogue waves in the output Q-switched pulses as a result of the coherent superposition of transverse modes. The simulated rogue wave statistics depends on the configuration of the lasing modes and take a more pronounced L-shaped form in the case of highly anisotropic mode distribution and reduced frequency spacing between the modes. For larger frequency spacing between the modes, the mode-locking effects result in the periodic dynamics of the transverse beam profile and formation of spatio-temporal rogue waves. These results indicate that transverse mode-locking and spatial symmetry breaking through anisotropy in the mode configuration represent factors responsible for spatial rogue wave emergence in multimode lasers with low nonlinearity.

Homoclinic breather, periodic wave, lump solution, and M-shaped rational solutions for cold bosonic atoms in a zig-zag optical lattice

Abstract In this article, the equation showing the cold bosonic atoms in a zig-zag optical lattice model for some breathers, M-shaped solution and lump soliton solution, homoclinic breather pulses, breather lump pulses, periodic-cross kink wave, kink cross-rational propagation, and interaction between lump periodic and kink wave was examined. Some M-shaped solution, M-shaped interaction with periodic and kink, M-shaped interaction with rogue and kink, M-shaped rational solution, M-shaped rational solution with one kink, M-shaped rational solution with two kink, solutions for lump soliton waves, lump one kink waves, lump two kink waves, periodic-cross lump wave propagation, periodic wave propagation, rogue wave propagation, and multiwave propagation were also acquired. Likewise, our solution was also graphically presented, and also their stability was checked.

SPH Simulation of the Interaction between Freak Waves and Bottom-Fixed Structures

In this paper, the Smoothed Particle Hydrodynamics (SPH) method is used in a C# environment to simulate the interaction between freak waves and bottom-fixed structures by establishing a fluid dynamics model. Paraview software 5.10.1 was used to analyze and visualize the simulation results. In order to simulate wave propagation accurately, the reliability of the model was verified by comparing experimental and simulated data. A two-dimensional numerical wave flume was established based on the SPH method, a conservative Riemann solver was introduced, a repulsive boundary condition was adopted, and a slope was used to eliminate wave reflection. Bottom-fixed structures of different heights and lengths, as well as different wave conditions, were selected to numerically simulate the interaction between freak waves and bottom-fixed structures. The results show that the height of bottom-fixed structures and wave conditions have a significant effect on hindering the propagation of rogue waves, while the length has little effect on the propagation of deformed waves. When the amplitude of the wave remains constant, both the period andthe duration of the deformed wave are longer. This research is of certain significance for the prediction of freak waves in marine engineering and the application and promotion of SPH methods.

The effects of viscosity on the linear stability of damped Stokes waves, downshifting, and rogue wave generation

AbstractWe investigate a higher order nonlinear Schrödinger equation with linear damping and weak viscosity, recently proposed as a model for deep water waves exhibiting frequency downshifting. Through analysis and numerical simulations, we discuss how the viscosity affects the linear stability of the Stokes wave solution, enhances rogue wave formation, and leads to permanent downshift in the spectral peak. The novel results in this work include the analysis of the transition from the initial Benjamin–Feir instability to a predominantly oscillatory behavior, which takes place in a time interval when most rogue wave activity occurs. In addition, we propose new criteria for downshifting in the spectral peak and determine the relation between the time of permanent downshift and the location of the global minimum of the momentum and the magnitude of its second derivative.

Formation, propagation, and excitation of matter solitons and rogue waves in chiral BECs with a current nonlinearity trapped in external potentials.

In this paper, we investigate formation and propagation of matter solitons and rogue waves (RWs) in chiral Bose-Einstein condensates modulated by different external potentials, modeled by the chiral Gross-Pitaevskii (GP) equation with the current nonlinearity and external potentials. On the one hand, the introduction of two potentials (Pöschl-Teller and harmonic-Gaussian potentials) enables the discovery of exact soliton solutions in both focusing and defocusing cases. We analyze the interplay effects of current nonlinearity and potential on soliton stability via associated Bogoliubov-de Gennes equations. Moreover, multiple families of numerical solitons (ground-state and dipole modes) trapped in potentials are found, exhibiting distinctive structures. The interactions between solitons trapped in potentials are studied, which exhibit the inelastic trajectories and repulsive interactions. On the other hand, we introduce the time-dependent potentials such that the controlled RWs are found in both focusing and defocusing GP equations with current nonlinearity. Furthermore, through the interaction between potentials and current nonlinearity, it is possible to enlarge the region of modulational instability, leading to the generation of RWs and chiral solitons. High-order RWs are generated from several Gaussian perturbations on a continuous wave. The presence of current nonlinearity disrupts the structures of these high-order RWs, causing them to undergo a transform into chiral lower-amplitude solitons. Finally, various types of soliton excitations are investigated by varying the strengths of potential and current nonlinearity, showing the abundant dynamic transforms of chrital matter solitons.

Enhanced spectral broadening via the optical rogue wave stimulated by spectral sinusoidal phase

We numerically investigate the extended spectral broadening via a spectral sinusoidal phase-modulated Gaussian pulse. The modulated pulse can create two predominant solitons that collide with each other to form a rogue wave (RW), resulting in an RW-induced dispersive wave emission. This leads to a further spectral broadening beyond the soliton-induced dispersive wave and can be manipulated by tuning the phase modulation parameters. Before the appearance of RW, the modulated pulse-propagation scenario is governed by the optical Newton’s cradles and the optical event horizons. These complex dynamics reveal a new method for controlling the RW generation as well as spectral broadening at relatively low power levels. Our results have potential implications for controllable excitation of RWs and broadband supercontinuum generation.

Effects of two weak femtosecond pulse seeds on promoting rogue wave generation

We numerically simulate the enhancement of rogue wave generation by adding two weak femtosecond pulse seeds at two fixed modulation frequencies. The results show that two weak pulse seeds have better promotion effect on rogue wave generation than one weak pulse seed. In addition, the modulation depth and pulse width of the weak pulse seeds also affect the generation of rogue wave. With the increase of the modulation depth and pulse width of the two weak pulse seeds, the control effect of rogue wave gradually becomes better.

Airy-type bichromatic wave pulses on the sea surface and generation of rogue waves

We present a theoretical study of bichromatic weakly non-collinear Airy-type waves propagating with various amplitudes in water of infinite depth. The coupled nonlinear Schrödinger equations are invoked to study the behavior of self- and cross-interacting Airy wave packets. We demonstrate that bichromatic pulses possess the main properties of single Airy wave packets—shape invariance and self-acceleration or self-deceleration—when propagating in a dispersive medium. Accounting for nonlinearity leads to a strong dependence of the structure, stability, and propagation velocity of wave pulses on their amplitude. We show that interacting pulses of Airy-type waves can form giant accelerating and decelerating waves.

Transient dynamics of dissipative solitons formation in a net-normal dispersion mode-locked fiber laser based on nonlinear polarization evolution.

In mode-locked fiber lasers, the formation of ultrashort pulses from noisy or unstable states is a crucial area of research. Investigating these complex nonlinear dynamics can lead to valuable insights and new practical engineering techniques, particularly for the design and optimization of optical systems. Time-stretch dispersive Fourier transform, utilized in our study to investigate dissipative solitons formation in a net-normal dispersion nonlinear polarization evolution mode-locked fiber laser, provides a window into the intricate dynamics of such systems. In our experiments, the identification of five distinct transient stages in the formation process sheds light on the underlying mechanisms of dissipative soliton (DS) formation. The five distinct transient stages involved in the formation process include relaxation oscillation, modulation instability, spectral broadening, soliton explosions (SEs), and stable mode-locking. Notably, we also observed the generation of dissipative rogue waves during the SE stage. Our findings shed light on the intricate dynamics of DS formation and offer valuable insights for the design and optimization of mode-locked fiber lasers.

Rogue wave generation using a chaotic semiconductor laser with energy redistribution.

We demonstrate for the first time that optical rogue waves (RWs) can be generated using a chaotic semiconductor laser with energy redistribution. Chaotic dynamics are numerically generated using the rate equation model of an optically injected laser. The chaotic emission is then sent to an energy redistribution module (ERM) that consists of a temporal phase modulation and a dispersive propagation. The process enables a temporal energy redistribution of the chaotic emission waveforms, where coherent summation of consecutive laser pulses leads to random generation of giant intensity pulses. Efficient generation of optical RWs are numerically demonstrated by varying the ERM operating parameters in the entire injection parameter space. The effects of the laser spontaneous emission noise on the generation of RWs are further investigated. The RW generation approach offers a relatively high flexibility and tolerance in the choice of ERM parameters according to the simulation results.

Contribution of solitons to enhanced rogue wave occurrence in shallow depths: a case study in the southern North Sea

Abstract. The shallow waters off the coast of Norderney in the southern North Sea are characterised by a higher frequency of rogue wave occurrences than expected. Here, rogue waves refer to waves exceeding twice the significant wave height. The role of nonlinear processes in the generation of rogue waves at this location is currently unclear. Within the framework of the Korteweg–de Vries (KdV) equation, we investigated the discrete soliton spectra of measured time series at Norderney to determine differences between time series with and without rogue waves. For this purpose, we applied a nonlinear Fourier transform (NLFT) based on the Korteweg–de Vries equation with vanishing boundary conditions (vKdV-NLFT). At measurement sites where the propagation of waves can be described by the KdV equation, the solitons in the discrete nonlinear vKdV-NLFT spectrum correspond to physical solitons. We do not know whether this is the case at the considered measurement site. In this paper, we use the nonlinear spectrum to classify rogue wave and non-rogue wave time series. More specifically, we investigate if the discrete nonlinear spectra of measured time series with visible rogue waves differ from those without rogue waves. Whether or not the discrete part of the nonlinear spectrum corresponds to solitons with respect to the conditions at the measurement site is not relevant in this case, as we are not concerned with how these spectra change during propagation. For each time series containing a rogue wave, we were able to identify at least one soliton in the nonlinear spectrum that contributed to the occurrence of the rogue wave in that time series. The amplitudes of these solitons were found to be smaller than the crest height of the corresponding rogue wave, and interaction with the continuous wave spectrum is needed to fully explain the observed rogue wave. Time series with and without rogue waves showed different characteristic soliton spectra. In most of the spectra calculated from rogue wave time series, most of the solitons clustered around similar heights, but the largest soliton was outstanding, with an amplitude significantly larger than all other solitons. The presence of a clearly outstanding soliton in the spectrum was found to be an indicator pointing towards the enhanced probability of the occurrence of a rogue wave in the time series. Similarly, when the discrete spectrum appears as a cluster of solitons without the presence of a clearly outstanding soliton, the presence of a rogue wave in the observed time series is unlikely. These results suggest that soliton-like and nonlinear processes substantially contribute to the enhanced occurrence of rogue waves off Norderney.

Generation and Controllability of High-Dimensional Rogue Waves in an Electromagnetically Induced Transparent Medium

We propose a scheme to generate and control high-dimensional rogue waves in a coherent three-level Λ-type atomic system via electromagnetically induced transparency (EIT). Under EIT conditions, the probe field envelopes obey the non-integrable nonlinear Schrödinger equations (NLSE) with or without the external potential, which result from the stark (Zeeman) effect contributed by an electric (magnetic) field. By adjusting the amplitude and width of the initial pulse, we can generate the high-dimensional rogue waves and obtain the phase-transition curves of high-dimensional rogue waves. In the system, the far-detuned electric field, the random weak magnetic field, and the Gauss weak magnetic field are not conducive to the excitation of high-dimensional rogue waves. The results not only provide a theoretical basis for the experimental realization or prevention of the high-dimensional rogue waves, but also prove the possibility of generating and controlling the rogue waves in other high-dimensional non-integrable systems.