Shats, M; Punzmann, H; Xia, H
2010-03-12
We report the first observation of extreme wave events (rogue waves) in parametrically driven capillary waves. Rogue waves are observed above a certain threshold in forcing. Above this threshold, frequency spectra broaden and develop exponential tails. For the first time we present evidence of strong four-wave coupling in nonlinear waves (high tricoherence), which points to modulation instability as the main mechanism in rogue waves. The generation of rogue waves is identified as the onset of a distinct tail in the probability density function of the wave heights. Their probability is higher than expected from the measured wave background.
Kedziora, David J; Ankiewicz, Adrian; Akhmediev, Nail
2011-11-01
Using the Darboux transformation technique and numerical simulations, we study the hierarchy of rational solutions of the nonlinear Schrödinger 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.
NASA Astrophysics Data System (ADS)
Yan, Zhenya
2011-11-01
The coupled nonlinear volatility and option pricing model presented recently by Ivancevic is investigated, which generates a leverage effect, i.e., stock volatility is (negatively) correlated to stock returns, and can be regarded as a coupled nonlinear wave alternative of the Black-Scholes option pricing model. In this Letter, we analytically propose vector financial rogue waves of the coupled nonlinear volatility and option pricing model without an embedded w-learning. Moreover, we exhibit their dynamical behaviors for chosen different parameters. The vector financial rogue wave (rogon) solutions may be used to describe the possible physical mechanisms for the rogue wave phenomena and to further excite the possibility of relative researches and potential applications of vector rogue waves in the financial markets and other related fields.
Solli, D R; Ropers, C; Koonath, P; Jalali, B
2007-12-13
Recent observations show that the probability of encountering an extremely large rogue wave in the open ocean is much larger than expected from ordinary wave-amplitude statistics. Although considerable effort has been directed towards understanding the physics behind these mysterious and potentially destructive events, the complete picture remains uncertain. Furthermore, rogue waves have not yet been observed in other physical systems. Here, we introduce the concept of optical rogue waves, a counterpart of the infamous rare water waves. Using a new real-time detection technique, we study a system that exposes extremely steep, large waves as rare outcomes from an almost identically prepared initial population of waves. Specifically, we report the observation of rogue waves in an optical system, based on a microstructured optical fibre, near the threshold of soliton-fission supercontinuum generation--a noise-sensitive nonlinear process in which extremely broadband radiation is generated from a narrowband input. We model the generation of these rogue waves using the generalized nonlinear Schrödinger equation and demonstrate that they arise infrequently from initially smooth pulses owing to power transfer seeded by a small noise perturbation.
Triangular rogue wave cascades.
Kedziora, David J; Ankiewicz, Adrian; Akhmediev, Nail
2012-11-01
By numerically applying the recursive Darboux transformation technique, we study high-order rational solutions of the nonlinear Schrödinger equation that appear spatiotemporally as triangular arrays of Peregrine solitons. These can be considered as rogue wave cascades and complement previously discovered circular cluster forms. In this analysis, we reveal a general parametric restriction for their existence and investigate the interplay between cascade and cluster forms. As a result, we demonstrate how to generate many more hybrid rogue wave solutions, including semicircular clusters that resemble claws.
NASA Astrophysics Data System (ADS)
Frisquet, Benoit; Kibler, Bertrand; Morin, Philippe; Baronio, Fabio; Conforti, Matteo; Millot, Guy; Wabnitz, Stefan
2016-02-01
Photonics enables to develop simple lab experiments that mimic water rogue wave generation phenomena, as well as relativistic gravitational effects such as event horizons, gravitational lensing and Hawking radiation. The basis for analog gravity experiments is light propagation through an effective moving medium obtained via the nonlinear response of the material. So far, analogue gravity kinematics was reproduced in scalar optical wave propagation test models. Multimode and spatiotemporal nonlinear interactions exhibit a rich spectrum of excitations, which may substantially expand the range of rogue wave phenomena, and lead to novel space-time analogies, for example with multi-particle interactions. By injecting two colliding and modulated pumps with orthogonal states of polarization in a randomly birefringent telecommunication optical fiber, we provide the first experimental demonstration of an optical dark rogue wave. We also introduce the concept of multi-component analog gravity, whereby localized spatiotemporal horizons are associated with the dark rogue wave solution of the two-component nonlinear Schrödinger system.
Frisquet, Benoit; Kibler, Bertrand; Morin, Philippe; Baronio, Fabio; Conforti, Matteo; Millot, Guy; Wabnitz, Stefan
2016-01-01
Photonics enables to develop simple lab experiments that mimic water rogue wave generation phenomena, as well as relativistic gravitational effects such as event horizons, gravitational lensing and Hawking radiation. The basis for analog gravity experiments is light propagation through an effective moving medium obtained via the nonlinear response of the material. So far, analogue gravity kinematics was reproduced in scalar optical wave propagation test models. Multimode and spatiotemporal nonlinear interactions exhibit a rich spectrum of excitations, which may substantially expand the range of rogue wave phenomena, and lead to novel space-time analogies, for example with multi-particle interactions. By injecting two colliding and modulated pumps with orthogonal states of polarization in a randomly birefringent telecommunication optical fiber, we provide the first experimental demonstration of an optical dark rogue wave. We also introduce the concept of multi-component analog gravity, whereby localized spatiotemporal horizons are associated with the dark rogue wave solution of the two-component nonlinear Schrödinger system. PMID:26864099
Frisquet, Benoit; Kibler, Bertrand; Morin, Philippe; Baronio, Fabio; Conforti, Matteo; Millot, Guy; Wabnitz, Stefan
2016-02-11
Photonics enables to develop simple lab experiments that mimic water rogue wave generation phenomena, as well as relativistic gravitational effects such as event horizons, gravitational lensing and Hawking radiation. The basis for analog gravity experiments is light propagation through an effective moving medium obtained via the nonlinear response of the material. So far, analogue gravity kinematics was reproduced in scalar optical wave propagation test models. Multimode and spatiotemporal nonlinear interactions exhibit a rich spectrum of excitations, which may substantially expand the range of rogue wave phenomena, and lead to novel space-time analogies, for example with multi-particle interactions. By injecting two colliding and modulated pumps with orthogonal states of polarization in a randomly birefringent telecommunication optical fiber, we provide the first experimental demonstration of an optical dark rogue wave. We also introduce the concept of multi-component analog gravity, whereby localized spatiotemporal horizons are associated with the dark rogue wave solution of the two-component nonlinear Schrödinger system.
NASA Astrophysics Data System (ADS)
Ding, Yingchun; Zhang, Bin; Feng, Qi; Tang, Xin; Liu, Zhongxuan; Chen, Zhaoyang; Lin, Chengyou
2017-01-01
The formation of extreme localization structures in nonlinear dispersive media (water or optical fibres) can be explained and described by the focusing nonlinear Schrödinger equation (NLSE). The NLSE is especially important in understanding how solitons on a condensate background (SCB) appear from a small perturbation through modulation instability. We have studied theoretically SCB solutions solved with the dressing method. A class of bipolar-rogue-wave structures that are constructed by collisions between elementary SCB or bipolar solitonic solutions was found. Besides, we have also found a new class of regular bright solitonic rogue waves that are originated from the collision between two bipolar-rogue-wave structures. The bipolar-rogue-wave structures can be considered to provide a new prototype for rogue-waves dynamics modeling. Our results extend previous studies in the area of rogue waves and may be important in the study of oceanography and optics.
Rogue waves in baroclinic flows
NASA Astrophysics Data System (ADS)
Zuo, Da-Wei; Gao, Yi-Tian; Feng, Yu-Jie; Xue, Long; Sun, Yu-Hao
2017-05-01
We investigate an AB system, which can be used to describe marginally unstable baroclinic wave packets in a geophysical fluid. Using the generalized Darboux transformation, we obtain higher-order rogue wave solutions and analyze rogue wave propagation and interaction. We obtain bright rogue waves with one and two peaks. For the wave packet amplitude and the mean-flow correction resulting from the self-rectification of the nonlinear wave, the positions and values of the wave crests and troughs are expressed in terms of a parameter describing the state of the basic flow, in terms of a parameter responsible for the interaction of the wave packet and the mean flow, and in terms of the group velocity. We show that the interaction of the wave packet and mean flow and also the group velocity affect the propagation and interaction of the amplitude of the wave packet and the self-rectification of the nonlinear wave.
Controllable parabolic-cylinder optical rogue wave.
Zhong, Wei-Ping; Chen, Lang; Belić, Milivoj; Petrović, Nikola
2014-10-01
We demonstrate controllable parabolic-cylinder optical rogue waves in certain inhomogeneous media. An analytical rogue wave solution of the generalized nonlinear Schrödinger equation with spatially modulated coefficients and an external potential in the form of modulated quadratic potential is obtained by the similarity transformation. Numerical simulations are performed for comparison with the analytical solutions and to confirm the stability of the rogue wave solution obtained. These optical rogue waves are built by the products of parabolic-cylinder functions and the basic rogue wave solution of the standard nonlinear Schrödinger equation. Such rogue waves may appear in different forms, as the hump and paw profiles.
Dark- and bright-rogue-wave solutions for media with long-wave-short-wave resonance.
Chen, Shihua; Grelu, Philippe; Soto-Crespo, J M
2014-01-01
Exact explicit rogue-wave solutions of intricate structures are presented for the long-wave-short-wave resonance equation. These vector parametric solutions feature coupled dark- and bright-field counterparts of the Peregrine soliton. Numerical simulations show the robustness of dark and bright rogue waves in spite of the onset of modulational instability. Dark fields originate from the complex interplay between anomalous dispersion and the nonlinearity driven by the coupled long wave. This unusual mechanism, not available in scalar nonlinear wave equation models, can provide a route to the experimental realization of dark rogue waves in, for instance, negative index media or with capillary-gravity waves.
Akhmediev, N.; Ankiewicz, A.; Soto-Crespo, J. M.
2009-10-15
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.
Are Rogue Waves Really Unexpected?
NASA Astrophysics Data System (ADS)
Fedele, Francesco
2016-05-01
An unexpected wave is defined by Gemmrich & Garrett (2008) as a wave that is much taller than a set of neighboring waves. Their definition of "unexpected" refers to a wave that is not anticipated by a casual observer. Clearly, unexpected waves defined in this way are predictable in a statistical sense. They can occur relatively often with a small or moderate crest height, but large unexpected waves that are rogue are rare. Here, this concept is elaborated and statistically described based on a third-order nonlinear model. In particular, the conditional return period of an unexpected wave whose crest exceeds a given threshold is developed. This definition leads to greater return periods or on average less frequent occurrences of unexpected waves than those implied by the conventional return periods not conditioned on a reference threshold. Ultimately, it appears that a rogue wave that is also unexpected would have a lower occurrence frequency than that of a usual rogue wave. As specific applications, the Andrea and WACSIS rogue wave events are examined in detail. Both waves appeared without warning and their crests were nearly $2$-times larger than the surrounding $O(10)$ wave crests, and thus unexpected. The two crest heights are nearly the same as the threshold~$h_{0.3\\cdot10^{6}}\\sim1.6H_{s}$ exceeded on average once every~$0.3\\cdot 10^{6}$ waves, where $H_s$ is the significant wave height. In contrast, the Andrea and WACSIS events, as both rogue and unexpected, would occur slightly less often and on average once every~$3\\cdot10^{6}$ and~$0.6\\cdot10^6$ waves respectively.
Rogue Waves and Modulational Instability
NASA Astrophysics Data System (ADS)
Zakharov, V. E.; Dyachenko, A.
2015-12-01
The most plausible cause of rogue wave formation in a deep ocean is development of modulational instability of quasimonochromatic wave trains. An adequate model for study of this phenomenon is the Euler equation for potential flow of incompressible fluid with free surface in 2-D geometry. Numerical integration of these equations confirms completely the conjecture of rogue wave formation from modulational instability but the procedure is time consuming for determination of rogue wave appearance probability for a given shape of wave energy spectrum. This program can be realized in framework of simpler model using replacement of the exact interaction Hamiltonian by more compact Hamiltonian. There is a family of such models. The popular one is the Nonlinear Schrodinger equation (NLSE). This model is completely integrable and suitable for numerical simulation but we consider that it is oversimplified. It misses such important phenomenon as wave breaking. Recently, we elaborated much more reliable model that describes wave breaking but is as suitable as NLSE from the point of numerical modeling. This model allows to perform massive numerical experiments and study statistics of rogue wave formation in details.
Evolution of rogue waves in dusty plasmas
Tolba, R. E. El-Bedwehy, N. A.; Moslem, W. M.; El-Labany, S. K.
2015-04-15
The evolution of rogue waves associated with the dynamics of positively charged dust grains that interact with streaming electrons and ions is investigated. Using a perturbation method, the basic set of fluid equations is reduced to a nonlinear Schrödinger equation (NLSE). The rational solution of the NLSE is presented, which proposed as an effective tool for studying the rogue waves in Jupiter. It is found that the existence region of rogue waves depends on the dust-acoustic speed and the streaming densities of the ions and electrons. Furthermore, the supersonic rogue waves are much taller than the subsonic rogue waves by ∼25 times.
Slow deterministic vector rogue waves
NASA Astrophysics Data System (ADS)
Sergeyev, S. V.; Kolpakov, S. A.; Mou, Ch.; Jacobsen, G.; Popov, S.; Kalashnikov, V.
2016-03-01
For an erbium-doped fiber laser mode-locked by carbon nanotubes, we demonstrate experimentally and theoretically a new type of the vector rogue waves emerging as a result of the chaotic evolution of the trajectories between two orthogonal states of polarization on the Poincare sphere. In terms of fluctuation induced phenomena, by tuning polarization controller for the pump wave and in-cavity polarization controller, we are able to control the Kramers time, i.e. the residence time of the trajectory in vicinity of each orthogonal state of polarization, and so can cause the rare events satisfying rogue wave criteria and having the form of transitions from the state with the long residence time to the state with a short residence time.
Acoustic Remote Sensing of Rogue Waves
NASA Astrophysics Data System (ADS)
Parsons, Wade; Kadri, Usama
2016-04-01
We propose an early warning system for approaching rogue waves using the remote sensing of acoustic-gravity waves (AGWs) - progressive sound waves that propagate at the speed of sound in the ocean. It is believed that AGWs are generated during the formation of rogue waves, carrying information on the rogue waves at near the speed of sound, i.e. much faster than the rogue wave. The capability of identifying those special sound waves would enable detecting rogue waves most efficiently. A lot of promising work has been reported on AGWs in the last few years, part of which in the context of remote sensing as an early detection of tsunami. However, to our knowledge none of the work addresses the problem of rogue waves directly. Although there remains some uncertainty as to the proper definition of a rogue wave, there is little doubt that they exist and no one can dispute the potential destructive power of rogue waves. An early warning system for such extreme waves would become a demanding safety technology. A closed form expression was developed for the pressure induced by an impulsive source at the free surface (the Green's function) from which the solution for more general sources can be developed. In particular, we used the model of the Draupner Wave of January 1st, 1995 as a source and calculated the induced AGW signature. In particular we studied the AGW signature associated with a special feature of this wave, and characteristic of rogue waves, of the absence of any local set-down beneath the main crest and the presence of a large local set-up.
The destructive impact of the rogue waves
NASA Astrophysics Data System (ADS)
Shamin, Roman
2013-04-01
In our talk rogue waves at the ocean will be considered. By means of numerical modeling dangerous impact of rogue waves on the ships and oil rigs is calculated. Cases when these waves can bring in accident are considered. Using statistics of emergence of waves (see [1]-[2]), it is possible to estimate risks in each case. These results can be used for safety of the ships and oil rigs from rogue waves. References [1] V.E. Zakharov, A.I. Dyachenko, R.V. Shamin. How probability for freak wave formation can be found // THE EUROPEAN PHYSICAL JOURNAL - SPECIAL TOPICS Volume 185, Number 1, 113-124, DOI: 10.1140/epjst/e2010-01242-y [2] V.E. Zakharov, R.V. Shamin. Statistics of rogue waves in computer experiments // JETP Letters, 2012, V. 96, Issue 1, pp 66-69.
Nonlinear Talbot effect of rogue waves.
Zhang, Yiqi; Belić, Milivoj R; Zheng, Huaibin; Chen, Haixia; Li, Changbiao; Song, Jianping; Zhang, Yanpeng
2014-03-01
Akhmediev and Kuznetsov-Ma breathers are rogue wave solutions of the nonlinear Schrödinger equation (NLSE). Talbot effect (TE) is an image recurrence phenomenon in the diffraction of light waves. We report the nonlinear TE of rogue waves in a cubic medium. It is different from the linear TE, in that the wave propagates in a NL medium and is an eigenmode of NLSE. Periodic rogue waves impinging on a NL medium exhibit recurrent behavior, but only at the TE length and at the half-TE length with a π-phase shift; the fractional TE is absent. The NL TE is the result of the NL interference of the lobes of rogue wave breathers. This interaction is related to the transverse period and intensity of breathers, in that the bigger the period and the higher the intensity, the shorter the TE length.
Rogue waves in a multistable system.
Pisarchik, Alexander N; Jaimes-Reátegui, Rider; Sevilla-Escoboza, Ricardo; Huerta-Cuellar, G; Taki, Majid
2011-12-30
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.
Rogue Waves in a Multistable System
NASA Astrophysics Data System (ADS)
Pisarchik, Alexander N.; Jaimes-Reátegui, Rider; Sevilla-Escoboza, Ricardo; Huerta-Cuellar, G.; Taki, Majid
2011-12-01
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.
Book review: Rogue waves in the ocean
Geist, Eric L.
2011-01-01
Review info: Rogue Waves in the Ocean. Advances in Geophysical and Environmental Mechanics and Mathematics. By Christian Kharif, Efim Pelinovsky and Alexey Slunyaev, 2009. ISBN: 978-3540884187, xiii, 216 pp.
NASA Astrophysics Data System (ADS)
Waseda, Takuji
2010-03-01
Giant episodic ocean waves that suddenly soar like a wall of water out of an otherwise calm sea are not just a legend. Such waves—which in the past have been called “abnormal,” “exceptional,” “extreme,” and even “vicious killer” waves—are now commonly known as “rogue waves” or “freak waves.” These waves have sunk or severely damaged 22 supercarriers in the world and caused the loss of more than 500 lives in the past 40 years. The largest wave registered by reliable instruments reached 30 meters in height, and the largest wave recorded by visual observation reached about 34 meters, equivalent to the height of an eight-story building. Tales of seafarers from Christopher Columbus to the passengers of luxury cruise ships had long been undervalued by scientists, but in the past 10 or so years, those historical notes and modern testimonies have been scientifically dissected to reveal the nature of these monster waves.
Line Rogue Waves in the Mel'nikov Equation
NASA Astrophysics Data System (ADS)
Shi, Yongkang
2017-07-01
General line rogue waves in the Mel'nikov equation are derived via the Hirota bilinear method, which are given in terms of determinants whose matrix elements have plain algebraic expressions. It is shown that fundamental rogue waves are line rogue waves, which arise from the constant background with a line profile and then disappear into the constant background again. By means of the regulation of free parameters, two subclass of nonfundamental rogue waves are generated, which are called as multirogue waves and higher-order rogue waves. The multirogue waves consist of several fundamental line rogue waves, which arise from the constant background and then decay back to the constant background. The higher-order rogue waves start from a localised lump and retreat back to it. The dynamical behaviours of these line rogue waves are demonstrated by the density and the three-dimensional figures.
Triggering rogue waves in opposing currents.
Onorato, Miguel; Proment, Davide; Toffoli, Alessandro
2011-10-28
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 Schrödinger equation with nonconstant coefficient is applicable. In particular, nonlinear optics laboratory experiments are natural candidates for verifying experimentally our results.
Optical rogue waves and stimulated supercontinuum generation
NASA Astrophysics Data System (ADS)
Solli, Daniel R.; Ropers, Claus; Jalali, Bahram
2010-06-01
Nonlinear action is known for its ability to create unusual phenomena and unexpected events. Optical rogue waves-freak pulses of broadband light arising in nonlinear fiber-testify to the fact that optical nonlinearities are no less capable of generating anomalous events than those in other physical contexts. In this paper, we will review our work on optical rogue waves, an ultrafast phenomenon counterpart to the freak ocean waves known to roam the open oceans. We will discuss the experimental observation of these rare events in real time and the measurement of their heavytailed statistical properties-a probabilistic form known to appear in a wide variety of other complex systems from financial markets to genetics. The nonlinear Schrödinger equation predicts the existence of optical rogue waves, offering a means to study their origins with simulations. We will also discuss the type of initial conditions behind optical rogue waves. Because a subtle but specific fluctuation leads to extreme waves, the rogue wave instability can be harnessed to produce these events on demand. By exploiting this property, it is possible to produce a new type of optical switch as well as a supercontinuum source that operates in the long pulse regime but still achieves a stable, coherent output.
Nonparaxial rogue waves in optical Kerr media.
Temgoua, D D Estelle; Kofane, T C
2015-06-01
We consider the inhomogeneous nonparaxial nonlinear Schrödinger (NLS) equation with varying dispersion, nonlinearity, and nonparaxiality coefficients, which governs the nonlinear wave propagation in an inhomogeneous optical fiber system. We present the similarity and Darboux transformations and for the chosen specific set of parameters and free functions, the first- and second-order rational solutions of the nonparaxial NLS equation are generated. In particular, the features of rogue waves throughout polynomial and Jacobian elliptic functions are analyzed, showing the nonparaxial effects. It is shown that the nonparaxiality increases the intensity of rogue waves by increasing the length and reducing the width simultaneously, by the way it increases their speed and penalizes interactions between them. These properties and the characteristic controllability of the nonparaxial rogue waves may give another opportunity to perform experimental realizations and potential applications in optical fibers.
Instabilities, breathers and rogue waves in optics
NASA Astrophysics Data System (ADS)
Dudley, John M.; Dias, Frédéric; Erkintalo, Miro; Genty, Goëry
2014-10-01
Optical rogue waves are rare, extreme fluctuations in the value of an optical field. The term 'optical rogue wave' was first used in the context of an analogy between pulse propagation in an optical fibre and wave group propagation on deep water, but has since been generalized to describe many other processes in optics. This Review provides an overview of the field, concentrating primarily on propagation in optical fibre systems that exhibit nonlinear breather and soliton dynamics, but also discussing other optical systems in which extreme events have been reported. Although statistical features such as long-tailed probability distributions are often considered to be the defining feature of rogue waves, we emphasize the underlying physical processes that drive the appearance of extreme optical structures.
NASA Astrophysics Data System (ADS)
Shukla, P. K.; Moslem, W. M.
2012-02-01
It is shown that the nonlinear interaction between the magnetic field-aligned circularly polarized (CP) dispersive Alfvén waves and low-frequency electrostatic perturbations give rise to Alfvénic rogue waves in magnetized plasmas. Our results reveal the left-hand CP Alfvénic wave supports both supersonic and subsonic Alfvénic rogue waves. The latter can propagate for backward wave only. The right-hand CP Alfvénic rouge waves appear on account of the amplitude modulation of the waves by quasi-stationary density modulations. The amplitude of the right-hand CP Alfvénic rogue waves decreases with the increase of the plasma number density, but it increases with the increase of the magnetic field strength. However, the amplitude of the subsonic left-hand CP Alfvénic rogue wave becomes stronger with the excess of the plasma number density, but it shrinks with stronger magnetic field strength. Finally, we briefly discuss the relevance of our investigation to the role of the nonlinear Alfvén waves that power the solar wind.
Rogue waves in Lugiato-Lefever equation with variable coefficients
NASA Astrophysics Data System (ADS)
Kol, Guy; Kingni, Sifeu; Woafo, Paul
2014-11-01
In this paper, we theoretically investigate the generation of optical rogue waves from a Lugiato-Lefever equation with variable coefficients by using the nonlinear Schrödinger equation-based constructive method. Exact explicit rogue-wave solutions of the Lugiato-Lefever equation with constant dispersion, detuning and dissipation are derived and presented. The bright rogue wave, intermediate rogue wave and the dark rogue wave are obtained by changing the value of one parameter in the exact explicit solutions corresponding to the external pump power of a continuous-wave laser.
Wind Generated Rogue Waves in an Annular Wave Flume.
Toffoli, A; Proment, D; Salman, H; Monbaliu, J; Frascoli, F; Dafilis, M; Stramignoni, E; Forza, R; Manfrin, M; Onorato, M
2017-04-07
We investigate experimentally the statistical properties of a wind-generated wave field and the spontaneous formation of rogue waves in an annular flume. Unlike many experiments on rogue waves where waves are mechanically generated, here the wave field is forced naturally by wind as it is in the ocean. What is unique about the present experiment is that the annular geometry of the tank makes waves propagating circularly in an unlimited-fetch condition. Within this peculiar framework, we discuss the temporal evolution of the statistical properties of the surface elevation. We show that rogue waves and heavy-tail statistics may develop naturally during the growth of the waves just before the wave height reaches a stationary condition. Our results shed new light on the formation of rogue waves in a natural environment.
Dynamics of nonautonomous rogue waves in Bose-Einstein condensate
Zhao, Li-Chen
2013-02-15
We study rogue waves of Bose-Einstein condensate (BEC) analytically in a time-dependent harmonic trap with a complex potential. Properties of the nonautonomous rogue waves are investigated analytically. It is reported that there are possibilities to 'catch' rogue waves through manipulating nonlinear interaction properly. The results provide many possibilities to manipulate rogue waves experimentally in a BEC system. - Highlights: Black-Right-Pointing-Pointer One more generalized rogue wave solutions are presented. Black-Right-Pointing-Pointer Present one possible way to catch a rouge wave. Black-Right-Pointing-Pointer Properties of rogue waves are investigated analytically for the first time. Black-Right-Pointing-Pointer Provide many possibilities to manipulate rogue waves in BEC.
Optical Rogue Waves in Vortex Turbulence.
Gibson, Christopher J; Yao, Alison M; Oppo, Gian-Luca
2016-01-29
We present a spatiotemporal mechanism for producing 2D optical rogue waves in the presence of a turbulent state with creation, interaction, and annihilation of optical vortices. Spatially periodic structures with bound phase lose stability to phase unbound turbulent states in complex Ginzburg-Landau and Swift-Hohenberg models with external driving. When the pumping is high and the external driving is low, synchronized oscillations are unstable and lead to spatiotemporal vortex-mediated turbulence with high excursions in amplitude. Nonlinear amplification leads to rogue waves close to turbulent optical vortices, where the amplitude tends to zero, and to probability density functions (PDFs) with long tails typical of extreme optical events.
Optical rogue waves associated with the negative coherent coupling in an isotropic medium
NASA Astrophysics Data System (ADS)
Sun, Wen-Rong; Tian, Bo; Jiang, Yan; Zhen, Hui-Ling
2015-02-01
Optical rogue waves of the coupled nonlinear Schrödinger equations with negative coherent coupling, which describe the propagation of orthogonally polarized optical waves in an isotropic medium, are reported. We construct and discuss a family of the vector rogue-wave solutions, including the bright rogue waves, four-petaled rogue waves, and dark rogue waves. A bright rogue wave without a valley can split up, giving birth to two bright rogue waves, and an eye-shaped rogue wave can split up, giving birth to two dark rogue waves.
Optical rogue waves associated with the negative coherent coupling in an isotropic medium.
Sun, Wen-Rong; Tian, Bo; Jiang, Yan; Zhen, Hui-Ling
2015-02-01
Optical rogue waves of the coupled nonlinear Schrödinger equations with negative coherent coupling, which describe the propagation of orthogonally polarized optical waves in an isotropic medium, are reported. We construct and discuss a family of the vector rogue-wave solutions, including the bright rogue waves, four-petaled rogue waves, and dark rogue waves. A bright rogue wave without a valley can split up, giving birth to two bright rogue waves, and an eye-shaped rogue wave can split up, giving birth to two dark rogue waves.
Crossing seas and occurrence of rogue waves
NASA Astrophysics Data System (ADS)
Bitner-Gregersen, Elzbieta; Toffoli, Alessandro
2017-04-01
The study is addressing crossing wave systems which may lead to formation of rogue waves. Onorato et al. (2006, 2010) have shown using the Nonlinear Schr?dringer (NLS) equations that the modulational instability and rogue waves can be triggered by a peculiar form of directional sea state, where two identical, crossing, narrow-banded random wave systems interact with each other. Such results have been underpinned by numerical simulations of the Euler equations solved with a Higher Order Spectral Method (HOSM) and experimental observations (Toffoli et al., 2011). They substantiate a dependence of the angle between the mean directions of propagation of the two crossing wave systems, with a maximum rogue wave probability for angles of approximately 40 degrees. Such an unusual sea state of two almost identical wave systems (approximately the same significant wave height and mean frequency) with high steepness and different directions was observed during the accident to the cruise ship Louis Majesty (Cavaleri et al. 2012). Occurrence of wind sea and swell having almost the same spectral period and significant wave height and crossing at the angle 40o < β < 60o has been investigated recently by Bitner-Gregersen and Toffoli (2014). The numerical simulations carried out by HOSM have shown that although directionality has an effect on the occurrence of extreme waves in crossing seas, rogue waves can occur not only for narrow-banded wave directional spreading but also broader spectral conditions. It seems that the most critical condition for occurrence of rogue waves in crossing seas is associated with energy and frequency of two wave systems while the angle between the wave systems and directional spreading will decide how large extreme waves will grow. The 40 degree angle and narrow-banded directional spreading seem to be generating the largest waves. The study shows that occurrence of rogue-prone crossing sea states is location specific, depending strongly on local
Breathing rogue wave observed in numerical experiment.
Ruban, V P
2006-09-01
Numerical simulations of the recently derived fully nonlinear equations of motion for long-crested water waves [V. P. Ruban, Phys. Rev. E 71, 055303(R) (2005)] with quasirandom initial conditions are reported, which show the spontaneous formation of a single extreme wave on deep water. This rogue wave behaves in an oscillating manner and exists for a relatively long time (many wave periods) without significant change of its maximal amplitude.
Complementary optical rogue waves in parametric three-wave mixing.
Chen, Shihua; Cai, Xian-Ming; Grelu, Philippe; Soto-Crespo, J M; Wabnitz, Stefan; Baronio, Fabio
2016-03-21
We investigate the resonant interaction of two optical pulses of the same group velocity with a pump pulse of different velocity in a weakly dispersive quadratic medium and report on the complementary rogue wave dynamics which are unique to such a parametric three-wave mixing. Analytic rogue wave solutions up to the second order are explicitly presented and their robustness is confirmed by numerical simulations, in spite of the onset of modulation instability activated by quantum noise.
Rogue-wave pattern transition induced by relative frequency.
Zhao, Li-Chen; Xin, Guo-Guo; Yang, Zhan-Ying
2014-08-01
We revisit a rogue wave in a two-mode nonlinear fiber whose dynamics is described by two-component coupled nonlinear Schrödinger equations. The relative frequency between two modes can induce different rogue wave patterns transition. In particular, we find a four-petaled flower structure rogue wave can exist in the two-mode coupled system, which possesses an asymmetric spectrum distribution. Furthermore, spectrum analysis is performed on these different type rogue waves, and the spectrum relations between them are discussed. We demonstrate qualitatively that different modulation instability gain distribution can induce different rogue wave excitation patterns. These results would deepen our understanding of rogue wave dynamics in complex systems.
Controlling rogue waves in inhomogeneous Bose-Einstein condensates.
Loomba, Shally; Kaur, Harleen; Gupta, Rama; Kumar, C N; Raju, Thokala Soloman
2014-05-01
We present the exact rogue wave solutions of the quasi-one-dimensional inhomogeneous Gross-Pitaevskii equation by using similarity transformation. Then, by employing the exact analytical solutions we have studied the controllable behavior of rogue waves in the Bose-Einstein condensates context for the experimentally relevant systems. Additionally, we have also investigated the nonlinear tunneling of rogue waves through a conventional hyperbolic barrier and periodic barrier. We have found that, for the conventional nonlinearity barrier case, rogue waves are localized in space and time and get amplified near the barrier, while for the dispersion barrier case rogue waves are localized in space and propagating in time and their amplitude is reduced at the barrier location. In the case of the periodic barrier, the interesting dynamical features of rogue waves are obtained and analyzed analytically.
Generation mechanisms of fundamental rogue wave spatial-temporal structure
NASA Astrophysics Data System (ADS)
Ling, Liming; Zhao, Li-Chen; Yang, Zhan-Ying; Guo, Boling
2017-08-01
We discuss the generation mechanism of fundamental rogue wave structures in N -component coupled systems, based on analytical solutions of the nonlinear Schrödinger equation and modulational instability analysis. Our analysis discloses that the pattern of a fundamental rogue wave is determined by the evolution energy and growth rate of the resonant perturbation that is responsible for forming the rogue wave. This finding allows one to predict the rogue wave pattern without the need to solve the N -component coupled nonlinear Schrödinger equation. Furthermore, our results show that N -component coupled nonlinear Schrödinger systems may possess N different fundamental rogue wave patterns at most. These results can be extended to evaluate the type and number of fundamental rogue wave structure in other coupled nonlinear systems.
Rogue waves of a (3 + 1) -dimensional nonlinear evolution equation
NASA Astrophysics Data System (ADS)
Shi, Yu-bin; Zhang, Yi
2017-03-01
General high-order rogue waves of a (3 + 1) -dimensional Nonlinear Evolution Equation ((3+1)-d NEE) are obtained by the Hirota bilinear method, which are given in terms of determinants, whose matrix elements possess plain algebraic expressions. It is shown that the simplest (fundamental) rogue waves are line rogue waves which arise from the constant background with a line profile and then disappear into the constant background again. Two subclass of nonfundamental rogue waves are analyzed in details. By proper means of the regulations of free parameters, the dynamics of multi-rogue waves and high-order rogue waves have been illustrated in (x,t) plane and (y,z) plane by three dimensional figures.
Rogue-wave pattern transition induced by relative frequency
NASA Astrophysics Data System (ADS)
Zhao, Li-Chen; Xin, Guo-Guo; Yang, Zhan-Ying
2014-08-01
We revisit a rogue wave in a two-mode nonlinear fiber whose dynamics is described by two-component coupled nonlinear Schrödinger equations. The relative frequency between two modes can induce different rogue wave patterns transition. In particular, we find a four-petaled flower structure rogue wave can exist in the two-mode coupled system, which possesses an asymmetric spectrum distribution. Furthermore, spectrum analysis is performed on these different type rogue waves, and the spectrum relations between them are discussed. We demonstrate qualitatively that different modulation instability gain distribution can induce different rogue wave excitation patterns. These results would deepen our understanding of rogue wave dynamics in complex systems.
Controllable optical rogue waves in the femtosecond regime.
Dai, Chao-Qing; Zhou, Guo-Quan; Zhang, Jie-Fang
2012-01-01
We derive analytical rogue wave solutions of variable-coefficient higher-order nonlinear Schrödinger equations describing the femtosecond pulse propagation via a transformation connected with the constant-coefficient Hirota equation. Then we discuss the propagation behaviors of controllable rogue waves, including recurrence, annihilation, and sustainment in a periodic distributed fiber system and an exponential dispersion decreasing fiber. Finally, we investigate nonlinear tunneling effects for rogue waves.
Spatial Rogue Waves in Photorefractive Ferroelectrics.
Pierangeli, D; Di Mei, F; Conti, C; Agranat, A J; DelRe, E
2015-08-28
Rogue waves are observed as light propagates in the extreme nonlinear regime that occurs when a photorefractive ferroelectric crystal is undergoing a structural phase transition. The transmitted spatial light distribution contains bright localized spots of anomalously large intensity that follow a signature long-tail statistics that disappears as the nonlinearity is weakened. The isolated wave events form as out-of-equilibrium response and disorder enhance the Kerr-saturated nonlinearity at the critical point. Self-similarity associable to the individual observed filaments and numerical simulations of the generalized nonlinear Schrödinger equation suggests that dynamics of soliton fusions and scale invariance can microscopically play an important role in the observed rogue intensities and statistics.
A coupled "AB" system: Rogue waves and modulation instabilities.
Wu, C F; Grimshaw, R H J; Chow, K W; Chan, H N
2015-10-01
Rogue waves are unexpectedly large and localized displacements from an equilibrium position or an otherwise calm background. For the nonlinear Schrödinger (NLS) model widely used in fluid mechanics and optics, these waves can occur only when dispersion and nonlinearity are of the same sign, a regime of modulation instability. For coupled NLS equations, rogue waves will arise even if dispersion and nonlinearity are of opposite signs in each component as new regimes of modulation instability will appear in the coupled system. The same phenomenon will be demonstrated here for a coupled "AB" system, a wave-current interaction model describing baroclinic instability processes in geophysical flows. Indeed, the onset of modulation instability correlates precisely with the existence criterion for rogue waves for this system. Transitions from "elevation" rogue waves to "depression" rogue waves are elucidated analytically. The dispersion relation as a polynomial of the fourth order may possess double pairs of complex roots, leading to multiple configurations of rogue waves for a given set of input parameters. For special parameter regimes, the dispersion relation reduces to a cubic polynomial, allowing the existence criterion for rogue waves to be computed explicitly. Numerical tests correlating modulation instability and evolution of rogue waves were conducted.
Generation of rogue waves in a wave tank
NASA Astrophysics Data System (ADS)
Lechuga, A.
2012-04-01
Rogue waves have been reported as causing damages and ship accidents all over the oceans of the world. For this reason in the past decades theoretical studies have been carried out with the double aim of improving the knowledge of their main characteristics and of attempting to predict its sudden appearance. As an effort on this line we are trying to generate them in a water tank. The description of the procedure to do that is the objective of this presentation. After Akhmediev et al. (2011) we use a symmetric spectrum as input on the wave maker to produce waves with a rate(Maximun wave height/ significant wave height) of 2.33 and a kurtosis of 4.77, clearly between the limits of rogue waves. As it was pointed out by Janssen (2003), Onorato et al. (2006) and Kharif, Pelinovsky and Slunyaev (2009) modulation instability is enhanced when waves depart from Gaussian statistics (i.e. big kurtosis) and therefore both numbers enforce the criterion that we are generating genuine rogue waves. The same is confirmed by Shemer (2010) and Dudley et al.(2009) from a different perspective. If besides being symmetrical the spectrum is triangular, following Akhmediev(2011),the generated waves are even more conspicuously rogue waves.
NASA Astrophysics Data System (ADS)
Polukhina, Oxana; Kurkin, Andrey; Pelinovsky, Efim
2010-05-01
The investigation of anomalously large amplitude surface gravity waves on the sea surface (rogue or freak waves), which can appear suddenly and disappear in the same abrupt way, is very extensive in the recent years (see e.g., book [Kharif, Pelinovsky, Slunyaev 2009] and references there). However, any sudden displacements of water level or changes in flow velocities can also appear in the ocean wave motions of other types, including geophysical large-scale fields. The number of observations of such waves is still very small, they are even almost absent, but the investigations of such possible processes seem to be important for the applications. In the present paper the problem of rogue waves is discussed for edge waves in the coastal zone. Such waves belong to the class of topographically trapped waves, which are supposed to play dominant role in the dynamics of oceanic coastal zone. The amplitude of the waves reaches a maximum at the edge, and they are attenuated offshore. Direct visual observations of such waves are difficult, but such waves have been detected instrumentally in the nearshore wave field many times (see e.g. [Huntley and Bowen 1973; Bryan, Hows and Bowen 1998]). Edge waves are often considered as the major factor of the long-term evolution of coastal line, forming the rhythmic crescentic bars [Dolan and Ferm 1968; Bowen and Inman 1971; Guza and Inman 1975; Guza and Bowen 1981; Holman and Bowen 1982; Komar 1998]. In the present paper we summarize the results of the study of the nonlinear mechanisms of possible freak edge wave appearance: nonlinear dispersion enhancement and modulation instability.
The Making of the Andrea Wave and other Rogues.
Donelan, Mark A; Magnusson, Anne-Karin
2017-03-08
Unexpectedly large ocean waves or 'rogues' are sometimes claimed to be the cause of damage to ships at sea and to offshore structures. While wind-driven wave models are capable of predicting the average characteristics of waves, the maximum height of rogues that may occur is yet unknown. Rogues form in the open ocean through the addition of elemental wave trains or groups and, infrequently, with many elements coming together in phase, producing rogues. Here we perform directional analyses on one of the steepest rogues ever recorded: the Andrea wave. We find that the Andrea wave was close to the breaking-limited height. Analysis of the 72 twenty minute records on the day of the Andrea wave yields encounter return periods of about 21 days for maximally steep waves, while less steep rogues occur about twice daily. An explicit formula is given for the encounter probability, based on the target area. This work answers the critical questions regarding rogues in the design and operation of ships and offshore structures: how high can rogues be and how frequently they occur.
Rogue waves in the Davey-Stewartson I equation.
Ohta, Yasuhiro; Yang, Jianke
2012-09-01
General rogue waves in the Davey-Stewartson-I equation are derived by the bilinear method. It is shown that the simplest (fundamental) rogue waves are line rogue waves which arise from the constant background with a line profile and then disappear into the constant background again. It is also shown that multirogue waves describe the interaction of several fundamental rogue waves. These multirogue waves also arise from the constant background and then decay back to it, but in the intermediate times, interesting curvy wave patterns appear. However, higher-order rogue waves exhibit different dynamics. Specifically, only part of the wave structure in the higher-order rogue waves rises from the constant background and then retreats back to it, and this transient wave possesses patterns such as parabolas. But the other part of the wave structure comes from the far distance as a localized lump, which decelerates to the near field and interacts with the transient rogue wave, and is then reflected back and accelerates to the large distance again.
Optical rogue waves in telecommunication data streams
Vergeles, Sergey; Turitsyn, Sergei K.
2011-06-15
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.
Rogue wave spectra of the Kundu-Eckhaus equation.
Bayındır, Cihan
2016-06-01
In this paper we analyze the rogue wave spectra of the Kundu-Eckhaus equation (KEE). We compare our findings with their nonlinear Schrödinger equation (NLSE) analogs and show that the spectra of the individual rogue waves significantly differ from their NLSE analogs. A remarkable difference is the one-sided development of the triangular spectrum before the rogue wave becomes evident in time. Also we show that increasing the skewness of the rogue wave results in increased asymmetry in the triangular Fourier spectra. Additionally, the triangular spectra of the rogue waves of the KEE begin to develop at earlier stages of their development compared to their NLSE analogs, especially for larger skew angles. This feature may be used to enhance the early warning times of the rogue waves. However, we show that in a chaotic wave field with many spectral components the triangular spectra remain as the main attribute as a universal feature of the typical wave fields produced through modulation instability and characteristic features of the KEE's analytical rogue wave spectra may be suppressed in a realistic chaotic wave field.
Rogue wave spectra of the Kundu-Eckhaus equation
NASA Astrophysics Data System (ADS)
Bayındır, Cihan
2016-06-01
In this paper we analyze the rogue wave spectra of the Kundu-Eckhaus equation (KEE). We compare our findings with their nonlinear Schrödinger equation (NLSE) analogs and show that the spectra of the individual rogue waves significantly differ from their NLSE analogs. A remarkable difference is the one-sided development of the triangular spectrum before the rogue wave becomes evident in time. Also we show that increasing the skewness of the rogue wave results in increased asymmetry in the triangular Fourier spectra. Additionally, the triangular spectra of the rogue waves of the KEE begin to develop at earlier stages of their development compared to their NLSE analogs, especially for larger skew angles. This feature may be used to enhance the early warning times of the rogue waves. However, we show that in a chaotic wave field with many spectral components the triangular spectra remain as the main attribute as a universal feature of the typical wave fields produced through modulation instability and characteristic features of the KEE's analytical rogue wave spectra may be suppressed in a realistic chaotic wave field.
Optical rogue wave statistics in laser filamentation.
Kasparian, Jérôme; Béjot, Pierre; Wolf, Jean-Pierre; Dudley, John M
2009-07-06
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.
Time-reversal generation of rogue waves.
Chabchoub, Amin; Fink, Mathias
2014-03-28
The formation of extreme localizations in nonlinear dispersive media can be explained and described within the framework of nonlinear evolution equations, such as the nonlinear Schrödinger equation (NLS). Within the class of exact NLS breather solutions on a finite background, which describe the modulational instability of monochromatic wave trains, the hierarchy of rational solutions localized in both time and space is considered to provide appropriate prototypes to model rogue wave dynamics. Here, we use the time-reversal invariance of the NLS to propose and experimentally demonstrate a new approach to constructing strongly nonlinear localized waves focused in both time and space. The potential applications of this time-reversal approach include remote sensing and motivated analogous experimental analysis in other nonlinear dispersive media, such as optics, Bose-Einstein condensates, and plasma, where the wave motion dynamics is governed by the NLS.
The Making of the Andrea Wave and other Rogues
NASA Astrophysics Data System (ADS)
Donelan, Mark A.; Magnusson, Anne-Karin
2017-03-01
Unexpectedly large ocean waves or ‘rogues’ are sometimes claimed to be the cause of damage to ships at sea and to offshore structures. While wind-driven wave models are capable of predicting the average characteristics of waves, the maximum height of rogues that may occur is yet unknown. Rogues form in the open ocean through the addition of elemental wave trains or groups and, infrequently, with many elements coming together in phase, producing rogues. Here we perform directional analyses on one of the steepest rogues ever recorded: the Andrea wave. We find that the Andrea wave was close to the breaking-limited height. Analysis of the 72 twenty minute records on the day of the Andrea wave yields encounter return periods of about 21 days for maximally steep waves, while less steep rogues occur about twice daily. An explicit formula is given for the encounter probability, based on the target area. This work answers the critical questions regarding rogues in the design and operation of ships and offshore structures: how high can rogues be and how frequently they occur.
The Making of the Andrea Wave and other Rogues
Donelan, Mark A.; Magnusson, Anne-Karin
2017-01-01
Unexpectedly large ocean waves or ‘rogues’ are sometimes claimed to be the cause of damage to ships at sea and to offshore structures. While wind-driven wave models are capable of predicting the average characteristics of waves, the maximum height of rogues that may occur is yet unknown. Rogues form in the open ocean through the addition of elemental wave trains or groups and, infrequently, with many elements coming together in phase, producing rogues. Here we perform directional analyses on one of the steepest rogues ever recorded: the Andrea wave. We find that the Andrea wave was close to the breaking-limited height. Analysis of the 72 twenty minute records on the day of the Andrea wave yields encounter return periods of about 21 days for maximally steep waves, while less steep rogues occur about twice daily. An explicit formula is given for the encounter probability, based on the target area. This work answers the critical questions regarding rogues in the design and operation of ships and offshore structures: how high can rogues be and how frequently they occur. PMID:28272520
Rogue waves emerging from the resonant interaction of three waves.
Baronio, Fabio; Conforti, Matteo; Degasperis, Antonio; Lombardo, Sara
2013-09-13
We introduce a novel family of analytic solutions of the three-wave resonant interaction equations for the purpose of modeling unique events, i.e., "amplitude peaks" which are isolated in space and time. The description of these solutions is likely to be a crucial step in the understanding and forecasting of rogue waves in a variety of multicomponent wave dynamics, from oceanography to optics and from plasma physics to acoustics.
Harnessing and control of optical rogue waves in supercontinuum generation.
Dudley, John M; Genty, Goëry; Eggleton, Benjamin J
2008-03-17
We present a numerical study of the evolution dynamics of "optical rogue waves", statistically-rare extreme red-shifted soliton pulses arising from supercontinuum generation in photonic crystal fiber [D. R. Solli, et al. Nature 450, 1054-1058 (2007)]. Our specific aim is to use nonlinear Schrödinger equation simulations to identify ways in which the rogue wave dynamics can be actively controlled, and we demonstrate that rogue wave generation can be enhanced by an order of magnitude through a small modulation across the input pulse envelope and effectively suppressed through the use of a sliding frequency filter.
Rogue waves in the ocean - review and progress
NASA Astrophysics Data System (ADS)
Pelinovsky, Efim; Kharif, Christian; Slunyaev, Alexey
2010-05-01
Rogue waves in the ocean and physical mechanisms of their appearance are discussed. Theyse waves are among waves naturally observed by people on the sea surface that represent inseparable feature of the Ocean. Rogue waves appear from nowhere, cause danger and disappear at once. They may occur at the surface of a relatively calm sea, reach not very high amplitudes, but be fatal for ships and crew due to their unexpectedness and abnormal features. The billows appear suddenly exceeding the surrounding waves twice and more, and obtained many names: abnormal, exceptional, extreme, giant, huge, sudden, episodic, freak, monster, rogue, vicious, killer, mad- or rabid-dog waves; cape rollers, holes in the sea, walls of water, three sisters… Freak monsters, though living for seconds, were able to arouse superstitious fear of the crew, cause damage, death of heedless sailors or the whole ship. All these epithets are full of human fear and feebleness. The serious studies of the phenomenon started about 20-30 years ago and have been intensified during the recent decade. The research is being conducted in different fields: in physics (search of physical mechanisms and adequate models of wave enhancement and statistics), in geoscience (determining the regions and weather conditions when rogue waves are most probable), and in ocean and coastal engineering (estimations of the wave loads on fixed and drifting floating structures). Thus, scientists and engineers specializing in different subject areas are involved in the solution of the problem. The state-of-art of the rogue wave study is summarized in our book [Kharif, Ch., Pelinovsky, E., and Slunyaev, A. Rogue Waves in the Ocean. Springer, 2009] and presented in given review. Firstly, we start with a brief introduction to the problem of freak waves aiming at formulating what is understood as rogue or freak waves, what consequences their existence imply in our life, why people are so worried about them. Then we discuss existing
Caustics and Rogue Waves in an Optical Sea
Mathis, Amaury; Froehly, Luc; Toenger, Shanti; Dias, Frédéric; Genty, Goëry; Dudley, John M.
2015-01-01
There are many examples in physics of systems showing rogue wave behaviour, the generation of high amplitude events at low probability. Although initially studied in oceanography, rogue waves have now been seen in many other domains, with particular recent interest in optics. Although most studies in optics have focussed on how nonlinearity can drive rogue wave emergence, purely linear effects have also been shown to induce extreme wave amplitudes. In this paper, we report a detailed experimental study of linear rogue waves in an optical system, using a spatial light modulator to impose random phase structure on a coherent optical field. After free space propagation, different random intensity patterns are generated, including partially-developed speckle, a broadband caustic network, and an intermediate pattern with characteristics of both speckle and caustic structures. Intensity peaks satisfying statistical criteria for rogue waves are seen especially in the case of the caustic network, and are associated with broader spatial spectra. In addition, the electric field statistics of the intermediate pattern shows properties of an “optical sea” with near-Gaussian statistics in elevation amplitude, and trough-to-crest statistics that are near-Rayleigh distributed but with an extended tail where a number of rogue wave events are observed. PMID:26245864
Caustics and Rogue Waves in an Optical Sea.
Mathis, Amaury; Froehly, Luc; Toenger, Shanti; Dias, Frédéric; Genty, Goëry; Dudley, John M
2015-08-06
There are many examples in physics of systems showing rogue wave behaviour, the generation of high amplitude events at low probability. Although initially studied in oceanography, rogue waves have now been seen in many other domains, with particular recent interest in optics. Although most studies in optics have focussed on how nonlinearity can drive rogue wave emergence, purely linear effects have also been shown to induce extreme wave amplitudes. In this paper, we report a detailed experimental study of linear rogue waves in an optical system, using a spatial light modulator to impose random phase structure on a coherent optical field. After free space propagation, different random intensity patterns are generated, including partially-developed speckle, a broadband caustic network, and an intermediate pattern with characteristics of both speckle and caustic structures. Intensity peaks satisfying statistical criteria for rogue waves are seen especially in the case of the caustic network, and are associated with broader spatial spectra. In addition, the electric field statistics of the intermediate pattern shows properties of an "optical sea" with near-Gaussian statistics in elevation amplitude, and trough-to-crest statistics that are near-Rayleigh distributed but with an extended tail where a number of rogue wave events are observed.
Potential changes of wave steepness and occurrence of rogue waves
NASA Astrophysics Data System (ADS)
Bitner-Gregersen, Elzbieta M.; Toffoli, Alessandro
2015-04-01
Wave steepness is an important characteristic of a sea state. It is also well established that wave steepness is one of the parameter responsible for generation of abnormal waves called also freak or rogue waves. The study investigates changes of wave steepness in the past and future wave climate in the North Atlantic. The fifth assessment report IPCC (2013) uses four scenarios for future greenhouse gas concentrations in the atmosphere called Representative Concentration Pathways (RCP). Two of these scenarios RCP 4.5 and RCP 8.5 have been selected to project future wave conditions in the North Atlantic. RCP 4.5 is believed to achieve the political target of a maximum global mean temperature increase of 2° C while RPC 8.5 is close to 'business as usual' and expected to give a temperature increase of 4° C or more. The analysis includes total sea, wind sea and swell. Potential changes of wave steepness for these wave systems are shown and compared with wave steepness derived from historical data. Three historical data sets with different wave model resolutions are used. The investigations show also changes in the mean wind direction as well as in the relative direction between wind sea and swell. Consequences of wave steepness changes for statistics of surface elevation and generation of rogue waves are demonstrated. Uncertainties associated with wave steepness projections are discussed.
Taming rogue waves in vector Bose-Einstein condensates.
Vinayagam, P S; Radha, R; Porsezian, K
2013-10-01
Using gauge transformation method, we generate rogue waves for the two-component Bose-Einstein condensates (BECs) governed by the symmetric coupled Gross-Pitaevskii (GP) equations and study their dynamics. We also suggest a mechanism to tame the rogue waves either by manipulating the scattering length through Feshbach resonance or the trapping frequency, a phenomenon not witnessed in the domain of BECs, and we believe that these results may have wider ramifications in the management of rogons.
NASA Astrophysics Data System (ADS)
Yu, Fajun
2016-05-01
We study multi-rogue wave solutions of a Schro¨dinger equation with higher-order terms employing the generalized Darboux transformation. Some properties of the nonautonomous rogue waves are investigated analytically for the combined Hirota-Lakshmanan-Porsezian-Daniel (LPD) equation. We consider the controllable behaviors of this nonautonomous rogue wave solution with the nonlinearity management function and gain/loss coefficient. It is reported that there are possibilities to 'catch' rogue waves through manipulating nonlinear function and gain/loss coefficient. Our approach can provide many possibilities to manipulate rogue waves and present the potential applications for the rogue wave phenomena.
Peregrine rogue waves induced by the interaction between a continuous wave and a soliton.
Yang, Guangye; Li, Lu; Jia, Suotang
2012-04-01
Based on the soliton solution on a continuous wave background for an integrable Hirota equation, the reduction mechanism and the characteristics of the Peregrine rogue wave in the propagation of femtosecond pulses of optical fiber are discussed. The results show that there exist two processes of the formation of the Peregrine rogue wave: one is the localized process of the continuous wave background, and the other is the reduction process of the periodization of the bright soliton. The characteristics of the Peregrine rogue wave are exhibited by strong temporal and spatial localization. Also, various initial excitations of the Peregrine rogue wave are performed and the results show that the Peregrine rogue wave can be excited by a small localized (single peak) perturbation pulse of the continuous wave background, even for the nonintegrable case. The numerical simulations show that the Peregrine rogue wave is unstable. Finally, through a realistic example, the influence of the self-frequency shift to the dynamics of the Peregrine rogue wave is discussed. The results show that in the absence of the self-frequency shift, the Peregrine rogue wave can split into several subpulses; however, when the self-frequency shift is considered, the Peregrine rogue wave no longer splits and exhibits mainly a peak changing and an increasing evolution property of the field amplitude.
Dynamics of rogue waves on multisoliton background in the Benjamin Ono equation
NASA Astrophysics Data System (ADS)
LIU, YUN-KAI; LI, BIAO
2017-04-01
For the Benjamin Ono equation, the Hirota bilinear method and long wave limit method are applied to obtain the breathers and the rogue wave solutions. Bright and dark rogue waves exist in the Benjamin Ono equation, and their typical dynamics are analysed and illustrated. The semirational solutions possessing rogue waves and solitons are also obtained, and demonstrated by the three-dimensional figures. Furthermore, the hybrid of rogue wave and breather solutions are also found in the Benjamin Ono equation.
Modulational Instability and Rogue Waves in Shallow Water Models
NASA Astrophysics Data System (ADS)
Grimshaw, R.; Chow, K. W.; Chan, H. N.
It is now well known that the focussing nonlinear Schrödinger equation allows plane waves to be modulationally unstable, and at the same time supports breather solutions which are often invoked as models for rogue waves. This suggests a direct connection between modulation instability and the existence of rogue waves. In this chapter we review this connection for a suite of long wave models, such as the Korteweg-de Vries equation, the extended Korteweg-de Vries (Gardner) equation, often used to describe surface and internal waves in shallow water, a Boussinesq equation and, also a coupled set of Korteweg-de Vries equations.
Rogue waves and breathers in Heisenberg spin chain
NASA Astrophysics Data System (ADS)
Mukhopadhyay, Aritra K.; Vyas, Vivek M.; Panigrahi, Prasanta K.
2015-07-01
Following the connection of the non-linear Schrödinger equation with the continuum Heisenberg spin chain, we find the rogue soliton equivalent in the spin system. The breathers are also mapped to the corresponding space or time localized oscillatory modes, through the moving curve analogy. The spatio-temporal evolution of the curvature and torsion of the curve, underlying these dynamical systems, are explicated to illustrate the localization property of the rogue waves.
Electrostatic rogue-waves in relativistically degenerate plasmas
Akbari-Moghanjoughi, M.
2014-10-15
In this paper, we investigate the modulational instability and the possibility of electrostatic rogue-wave propagations in a completely degenerate plasma with arbitrary degree of degeneracy, i.e., relativistically degenerate plasma, ranging from solid density to the astrophysical compact stars. The hydrodynamic approach along with the perturbation method is used to reduce the governing equations to the nonlinear Schrödinger equation from which the modulational instability, the growth rate of envelope excitations and the occurrence of rogue as well as super-rogue waves in the plasma, is evaluated. It is observed that the modulational instability in a fully degenerate plasma can be quite sensitive to the plasma number-density and the wavenumber of envelop excitations. It is further revealed that the relativistically degeneracy plasmas (R{sub 0} > 1) are almost always modulationally unstable. It is found, however, that the highly energetic sharply localized electrostatic rogue as well as super-rogue waves can exist in the astrophysical compact objects like white dwarfs and neutron star crusts. The later may provide a link to understand many physical processes in such stars and it may lead us to the origin of the random-localized intense short gamma-ray bursts, which “appear from nowhere and disappear without a trace” quite similar to oceanic rogue structures.
Rogue wave observation in a water wave tank.
Chabchoub, A; Hoffmann, N P; Akhmediev, N
2011-05-20
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 Schrödinger 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.
Langmuir rogue waves in electron-positron plasmas
Moslem, W. M.
2011-03-15
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 Schroedinger 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.
Real world ocean rogue waves explained without the modulational instability
NASA Astrophysics Data System (ADS)
Fedele, Francesco; Brennan, Joseph; Ponce de León, Sonia; Dudley, John; Dias, Frédéric
2016-06-01
Since the 1990s, the modulational instability has commonly been used to explain the occurrence of rogue waves that appear from nowhere in the open ocean. However, the importance of this instability in the context of ocean waves is not well established. This mechanism has been successfully studied in laboratory experiments and in mathematical studies, but there is no consensus on what actually takes place in the ocean. In this work, we question the oceanic relevance of this paradigm. In particular, we analyze several sets of field data in various European locations with various tools, and find that the main generation mechanism for rogue waves is the constructive interference of elementary waves enhanced by second-order bound nonlinearities and not the modulational instability. This implies that rogue waves are likely to be rare occurrences of weakly nonlinear random seas.
Real world ocean rogue waves explained without the modulational instability
Fedele, Francesco; Brennan, Joseph; Ponce de León, Sonia; Dudley, John; Dias, Frédéric
2016-01-01
Since the 1990s, the modulational instability has commonly been used to explain the occurrence of rogue waves that appear from nowhere in the open ocean. However, the importance of this instability in the context of ocean waves is not well established. This mechanism has been successfully studied in laboratory experiments and in mathematical studies, but there is no consensus on what actually takes place in the ocean. In this work, we question the oceanic relevance of this paradigm. In particular, we analyze several sets of field data in various European locations with various tools, and find that the main generation mechanism for rogue waves is the constructive interference of elementary waves enhanced by second-order bound nonlinearities and not the modulational instability. This implies that rogue waves are likely to be rare occurrences of weakly nonlinear random seas. PMID:27323897
Twisted rogue-wave pairs in the Sasa-Satsuma equation.
Chen, Shihua
2013-08-01
Exact explicit rogue wave solutions of the Sasa-Satsuma equation are obtained by use of a Darboux transformation. In addition to the double-peak structure and an analog of the Peregrine soliton, the rogue wave can exhibit an intriguing twisted rogue-wave pair that involves four well-defined zero-amplitude points. This exotic structure may enrich our understanding on the nature of rogue waves.
Simple determinant representation for rogue waves of the nonlinear Schrödinger equation.
Ling, Liming; Zhao, Li-Chen
2013-10-01
We present a simple representation for arbitrary-order rogue wave solution and a study on the trajectories of them explicitly. We find that the trajectories of two valleys on whole temporal-spatial distribution all look "X" -shaped for rogue waves. Additionally, we present different types of high-order rogue wave structures, which could be helpful towards realizing the complex dynamics of rogue waves.
Optical rogue waves for the inhomogeneous generalized nonlinear Schrödinger equation.
Loomba, Shally; Kaur, Harleen
2013-12-01
We present optical rogue wave solutions for a generalized nonlinear Schrodinger equation by using similarity transformation. We have predicted the propagation of rogue waves through a nonlinear optical fiber for three cases: (i) dispersion increasing (decreasing) fiber, (ii) periodic dispersion parameter, and (iii) hyperbolic dispersion parameter. We found that the rogue waves and their interactions can be tuned by properly choosing the parameters. We expect that our results can be used to realize improved signal transmission through optical rogue waves.
Capturing rogue waves by multi-point statistics
NASA Astrophysics Data System (ADS)
Hadjihosseini, A.; Wächter, Matthias; Hoffmann, N. P.; Peinke, J.
2016-01-01
As an example of a complex system with extreme events, we investigate ocean wave states exhibiting rogue waves. We present a statistical method of data analysis based on multi-point statistics which for the first time allows the grasping of extreme rogue wave events in a highly satisfactory statistical manner. The key to the success of the approach is mapping the complexity of multi-point data onto the statistics of hierarchically ordered height increments for different time scales, for which we can show that a stochastic cascade process with Markov properties is governed by a Fokker-Planck equation. Conditional probabilities as well as the Fokker-Planck equation itself can be estimated directly from the available observational data. With this stochastic description surrogate data sets can in turn be generated, which makes it possible to work out arbitrary statistical features of the complex sea state in general, and extreme rogue wave events in particular. The results also open up new perspectives for forecasting the occurrence probability of extreme rogue wave events, and even for forecasting the occurrence of individual rogue waves based on precursory dynamics.
Rogue Waves in the Ocean, Understanding and Prediction
NASA Astrophysics Data System (ADS)
Babanin, A. V.; Rogers, W.
2013-12-01
Rogue waves are abnormally high, with respect to the mean, waves in the ocean. Here, deep-water wind-generated dominant waves in absence of currents will be considered. Present understanding of their nature, and pathways to their prediction will be reviewed and discussed. Rogue waves can be due to quasi-linear superpositions of waves, and nonlinear effects such as instabilities of wave trains. Both mechanisms appear to be important and possible. Individual waves can be focused into a superposition due to either dispersive or directional features of wave fields. While probability of the former to lead to a relatively very high wave in oceanic conditions is low, the directional focusing appears to cause rare but regular extreme events. Nonlinear wave fields should be separated into stable and unstable conditions, with different probability distributions for wave heights/crests. In stable conditions, wave statistics is determined by the quasi-linear focusing, whereas in unstable wave trains high transient wave events can occur. Their maximal height/steepness is determined by combined dynamics of the instability growth and the limiting wave breaking. Both instability and breaking depend on mean wave steepness, spectral bandwidth, wave directionality, spectrum tail, wind forcing. In extreme wind-forcing conditions, such as hurricanes, modulational instability of wave fields may be suppressed, and the breaking process is controlled by different physics. Therefore, it is argued that rogue wave statistics in such circumstances is expected to be essentially altered.
High-order rogue waves for the Hirota equation
Li, Linjing; Wu, Zhiwei; Wang, Lihong; He, Jingsong
2013-07-15
The Hirota equation is better than the nonlinear Schrödinger equation when approximating deep ocean waves. In this paper, high-order rational solutions for the Hirota equation are constructed based on the parameterized Darboux transformation. Several types of this kind of solutions are classified by their structures. -- Highlights: •The determinant representation of the N-fold Darboux transformation of the Hirota equation. •Properties of the fundamental pattern of the higher order rogue wave. •Ring structure and triangular structure of the higher order rogue waves.
Rogue waves in a normal-dispersion fiber laser.
Liu, Zhanwei; Zhang, Shumin; Wise, F W
2015-04-01
Experimental evidence of rogue-wave formation in a normal-dispersion ytterbium fiber laser is reported. Spectral filtering is a primary component of pulse-shaping in normal-dispersion lasers, and we find that the choice of filter dramatically influences the distribution of noise-pulse energies produced by these lasers. With an interference filter in the cavity, non-Gaussian distributions with pulses as large as 6 times the significant wave height are observed. These correspond to pulse energies as high as ∼50 nJ. To our knowledge, the results presented are not accounted for by existing theoretical models of rogue-wave formation.
Vector rogue waves and baseband modulation instability in the defocusing regime.
Baronio, Fabio; Conforti, Matteo; Degasperis, Antonio; Lombardo, Sara; Onorato, Miguel; Wabnitz, Stefan
2014-07-18
We report and discuss analytical solutions of the vector nonlinear Schrödinger equation that describe rogue waves in the defocusing regime. This family of solutions includes bright-dark and dark-dark rogue waves. The link between modulational instability (MI) and rogue waves is displayed by showing that only a peculiar kind of MI, namely baseband MI, can sustain rogue-wave formation. The existence of vector rogue waves in the defocusing regime is expected to be a crucial progress in explaining extreme waves in a variety of physical scenarios described by multicomponent systems, from oceanography to optics and plasma physics.
On shallow water rogue wave formation in strongly inhomogeneous channels
NASA Astrophysics Data System (ADS)
Didenkulova, Ira; Pelinovsky, Efim
2016-05-01
Rogue wave formation in shallow water is often governed by dispersive focusing and wave-bottom interaction. In this study we try to combine these mechanisms by considering dispersive nonreflecting wave propagation in shallow strongly inhomogeneous channels. Nonreflecting wave propagation provides extreme wave amplification and the transfer of wave energy over large distances, while dispersive effects allow formation of a short-lived wave of extreme height (rogue wave). We found several types of water channels, where this mechanism can be realized, including (i) channels with a monotonically decreasing cross-section (normal dispersion), (ii) an inland basin described by a half of elliptic paraboloid (abnormal dispersion) and (iii) an underwater hill described by a half of hyperbolic paraboloid (normal dispersion). Conditions for variations of local frequency in the wave train providing optimal focusing of the wave train are also found.
Sensitivity of Rogue Waves Predictions to the Oceanic Stratification
NASA Astrophysics Data System (ADS)
Guo, Qiuchen; Alam, Mohammad-Reza
2014-11-01
Oceanic rogue waves are short-lived very large amplitude waves (a giant crest typically followed or preceded by a deep trough) that appear and disappear suddenly in the ocean causing damages to ships and offshore structures. Assuming that the state of the ocean at the present time is perfectly known, then the upcoming rogue waves can be predicted via numerically solving the equations that govern the evolution of the waves. The state of the art radar technology can now provide accurate wave height measurement over large spatial domains and when combined with advanced wave-field reconstruction techniques together render deterministic details of the current state of the ocean (i.e. surface elevation and velocity field) at any given moment of the time with a very high accuracy. The ocean water density is, however, stratified (mainly due to the salinity and temperature differences). This density stratification, with today's technology, is very difficult to be measured accurately. As a result in most predictive schemes these density variations are neglected. While the overall effect of the stratification on the average state of the ocean may not be significant, here we show that these density variations can strongly affect the prediction of oceanic rogue waves. Specifically, we consider a broadband oceanic spectrum in a two-layer density stratified fluid, and study via extensive statistical analysis the effects of strength of the stratification (difference between densities) and the depth of the thermocline on the prediction of upcoming rogue waves.
Rogue Waves Associated with Circularly Polarized Waves in Magnetized Plasmas
NASA Astrophysics Data System (ADS)
Kourakis, I.; Borhanian, J.; Saxena, V.; Veldes, G.; Frantzeskakis, D. J.
2012-10-01
Extreme events occur in abundance in the ocean: an ultra-high ``ghost wave" often appears unexpectedly, against an otherwise moderate-on-average sea surface elevation, propagating for a short while and then disappearing without leaving a trace. Rogue waves are now recognized as proper nonlinear structures on their own. Unlike solitary waves, these events are localized in space and in time. Various approaches exist to model their dynamics, including nonlinear Schrodinger models, Ginzburg-Landau models, kinetic-theoretical models, and probabilistic models. We have undertaken an investigation, from first principles, of rogue waves in plasmas in the form of localized events associated with electromagnetic pulses. A multiple scale technique is employed to solve the fluid-Maxwell equations for nonlinear circularly polarized electromagnetic pulses. A nonlinear Schrodinger (NLS) type equation is shown to govern the amplitude of the vector potential. A set of non-stationary envelope solutions of the NLS equation is presented, and the variation of their structural properties with the magnetic field are investigated.
New Types of Rogue Wave in an Erbium-Doped Fibre System
NASA Astrophysics Data System (ADS)
He, Jingsong; Xu, Shuwei; Porsezian, Kuppuswamy
2012-03-01
We report a novel and new types of rogue optical wave propagation in an erbium-doped fibre system governed by the nonlinear Schrödinger and the Maxwell--Bloch equation. The breather solutions of the three fields, namely field envelop, polarization and population inversion, are used to generate the rogue waves. For the first time, we report bright and, in particular, dark rogue waves in a coupled nonlinear optical systems. The distinction between bright and dark rogue waves are discussed in detail through figures. The rogue wave formation in our model can also be connected to the generation of supercontinuum generation in resonant optical fibre.
Observation of three dimensional optical rogue waves through obstacles
Leonetti, Marco; Conti, Claudio
2015-06-22
We observe three-dimensional rogue waves in the speckle distribution of a spatially modulated optical beam. Light is transmitted beyond a partially reflecting obstacle generating optical rogue waves at a controlled position in the shadow of the barrier. When the barrier transmits only 0.07% of the input laser power, we observe the mostly localized event. These results demonstrate that an optimum amount of spatial non-homogeneity maximizes the probability of a gigantic event while the technique we exploit enables to control light behind a fully reflective wall.
Observation of three dimensional optical rogue waves through obstacles
NASA Astrophysics Data System (ADS)
Leonetti, Marco; Conti, Claudio
2015-06-01
We observe three-dimensional rogue waves in the speckle distribution of a spatially modulated optical beam. Light is transmitted beyond a partially reflecting obstacle generating optical rogue waves at a controlled position in the shadow of the barrier. When the barrier transmits only 0.07% of the input laser power, we observe the mostly localized event. These results demonstrate that an optimum amount of spatial non-homogeneity maximizes the probability of a gigantic event while the technique we exploit enables to control light behind a fully reflective wall.
Experiments on Rogue Waves in Superfluid 4He
NASA Astrophysics Data System (ADS)
Efimov, Viktor; McClintock, Peter; Ganshin, Andrei; Kolmakov, German; Mezhov-Deglin, Leonid
2010-05-01
We describe an experimental and theoretical study of nonlinear wave interactions in superfluid helium and report the observation of rogue waves. Rogue waves (or freak waves, or killer waves, or extreme waves) have long been recognized by sailors as a menace to shipping and are believed to have been responsible for the unexplained losses of vessels of all sizes, including e.g. 22 super-carriers between 1968 and 1994 [1, 2]. Rogue waves on the ocean are rare, and are much higher (and steeper) than all the other waves around them. They seem to appear from nowhere and subsequently to disappear without trace [3]. Following the famous 'New Year wave' measured by instruments on the Draupner North Sea oil rig at the beginning of 1995, the existence of oceanic rogue waves is no longer in doubt. There have been several suggestions about possible mechanisms for the creation of rogue waves. These include the combined effects of wind and currents, and the focusing effects associated with the profile of the ocean floor and nearby shorelines. Where rogue waves appear in deep water far from any shore, which they sometimes do, it seems likely that they must evolve through nonlinear interactions within the 'noisy background" of smaller wind-blown waves [4]. Rogue waves have been modeled theoretically, especially by exploiting the special properties of the nonlinear Schrödinger equation. They have been sought experimentally and/or studied in large wave tanks [5], optical systems [6, 7], and superfluid 4He [8]. Our experimental system consists of high intensity second sound (temperature-entropy) waves within a resonant cavity filled with superfluid 4He at 2.1 K. Under steady state conditions, with a constant oscillatory driving force at the resonant frequency, the second sound waves are turbulent and fluxes of energy flow towards both high and low frequencies. It is found that rogue waves appear under the nonequilibrium conditions that prevail shortly after the drive has been
Coexisting rogue waves within the (2+1)-component long-wave-short-wave resonance.
Chen, Shihua; Soto-Crespo, Jose M; Grelu, Philippe
2014-09-01
The coexistence of two different types of fundamental rogue waves is unveiled, based on the coupled equations describing the (2+1)-component long-wave-short-wave resonance. For a wide range of asymptotic background fields, each family of three rogue wave components can be triggered by using a slight deterministic alteration to the otherwise identical background field. The ability to trigger markedly different rogue wave profiles from similar initial conditions is confirmed by numerical simulations. This remarkable feature, which is absent in the scalar nonlinear Schrödinger equation, is attributed to the specific three-wave interaction process and may be universal for a variety of multicomponent wave dynamics spanning from oceanography to nonlinear optics.
Solar wind implication on dust ion acoustic rogue waves
Abdelghany, A. M. Abd El-Razek, H. N. El-Labany, S. K.; Moslem, W. M.
2016-06-15
The relevance of the solar wind with the magnetosphere of Jupiter that contains positively charged dust grains is investigated. The perturbation/excitation caused by streaming ions and electron beams from the solar wind could form different nonlinear structures such as rogue waves, depending on the dominant role of the plasma parameters. Using the reductive perturbation method, the basic set of fluid equations is reduced to modified Korteweg-de Vries (KdV) and further modified (KdV) equation. Assuming that the frequency of the carrier wave is much smaller than the ion plasma frequency, these equations are transformed into nonlinear Schrödinger equations with appropriate coefficients. Rational solution of the nonlinear Schrödinger equation shows that rogue wave envelopes are supported by the present plasma model. It is found that the existence region of rogue waves depends on the dust-acoustic speed and the streaming temperatures for both the ions and electrons. The dependence of the maximum rogue wave envelope amplitude on the system parameters has been investigated.
Solar wind implication on dust ion acoustic rogue waves
NASA Astrophysics Data System (ADS)
Abdelghany, A. M.; Abd El-Razek, H. N.; Moslem, W. M.; El-Labany, S. K.
2016-06-01
The relevance of the solar wind with the magnetosphere of Jupiter that contains positively charged dust grains is investigated. The perturbation/excitation caused by streaming ions and electron beams from the solar wind could form different nonlinear structures such as rogue waves, depending on the dominant role of the plasma parameters. Using the reductive perturbation method, the basic set of fluid equations is reduced to modified Korteweg-de Vries (KdV) and further modified (KdV) equation. Assuming that the frequency of the carrier wave is much smaller than the ion plasma frequency, these equations are transformed into nonlinear Schrödinger equations with appropriate coefficients. Rational solution of the nonlinear Schrödinger equation shows that rogue wave envelopes are supported by the present plasma model. It is found that the existence region of rogue waves depends on the dust-acoustic speed and the streaming temperatures for both the ions and electrons. The dependence of the maximum rogue wave envelope amplitude on the system parameters has been investigated.
Spatial rogue waves in a photorefractive pattern-forming system.
Marsal, N; Caullet, V; Wolfersberger, D; Sciamanna, M
2014-06-15
We have experimentally analyzed pattern formation in an optical system composed of a bulk photorefractive crystal subjected to a single optical feedback. In a highly nonlinear regime far above the modulational instability threshold, we are reporting on turbulent spatiotemporal dynamics that leads to rare, intense localized optical peaks. We have proven that the statistics and features of those peaks correspond to the signatures of two-dimensional spatial rogue events. These optical rogue waves occur erratically in space and time and live typically the same amount of time as the response time of the photorefractive material.
Three-dimensional rogue waves in nonstationary parabolic potentials.
Yan, Zhenya; Konotop, V V; Akhmediev, N
2010-09-01
Using symmetry analysis we systematically present a higher-dimensional similarity transformation reducing the (3+1) -dimensional inhomogeneous nonlinear Schrödinger (NLS) equation with variable coefficients and parabolic potential to the (1+1) -dimensional NLS equation with constant coefficients. This transformation allows us to relate certain class of localized exact solutions of the (3+1) -dimensional case to the variety of solutions of integrable NLS equation of the (1+1) -dimensional case. As an example, we illustrated our technique using two lowest-order rational solutions of the NLS equation as seeding functions to obtain rogue wavelike solutions localized in three dimensions that have complicated evolution in time including interactions between two time-dependent rogue wave solutions. The obtained three-dimensional rogue wavelike solutions may raise the possibility of relative experiments and potential applications in nonlinear optics and Bose-Einstein condensates.
Three-dimensional rogue waves in nonstationary parabolic potentials
Yan Zhenya; Konotop, V. V.; Akhmediev, N.
2010-09-15
Using symmetry analysis we systematically present a higher-dimensional similarity transformation reducing the (3+1)-dimensional inhomogeneous nonlinear Schroedinger (NLS) equation with variable coefficients and parabolic potential to the (1+1)-dimensional NLS equation with constant coefficients. This transformation allows us to relate certain class of localized exact solutions of the (3+1)-dimensional case to the variety of solutions of integrable NLS equation of the (1+1)-dimensional case. As an example, we illustrated our technique using two lowest-order rational solutions of the NLS equation as seeding functions to obtain rogue wavelike solutions localized in three dimensions that have complicated evolution in time including interactions between two time-dependent rogue wave solutions. The obtained three-dimensional rogue wavelike solutions may raise the possibility of relative experiments and potential applications in nonlinear optics and Bose-Einstein condensates.
Electromagnetic rogue waves in beam-plasma interactions
NASA Astrophysics Data System (ADS)
Veldes, G. P.; Borhanian, J.; McKerr, M.; Saxena, V.; Frantzeskakis, D. J.; Kourakis, I.
2013-06-01
The occurrence of rogue waves (freak waves) associated with electromagnetic pulse propagation interacting with a plasma is investigated, from first principles. A multiscale technique is employed to solve the fluid Maxwell equations describing weakly nonlinear circularly polarized electromagnetic pulses in magnetized plasmas. A nonlinear Schrödinger (NLS) type equation is shown to govern the amplitude of the vector potential. A set of non-stationary envelope solutions of the NLS equation are considered as potential candidates for the modeling of rogue waves (freak waves) in beam-plasma interactions, namely in the form of the Peregrine soliton, the Akhmediev breather and the Kuznetsov-Ma breather. The variation of the structural properties of the latter structures with relevant plasma parameters is investigated, in particular focusing on the ratio between the (magnetic field dependent) cyclotron (gyro-)frequency and the plasma frequency.
W-shaped soliton complexes and rogue-wave pattern transitions for the AB system
NASA Astrophysics Data System (ADS)
Wang, Xin; Liu, Chong
2017-07-01
With the help of a general Nth-order rogue wave solution in a compact determinant form for the AB system, we illuminate that, by suitably choosing the wavenumber and frequency of the background wave of the component A, W-shaped soliton complex containing a fixed number of algebraic solitons merging or separating with each other exists in the component A, and rogue-wave pattern transition between the four-petaled structure and dark structure occurs in the component B. The more complicated rogue-wave pattern transitions due to the nonlinear superposition corresponding to the higher-order four-petaled rogue waves and higher-order dark rogue waves of fundamental, triangular and circular dynamical structures up to third order are demonstrated, respectively. The spectrum properties which are related to the rogue-wave pattern transitions are revealed.
Optical rogue waves generated on Gaussian background beam.
Liu, Chong; Yang, Zhan-Ying; Zhao, Li-Chen; Xin, Guo-Guo; Yang, Wen-Li
2014-02-15
We study optical rogue waves (RWs) in a nonlinear graded-index waveguide with variable coefficients. An exact RW solution on Gaussian background beam is presented, in contrast to the previous studies about RWs, on plane wave background. It is shown that the characteristics of RWs are maintained on Gaussian background beam and that the beam's width is even a bit smaller than the RWs scale. These results may raise the possibility of related experiments and potential applications in nonlinear optics.
Integrable Turbulence and Rogue Waves: Breathers or Solitons?
Soto-Crespo, J M; Devine, N; Akhmediev, N
2016-03-11
Turbulence in dynamical systems is one of the most intriguing phenomena of modern science. Integrable systems offer the possibility to understand, to some extent, turbulence. Recent numerical and experimental data suggest that the probability of the appearance of rogue waves in a chaotic wave state in such systems increases when the initial state is a random function of sufficiently high amplitude. We provide explanations for this effect.
Watch-hand-like optical rogue waves in three-wave interactions.
Chen, Shihua; Soto-Crespo, Jose M; Grelu, Philippe
2015-01-12
We investigate the resonant interaction of three optical pulses of different group velocity in quadratic media and report on the novel watch-hand-like super rogue wave patterns. In addition to having a giant wall-like hump, each rogue-wave hand involves a peak amplitude more than five times its background height. We attribute such peculiar structures to the nonlinear superposition of six Peregrine-type solitons. The robustness has been confirmed by numerical simulations. This stability along with the non-overlapping distribution property may facilitate the experimental diagnostics and observation of these super rogue waves.
Circularly polarized few-cycle optical rogue waves: Rotating reduced Maxwell-Bloch equations
NASA Astrophysics Data System (ADS)
Xu, Shuwei; Porsezian, K.; He, Jingsong; Cheng, Yi
2013-12-01
The rotating reduced Maxwell-Bloch (RMB) equations, which describe the propagation of few-cycle optical pulses in a transparent media with two isotropic polarized electronic field components, are derived from a system of complete Maxwell-Bloch equations without using the slowly varying envelope approximations. Two hierarchies of the obtained rational solutions, including rogue waves, which are also called few-cycle optical rogue waves, of the rotating RMB equations are constructed explicitly through degenerate Darboux transformation. In addition to the above, the dynamical evolution of the first-, second-, and third-order few-cycle optical rogue waves are constructed with different patterns. For an electric field E in the three lower-order rogue waves, we find that rogue waves correspond to localized large amplitude oscillations of the polarized electric fields. Further a complementary relationship of two electric field components of rogue waves is discussed in terms of analytical formulas as well as numerical figures.
Dust-acoustic rogue waves in a nonextensive plasma
Moslem, W. M.; Shukla, P. K.; Sabry, R.; El-Labany, S. K.
2011-12-15
We present an investigation for the generation of a dust-acoustic rogue wave in a dusty plasma composed of negatively charged dust grains, as well as nonextensive electrons and ions. For this purpose, the reductive perturbation technique is used to obtain a nonlinear Schroedinger equation. The critical wave-number threshold k{sub c}, which indicates where the modulational instability sets in, has been determined precisely for various regimes. Two different behaviors of k{sub c} against the nonextensive parameter q are found. For small k{sub c}, it is found that increasing q would lead to an increase of k{sub c} until q approaches a certain value q{sub c}, then further increase of q beyond q{sub c} decreases the value of k{sub c}. For large k{sub c}, the critical wave-number threshold k{sub c} is always increasing with q. Within the modulational instability region, a random perturbation of the amplitude grows and thus creates dust-acoustic rogue waves. In order to show that the characteristics of the rogue waves are influenced by the plasma parameters, the relevant numerical analysis of the appropriate nonlinear solution is presented. The nonlinear structure, as reported here, could be useful for controlling and maximizing highly energetic pulses in dusty plasmas.
Dust-acoustic rogue waves in a nonextensive plasma.
Moslem, W M; Sabry, R; El-Labany, S K; Shukla, P K
2011-12-01
We present an investigation for the generation of a dust-acoustic rogue wave in a dusty plasma composed of negatively charged dust grains, as well as nonextensive electrons and ions. For this purpose, the reductive perturbation technique is used to obtain a nonlinear Schrödinger equation. The critical wave-number threshold k(c), which indicates where the modulational instability sets in, has been determined precisely for various regimes. Two different behaviors of k(c) against the nonextensive parameter q are found. For small k(c), it is found that increasing q would lead to an increase of k(c) until q approaches a certain value q(c), then further increase of q beyond q(c) decreases the value of k(c). For large k(c), the critical wave-number threshold k(c) is always increasing with q. Within the modulational instability region, a random perturbation of the amplitude grows and thus creates dust-acoustic rogue waves. In order to show that the characteristics of the rogue waves are influenced by the plasma parameters, the relevant numerical analysis of the appropriate nonlinear solution is presented. The nonlinear structure, as reported here, could be useful for controlling and maximizing highly energetic pulses in dusty plasmas.
Emergent rogue wave structures and statistics in spontaneous modulation instability.
Toenger, Shanti; Godin, Thomas; Billet, Cyril; Dias, Frédéric; Erkintalo, Miro; Genty, Goëry; Dudley, John M
2015-05-20
The nonlinear Schrödinger equation (NLSE) is a seminal equation of nonlinear physics describing wave packet evolution in weakly-nonlinear dispersive media. The NLSE is especially important in understanding how high amplitude "rogue waves" emerge from noise through the process of modulation instability (MI) whereby a perturbation on an initial plane wave can evolve into strongly-localised "breather" or "soliton on finite background (SFB)" structures. Although there has been much study of such structures excited under controlled conditions, there remains the open question of how closely the analytic solutions of the NLSE actually model localised structures emerging in noise-seeded MI. We address this question here using numerical simulations to compare the properties of a large ensemble of emergent peaks in noise-seeded MI with the known analytic solutions of the NLSE. Our results show that both elementary breather and higher-order SFB structures are observed in chaotic MI, with the characteristics of the noise-induced peaks clustering closely around analytic NLSE predictions. A significant conclusion of our work is to suggest that the widely-held view that the Peregrine soliton forms a rogue wave prototype must be revisited. Rather, we confirm earlier suggestions that NLSE rogue waves are most appropriately identified as collisions between elementary SFB solutions.
Emergent rogue wave structures and statistics in spontaneous modulation instability
Toenger, Shanti; Godin, Thomas; Billet, Cyril; Dias, Frédéric; Erkintalo, Miro; Genty, Goëry; Dudley, John M.
2015-01-01
The nonlinear Schrödinger equation (NLSE) is a seminal equation of nonlinear physics describing wave packet evolution in weakly-nonlinear dispersive media. The NLSE is especially important in understanding how high amplitude “rogue waves” emerge from noise through the process of modulation instability (MI) whereby a perturbation on an initial plane wave can evolve into strongly-localised “breather” or “soliton on finite background (SFB)” structures. Although there has been much study of such structures excited under controlled conditions, there remains the open question of how closely the analytic solutions of the NLSE actually model localised structures emerging in noise-seeded MI. We address this question here using numerical simulations to compare the properties of a large ensemble of emergent peaks in noise-seeded MI with the known analytic solutions of the NLSE. Our results show that both elementary breather and higher-order SFB structures are observed in chaotic MI, with the characteristics of the noise-induced peaks clustering closely around analytic NLSE predictions. A significant conclusion of our work is to suggest that the widely-held view that the Peregrine soliton forms a rogue wave prototype must be revisited. Rather, we confirm earlier suggestions that NLSE rogue waves are most appropriately identified as collisions between elementary SFB solutions. PMID:25993126
Midinfrared optical rogue waves in soft glass photonic crystal fiber.
Buccoliero, Daniel; Steffensen, Henrik; Ebendorff-Heidepriem, Heike; Monro, Tanya M; Bang, Ole
2011-09-12
We investigate numerically the formation of extreme events or rogue waves in soft glass tellurite fibers and demonstrate that optical loss drastically diminishes shot-to-shot fluctuations characteristic of picosecond pumped supercontinuum (SC). When loss is neglected these fluctuations include extreme events such as formation of highly energetic pulses located at the red end of the spectrum and we obtain right-skewed heavy-tailed distributions characteristic of extreme events statistics. On the other hand, when loss is included bandwidth fluctuations follow Gaussian-like statistical distributions. Our results thus implicitly show that rogue waves will not occur in any SC spectrum that is limited by loss, such as commercial silica fiber based SC sources.
Optical rogue waves in whispering-gallery-mode resonators
NASA Astrophysics Data System (ADS)
Coillet, Aurélien; Dudley, John; Genty, Goëry; Larger, Laurent; Chembo, Yanne K.
2014-01-01
We report a theoretical study showing that rogue waves can emerge in whispering-gallery-mode resonators as the result of the chaotic interplay between Kerr nonlinearity and anomalous group-velocity dispersion. The nonlinear dynamics of the propagation of light in a whispering-gallery-mode resonator is investigated using the Lugiato-Lefever equation, and we give evidence of a range of parameters where rare and extreme events associated with non-Gaussian statistics of the field maxima are observed.
Energy cascades and rogue waves in superfluid 4He
NASA Astrophysics Data System (ADS)
Ganshin, A. N.; Efimov, V. B.; Kolmakov, G. V.; Mezhov-Deglin, L. P.; McClintock, P. V. E.
2009-02-01
We report the results of recent experiments on second sound in a high Q resonator. Nonlinear wave interactions give rise to a form of acoustic turbulence in which there is a Kolmogorov-like cascade of energy through the frequency scales from the frequency at which it is injected towards higher frequencies until, eventually, dissipative processes come to dominate and terminate the energy flux. We report that that, under some circumstances, an inverse energy cascade occurs, whereby there is a steady flux of energy towards lower frequencies, a wholly unexpected result that bears on the suggestion that rogue waves on the ocean may arise through nonlinear interactions between conventional wind-blown waves.
Optical amplification and reshaping based on the Peregrine rogue wave.
Wang, Yan; Song, Lijun; Li, Lu
2016-09-10
Based on the characteristics of the Peregrine rogue wave, the amplification and the reshaping of solitons are investigated. The numerical results show that the amplification and the reshaping of solitons can be realized by injecting a continuous wave (CW) and filtering the CW at suitable positions. The combination of a continuous-wave pump and a spectral filter placed suitably in fiber plays the role of the amplifier, which can be used to long-haul the transmission of solitons. As an example, a long-haul transmission with four amplification periods is demonstrated.
Roadmap on optical rogue waves and extreme events
NASA Astrophysics Data System (ADS)
Akhmediev, Nail; Kibler, Bertrand; Baronio, Fabio; Belić, Milivoj; Zhong, Wei-Ping; Zhang, Yiqi; Chang, Wonkeun; Soto-Crespo, Jose M.; Vouzas, Peter; Grelu, Philippe; Lecaplain, Caroline; Hammani, K.; Rica, S.; Picozzi, A.; Tlidi, Mustapha; Panajotov, Krassimir; Mussot, Arnaud; Bendahmane, Abdelkrim; Szriftgiser, Pascal; Genty, Goery; Dudley, John; Kudlinski, Alexandre; Demircan, Ayhan; Morgner, Uwe; Amiraranashvili, Shalva; Bree, Carsten; Steinmeyer, Günter; Masoller, C.; Broderick, Neil G. R.; Runge, Antoine F. J.; Erkintalo, Miro; Residori, S.; Bortolozzo, U.; Arecchi, F. T.; Wabnitz, Stefan; Tiofack, C. G.; Coulibaly, S.; Taki, M.
2016-06-01
The pioneering paper ‘Optical rogue waves’ by Solli et al (2007 Nature 450 1054) started the new subfield in optics. This work launched a great deal of activity on this novel subject. As a result, the initial concept has expanded and has been enriched by new ideas. Various approaches have been suggested since then. A fresh look at the older results and new discoveries has been undertaken, stimulated by the concept of ‘optical rogue waves’. Presently, there may not by a unique view on how this new scientific term should be used and developed. There is nothing surprising when the opinion of the experts diverge in any new field of research. After all, rogue waves may appear for a multiplicity of reasons and not necessarily only in optical fibers and not only in the process of supercontinuum generation. We know by now that rogue waves may be generated by lasers, appear in wide aperture cavities, in plasmas and in a variety of other optical systems. Theorists, in turn, have suggested many other situations when rogue waves may be observed. The strict definition of a rogue wave is still an open question. For example, it has been suggested that it is defined as ‘an optical pulse whose amplitude or intensity is much higher than that of the surrounding pulses’. This definition (as suggested by a peer reviewer) is clear at the intuitive level and can be easily extended to the case of spatial beams although additional clarifications are still needed. An extended definition has been presented earlier by N Akhmediev and E Pelinovsky (2010 Eur. Phys. J. Spec. Top. 185 1-4). Discussions along these lines are always useful and all new approaches stimulate research and encourage discoveries of new phenomena. Despite the potentially existing disagreements, the scientific terms ‘optical rogue waves’ and ‘extreme events’ do exist. Therefore coordination of our efforts in either unifying the concept or in introducing alternative definitions must be continued. From
Rogue waves and unbounded solutions of the NLSE
NASA Astrophysics Data System (ADS)
Lechuga, Antonio
2017-04-01
Since the pioneering work of Zakharov has been generally admitted that rogue waves can be studied in the framework of the Nonlinear Schrödinger Equation (NLSE). Many researchers, Akhmediev, Peregrine, Matveev among others gave different solutions to this equation that, in some way, could be linked to rogue waves and also to its more important characteristic: its unexpectedness. Janssen (2003, 2004), Onorato (2004, 2006) and Waseda (2006) linked the coefficient of the nonlinear term of the Schrödinger equation with the Benjamin-Feir index (BFI) that, we know, is a measure of the modulational instability of the waves. From this point of view the value of this coefficient of the NLSE could be known from statistics. Thus the relationship between sea states and the mechanism of generation of rogue waves could be found out. Following the well-known Lie group theory researchers have been studying the Lie point symmetries of the NLSE: the scaling transformations, Galilean transformations and phase transformations. Basically these transformations turn the NLSE into a nonlinear ordinary differential equation called Duffing equation (also called eikonal equation). There are different ways to do this, but in most of them the independent variable that could be seen as a space variable is a kind of moving frame with the time incorporated in this way. The main aim of this work is to classify solutions of the Duffing equation (periodic and nonperiodic waves and also bounded and unbounded waves) bearing in mind that the coefficient of the nonlinear term in the NLSE is left unaltered in the process of the transformation.
Dust-acoustic waves modulational instability and rogue waves in a polarized dusty plasma
NASA Astrophysics Data System (ADS)
Bouzit, Omar; Tribeche, Mouloud
2015-10-01
The polarization force-induced changes in the dust-acoustic waves (DAWs) modulational instability (MI) are examined. Using the reductive perturbation method, the nonlinear Schrödinger equation that governs the MI of the DAWs is obtained. It is found that the effect of the polarization term R is to narrow the wave number domain for the onset of instability. The amplitude of the wave envelope decreases as R increases, meaning that the polarization force effects render weaker the associated DA rogue waves. The latter may therefore completely damp in the vicinity of R ˜ 1, i.e., as the polarization force becomes close to the electrostatic one (the net force acting on the dust particles becomes vanishingly small). The DA rogue wave profile is very sensitive to any change in the restoring force acting on the dust particles. It turns out that the polarization effects may completely smear out the DA rogue waves.
Rogue waves of the Kundu-Eckhaus equation in a chaotic wave field.
Bayindir, Cihan
2016-03-01
In this paper we study the properties of the chaotic wave fields generated in the frame of the Kundu-Eckhaus equation (KEE). Modulation instability results in a chaotic wave field which exhibits small-scale filaments with a free propagation constant, k. The average velocity of the filaments is approximately given by the average group velocity calculated from the dispersion relation for the plane-wave solution; however, direction of propagation is controlled by the β parameter, the constant in front of the Raman-effect term. We have also calculated the probabilities of the rogue wave occurrence for various values of propagation constant k and showed that the probability of rogue wave occurrence depends on k. Additionally, we have showed that the probability of rogue wave occurrence significantly depends on the quintic and the Raman-effect nonlinear terms of the KEE. Statistical comparisons between the KEE and the cubic nonlinear Schrödinger equation have also been presented.
Dust-acoustic waves modulational instability and rogue waves in a polarized dusty plasma
Bouzit, Omar; Tribeche, Mouloud
2015-10-15
The polarization force-induced changes in the dust-acoustic waves (DAWs) modulational instability (MI) are examined. Using the reductive perturbation method, the nonlinear Schrödinger equation that governs the MI of the DAWs is obtained. It is found that the effect of the polarization term R is to narrow the wave number domain for the onset of instability. The amplitude of the wave envelope decreases as R increases, meaning that the polarization force effects render weaker the associated DA rogue waves. The latter may therefore completely damp in the vicinity of R ∼ 1, i.e., as the polarization force becomes close to the electrostatic one (the net force acting on the dust particles becomes vanishingly small). The DA rogue wave profile is very sensitive to any change in the restoring force acting on the dust particles. It turns out that the polarization effects may completely smear out the DA rogue waves.
Rogue-wave-like characteristics in femtosecond supercontinuum generation.
Erkintalo, M; Genty, G; Dudley, J M
2009-08-15
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.
On the rogue wave propagation in ion pair superthermal plasma
Abdelwahed, H. G. E-mail: hgomaa-eg@mans.edu.eg; Zahran, M. A.; El-Shewy, E. K. Elwakil, S. A.
2016-02-15
Effects of superthermal electron on the features of nonlinear acoustic waves in unmagnetized collisionless ion pair plasma with superthermal electrons have been examined. The system equations are reduced in the form of the nonlinear Schrodinger equation. The rogue wave characteristics dependences on the ionic density ratio (ν = n{sub –0}/n{sub +0}), ionic mass ratio (Q = m{sub +}/m{sub −}), and superthermality index (κ) are investigated. It is worth mentioning that the results present in this work could be applicable in the Earth's ionosphere plasmas.
Self-similar rogue waves and nonlinear tunneling effects in inhomogeneous nonlinear fiber optics
NASA Astrophysics Data System (ADS)
Wang, Lei; Zhu, Yu-Jie; Jiang, Dong-Yang
2016-04-01
Analytical first- and second-order rogue wave solutions of the inhomogeneous modified nonlinear Schrödinger equation are presented by using similarity transformation. Then, by the proper choices of the inhomogeneous coefficients and free parameters, the controllable behaviors of the optical rogue waves are graphically discussed in the nonlinear fiber optics context. It is found that the width of the rogue wave can be tuned by adjusting the parameter ? and the locations of the rogue waves are linearly controlled by the parameter ?. The intensities of the rogue waves are influenced by the inhomogeneous linear gain/loss coefficient ? and parameter ?. The dispersion management function ? has effects on the periods and trajectories of the rogue waves and can induce maintenance (or annihilation) along ? direction. Interestingly, the composite rogue waves are revealed, the location of which is manipulated through changing the dispersion management function ?. Additionally, the nonlinear tunneling of those rogue waves is investigated as they propagate through a dispersion barrier (or well) and nonlinear barrier (or well).
NASA Astrophysics Data System (ADS)
Zhao, Li-Chen; Ling, Liming; Qi, Jian-Wen; Yang, Zhan-Ying; Yang, Wen-Li
2017-08-01
We study rogue wave excitation pattern in a two-component Bose-Einstein condensate with pair-transition effects. The results indicate that rogue wave excitation can exist on a stripe phase background for which there are cosine and sine wave background in the two components respectively. The rogue wave peak can be much lower than the ones of scalar matter wave rogue waves, and varies with the wave period changing. Both rogue wave pattern and rogue wave number on temporal-spatial plane are much more abundant than the ones reported before. Furthermore, we prove that the rogue wave number can be n(n + 1) / 2 + m(m + 1) / 2 (where m, n are arbitrary non-negative integers), in contrast to n(n + 1) / 2 for scalar nonlinear Schrödinger equation described systems. These results would enrich our knowledge on nonlinear excitations in multi-component Bose-Einstein condensate with transition coupling effects.
Two-dimensional dissipative rogue waves due to time-delayed feedback in cavity nonlinear optics
NASA Astrophysics Data System (ADS)
Tlidi, Mustapha; Panajotov, Krassimir
2017-01-01
We demonstrate a way to generate two-dimensional rogue waves in two types of broad area nonlinear optical systems subject to time-delayed feedback: in the generic Lugiato-Lefever model and in the model of a broad-area surface-emitting laser with saturable absorber. The delayed feedback is found to induce a spontaneous formation of rogue waves. In the absence of delayed feedback, spatial pulses are stationary. The rogue waves are exited and controlled by the delay feedback. We characterize their formation by computing the probability distribution of the pulse height. The long-tailed statistical contribution, which is often considered as a signature of the presence of rogue waves, appears for sufficiently strong feedback. The generality of our analysis suggests that the feedback induced instability leading to the spontaneous formation of two-dimensional rogue waves is a universal phenomenon.
Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation
NASA Astrophysics Data System (ADS)
Bertola, Marco; El, Gennady A.; Tovbis, Alexander
2016-10-01
Rogue waves appearing on deep water or in optical fibres are often modelled by certain breather solutions of the focusing nonlinear Schrödinger (fNLS) equation which are referred to as solitons on finite background (SFBs). A more general modelling of rogue waves can be achieved via the consideration of multiphase, or finite-band, fNLS solutions of whom the standard SFBs and the structures forming due to their collisions represent particular, degenerate, cases. A generalized rogue wave notion then naturally enters as a large-amplitude localized coherent structure occurring within a finite-band fNLS solution. In this paper, we use the winding of real tori to show the mechanism of the appearance of such generalized rogue waves and derive an analytical criterion distinguishing finite-band potentials of the fNLS equation that exhibit generalized rogue waves.
Controlling formation and suppression of fiber-optical rogue waves.
Brée, Carsten; Steinmeyer, Günter; Babushkin, Ihar; Morgner, Uwe; Demircan, Ayhan
2016-08-01
Fiber-optical rogue waves appear as rare but extreme events during optical supercontinuum generation in photonic crystal fibers. This process is typically initiated by the decay of a high-order fundamental soliton into fundamental solitons. Collisions between these solitons as well as with dispersive radiation affect the soliton trajectory in frequency and time upon further propagation. Launching an additional dispersive wave at carefully chosen delay and wavelength enables statistical manipulation of the soliton trajectory in such a way that the probability of rogue wave formation is either enhanced or reduced. To enable efficient control, parameters of the dispersive wave have to be chosen to allow trapping of dispersive radiation in the nonlinear index depression created by the soliton. Under certain conditions, direct manipulation of soliton properties is possible by the dispersive wave. In other more complex scenarios, control is possible via increasing or decreasing the number of intersoliton collisions. The control mechanism reaches a remarkable efficiency, enabling control of relatively large soliton energies. This scenario appears promising for highly dynamic all-optical control of supercontinua.
NASA Astrophysics Data System (ADS)
Yang, Jin-Wei; Gao, Yi-Tian; Sun, Yu-Hao; Shen, Yu-Jia; Su, Chuan-Qi
2016-11-01
In this paper, a two-component (2 + 1) -dimensional long-wave-short-wave (LWSW) system with nonlinearity coefficients, which describes the nonlinear resonance interaction between two short waves and a long wave, is studied. Via the Hirota's bilinear method and Pfaffian, N -order rogue waves for the LWSW system are constructed. Furthermore, correction of the N -order rogue waves is proved directly via the Pfaffian, which is cumbersome or inaccessible in other methods. Results of the first- and second-order rogue waves are presented: 1) For the first-order rogue waves, the two short-wave components are bright, while the long-wave component is dark. The position of maximum amplitude of the rogue wave is analyzed. Evolution process for the first-order rogue wave is also presented and discussed. 2) Choosing different forms of the elements defined in the Pfaffian, we obtain some kinds of the second-order rogue waves with new spatial distributions: when the elements defined in Pfaffian are the same as the first-order rogue waves, we find that the second-order rogue waves for the two short-wave components are split into two first-order rogue waves and the two bumps coexist and interact with each other; when we change the combination of the elements in Pfaffian, we find that the second-order rogue waves for the two short-wave components are split into three and four first-order rogue waves. 3) N -order rogue waves for a general M -component LWSW system are constructed.
Characterization and statistics of rogue waves in random sea states
NASA Astrophysics Data System (ADS)
Schober, Constance
2015-04-01
Rogue waves are frequently modeled using the nonlinear Schrodinger (NLS) equation and it's higher order extensions due to Dyste and Trulsen (HONLS). In [2] Sura shows that the kurtosis (κ) and skewness (s) of deep ocean field data obey the quadratic inequality κ ≥ 3/2s2 + κ0 which is not satisfied by Gaussian or double exponential noise. Here we show that sea states modeled using the HONLS equation and random phase JONSWAP initial data exhibit a significant deviation from Gaussianity and satisfy Sura's relation between the skewness and kurtosis, thus providing a realistic picture of sea surface height variability. In [1] we introduced the 'splitting distance', δ, between two consecutive simple points in the Floquet spectrum of the associated Zakharov-Shabaat problem of the NLS equation, as a spectral measure of proximity to instabilities in the wavefield and correlated the development of localized rogue waves in random sea states characterized by JONSWAP spectra with δ. Here we take a closer look at the nonlinear spectral decomposition and characterization of JONSWAP solutions of the NLS equation. For the HONLS equation, δ evolves in time. We determine both the initial splitting distance δ0 and the time averaged splitting distance δavg. From a practical standpoint the use of δavg doesn't allow for a useful predictive tool as one must follow the evolution of δ(t). However, we show δ(t) remains close to δ0 and the the maximum strength, skewness, and kurtosis of the sea states are well predicted by the initial δ0. References [1] A.L. Islas and C.M. Schober, Predicting rogue waves in random oceanic sea states, Phys. Fluids 17 (2005). [2] P. Sura and S.T. Gille, Stochastic dynamics of sea surface height variability, J. Phys. Oceanogr. 40 (2010).
NASA Astrophysics Data System (ADS)
El-Tantawy, S. A.
2017-02-01
Progress is reported on the modulational instability (MI) of ion-acoustic waves (IAWs) and dissipative rogue waves (RWs) in ultracold neutral plasmas (UNPs). The UNPs consist of inertial ions fluid and Maxwellian inertialess hot electrons, and the presence of an ion kinematic viscosity is allowed. For this purpose, a modified nonlinear Schrödinger equation (NLSE) is derived and then solved analytically to show the occurrence of MI. It is found that the (in)stability regions of the wavepacks are dependent on time due to of the existence of the dissipative term. The existing regions of the MI of the IAWs are inventoried precisely. After that, we use a suitable transformation to convert the modified NLSE into the normal NLSE whose analytical solutions for rogue waves are known. The rogue wave propagation condition and its behavior are discussed. The impact of the relevant physical parameters on the profile of the RWs is examined.
Non-Rational Rogue Waves Induced by Inhomogeneity
NASA Astrophysics Data System (ADS)
He, Jing-Song; Wang, You-Ying; Li, Lin-Jing
2012-06-01
The variable Sine—Gordon (VSG) equation is often used to model several kinds of systems with inhomogeneity and it can be realized by the management of dispersion and nonlinearity in optics and Feschbach resonance in Bose-Einstein condensates. We derive four new kinds of non-rational rogue wave (RW) of the VSG by using an explicit transformation and the designable integrability. These RWs have novel profiles and interesting internal structures. It is shown that the RW is induced by the inhomogeneity of the system modeled by the VSG. The theoretical prediction of the corresponding relations between the RWs and some extreme events in DNA is discussed.
Generation and Limiters of Rogue Waves
2014-06-01
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Rational solitary wave and rogue wave solutions in coupled defocusing Hirota equation
NASA Astrophysics Data System (ADS)
Huang, Xin
2016-06-01
We derive and study a general rational solution of a coupled defocusing Hirota equation which can be used to describe evolution of light in a two-mode fiber with defocusing Kerr effect and some certain high-order effects. We find some new excitation patterns in the model, such as M-shaped soliton, W-shaped soliton, anti-eye-shaped rogue wave and four-petaled flower rogue wave. The results are compared with the solutions obtained in other coupled systems like vector nonlinear Schrödinger equation, coupled focusing Hirota and Sasa-Satsuma equations. We explain the new characters by modulational instability properties. This further indicates that rational solution does not necessarily correspond to rogue wave excitation dynamics and the quantitative relation between nonlinear excitations and modulational instability should exist.
Controlled generation of high-intensity optical rogue waves by induced modulation instability
NASA Astrophysics Data System (ADS)
Zhao, Saili; Yang, Hua; Chen, Nengsong; Zhao, Chujun
2017-01-01
Optical rogue waves are featured as the generation of high amplitude events at low probability in optical systems. Moreover, the formation of optical rogue waves is unpredictable and transient in photonic crystal fibers. In this paper, we put forward a method to generate high-intensity optical rogue waves in a more controlled way based on induced modulation instability, which can suppress the noise effect and hence play a leading role in the process of pulse evolution. Our numerical simulations indicate that the generation of rogue wave can be controlled when seeding at the optimal modulation frequency and the intensity of rogue wave can be enhanced with appropriate modulation depth. Further, high-intensity rogue wave can also be ejected in the fiber with a shorter propagation length by regulating the modulation depth. These results all provide a better understanding of optical rogue wave, which can contribute to the generation of tunable long-wavelength spectral components and selective excitation of mid-infrared supercontinuum.
Few-cycle optical rogue waves: complex modified Korteweg-de Vries equation.
He, Jingsong; Wang, Lihong; Li, Linjing; Porsezian, K; Erdélyi, R
2014-06-01
In this paper, we consider the complex modified Korteweg-de Vries (mKdV) equation as a model of few-cycle optical pulses. Using the Lax pair, we construct a generalized Darboux transformation and systematically generate the first-, second-, and third-order rogue wave solutions and analyze the nature of evolution of higher-order rogue waves in detail. Based on detailed numerical and analytical investigations, we classify the higher-order rogue waves with respect to their intrinsic structure, namely, fundamental pattern, triangular pattern, and ring pattern. We also present several new patterns of the rogue wave according to the standard and nonstandard decomposition. The results of this paper explain the generalization of higher-order rogue waves in terms of rational solutions. We apply the contour line method to obtain the analytical formulas of the length and width of the first-order rogue wave of the complex mKdV and the nonlinear Schrödinger equations. In nonlinear optics, the higher-order rogue wave solutions found here will be very useful to generate high-power few-cycle optical pulses which will be applicable in the area of ultrashort pulse technology.
Controlled generation of high-intensity optical rogue waves by induced modulation instability.
Zhao, Saili; Yang, Hua; Chen, Nengsong; Zhao, Chujun
2017-01-04
Optical rogue waves are featured as the generation of high amplitude events at low probability in optical systems. Moreover, the formation of optical rogue waves is unpredictable and transient in photonic crystal fibers. In this paper, we put forward a method to generate high-intensity optical rogue waves in a more controlled way based on induced modulation instability, which can suppress the noise effect and hence play a leading role in the process of pulse evolution. Our numerical simulations indicate that the generation of rogue wave can be controlled when seeding at the optimal modulation frequency and the intensity of rogue wave can be enhanced with appropriate modulation depth. Further, high-intensity rogue wave can also be ejected in the fiber with a shorter propagation length by regulating the modulation depth. These results all provide a better understanding of optical rogue wave, which can contribute to the generation of tunable long-wavelength spectral components and selective excitation of mid-infrared supercontinuum.
Controlled generation of high-intensity optical rogue waves by induced modulation instability
Zhao, Saili; Yang, Hua; Chen, Nengsong; Zhao, Chujun
2017-01-01
Optical rogue waves are featured as the generation of high amplitude events at low probability in optical systems. Moreover, the formation of optical rogue waves is unpredictable and transient in photonic crystal fibers. In this paper, we put forward a method to generate high-intensity optical rogue waves in a more controlled way based on induced modulation instability, which can suppress the noise effect and hence play a leading role in the process of pulse evolution. Our numerical simulations indicate that the generation of rogue wave can be controlled when seeding at the optimal modulation frequency and the intensity of rogue wave can be enhanced with appropriate modulation depth. Further, high-intensity rogue wave can also be ejected in the fiber with a shorter propagation length by regulating the modulation depth. These results all provide a better understanding of optical rogue wave, which can contribute to the generation of tunable long-wavelength spectral components and selective excitation of mid-infrared supercontinuum. PMID:28051149
Yomba, Emmanuel; Zakeri, Gholam-Ali
2016-08-01
The coupled inhomogeneous Schrödinger equations with a wide range of applications describing a field of pluses with the right and the left polarizations that take into account cross-phase modulations, stimulated Ramani scattering, and absorption effects are investigated. A combination of several different approaches is used in a novel way to obtain the explicit expressions for the rogue-pair and dark-bright-rogue waves. We study the dynamics of these structurally stable rogues and analyze the effects of a parameter that controls the region of stability that intrinsically connects the cross-phase modulation and other Kerr nonlinearity factors. The effects of the right and left polarizations on the shape of the rogue-pair and other solitary rogue waves are graphically analyzed. These rogue-pair waves are studied on periodic and non-periodic settings. We observe that rogue-pair wave from the right and left polarizations has a similar structure while the dark-bright-rogue waves have quite different intensity profiles.
NASA Astrophysics Data System (ADS)
Yomba, Emmanuel; Zakeri, Gholam-Ali
2016-08-01
The coupled inhomogeneous Schrödinger equations with a wide range of applications describing a field of pluses with the right and the left polarizations that take into account cross-phase modulations, stimulated Ramani scattering, and absorption effects are investigated. A combination of several different approaches is used in a novel way to obtain the explicit expressions for the rogue-pair and dark-bright-rogue waves. We study the dynamics of these structurally stable rogues and analyze the effects of a parameter that controls the region of stability that intrinsically connects the cross-phase modulation and other Kerr nonlinearity factors. The effects of the right and left polarizations on the shape of the rogue-pair and other solitary rogue waves are graphically analyzed. These rogue-pair waves are studied on periodic and non-periodic settings. We observe that rogue-pair wave from the right and left polarizations has a similar structure while the dark-bright-rogue waves have quite different intensity profiles.
The management of matter rogue waves in F = 1 spinor Bose-Einstein condensates
NASA Astrophysics Data System (ADS)
Loomba, Shally
2015-06-01
We have reported the matter rogue wave solutions for the nonautonomous three coupled Gross-Pitaevskii (GP) equation which governs the pulse propagation in spin-1 Bose-Einstein condensates (BECs) with time modulated nonlinearities. The system under consideration has attractive mean-field interactions and ferromagnetic spin-exchange interactions. The exact solutions have been worked out by using similarity and scaling transformations. We have depicted the controllable center characteristics of rogue waves for the kink-type spin-exchange interactions. Additionally, we have also discussed the management of rogue waves for the hyperbolic form of spin-exchange interactions by invoking isospectral Hamiltonian deformation technique.
Tao, Yongsheng; He, Jingsong
2012-02-01
The determinant representation of the n-fold Darboux transformation of the Hirota equation is given. Based on our analysis, the 1-soliton, 2-soliton, and breathers solutions are given explicitly. Further, the first order rogue wave solutions are given by a Taylor expansion of the breather solutions. In particular, the explicit formula of the rogue wave has several parameters, which is more general than earlier reported results and thus provides a systematic way to tune experimentally the rogue waves by choosing different values for them.
Localized modes of the Hirota equation: Nth order rogue wave and a separation of variable technique
NASA Astrophysics Data System (ADS)
Mu, Gui; Qin, Zhenyun; Chow, Kwok Wing; Ee, Bernard K.
2016-10-01
The Hirota equation is a special extension of the intensively studied nonlinear Schrödinger equation, by incorporating third order dispersion and one form of the self-steepening effect. Higher order rogue waves of the Hirota equation can be calculated theoretically through a Darboux-dressing transformation by a separation of variable approach. A Taylor expansion is used and no derivative calculation is invoked. Furthermore, stability of these rogue waves is studied computationally. By tracing the evolution of an exact solution perturbed by random noise, it is found that second order rogue waves are generally less stable than first order ones.
Weerasekara, Gihan; Tokunaga, Akihiro; Terauchi, Hiroki; Eberhard, Marc; Maruta, Akihiro
2015-01-12
One of the extraordinary aspects of nonlinear wave evolution which has been observed as the spontaneous occurrence of astonishing and statistically extraordinary amplitude wave is called rogue wave. We show that the eigenvalues of the associated equation of nonlinear Schrödinger equation are almost constant in the vicinity of rogue wave and we validate that optical rogue waves are formed by the collision between quasi-solitons in anomalous dispersion fiber exhibiting weak third order dispersion.
NASA Astrophysics Data System (ADS)
Su, Chuan-Qi; Wang, Yong-Yan; Liu, Xue-Qing; Qin, Nan
2017-07-01
Under investigation in this paper is an integrable equation which can describe the localized magnetization with spin torque under the long-wavelength approximation. In order to obtain the rogue wave solutions, a new Lax pair is derived. Infinitely-many conservation laws are also constructed. Based on the generalized Darboux transformation, the first-, second- and third-order rogue wave solutions are derived. Property of the rogue waves are analyzed and influence of parameters α, β and separating function f(ɛ) on the rogue waves and spatial-temporal structures are also discussed (the meaning of α and β can be found in the paper). For the case of f(ɛ) = 0 , the modulus of the kth-order rogue wave (k = 1 , 2 , 3) is irrelevant to parameter α. Parameter β influences the spatial-temporal range where the rogue wave appears. Spatial-temporal range enlarges with the increase of β. In addition, β also produces a skew angle and the skew angle rotates in the counter clockwise direction with the increase of β. f(ɛ) influences the spatial-temporal structures of the second- and third-order rouge waves. If f(ɛ) ≠ 0, the second-order rogue wave will split into three single first-order rouge waves and the triangular pattern can be formed, while the third-order rogue wave will split into six ones and the triangular pattern and pentagon pattern can be formed. The linear stability analysis is carried out, which shows that the modulation instability process is influenced by the amplitude of the harmonic wave and the wave number.
Nonlinear dynamics of trapped waves on jet currents and rogue waves.
Shrira, V I; Slunyaev, A V
2014-04-01
Nonlinear dynamics of surface gravity waves trapped by an opposing jet current is studied analytically and numerically. For wave fields narrow band in frequency but not necessarily with narrow angular distributions the developed asymptotic weakly nonlinear theory based on the modal approach of Shrira and Slunyaev [J. Fluid. Mech. 738, 65 (2014)] leads to the one-dimensional modified nonlinear Schrödinger equation of self-focusing type for a single mode. Its solutions such as envelope solitons and breathers are considered to be prototypes of rogue waves; these solutions, in contrast to waves in the absence of currents, are robust with respect to transverse perturbations, which suggests a potentially higher probability of rogue waves. Robustness of the long-lived analytical solutions describing modulated trapped waves and solitary wave groups is verified by direct numerical simulations of potential Euler equations.
Xie, Xi-Yang; Tian, Bo Wang, Yu-Feng; Sun, Ya; Jiang, Yan
2015-11-15
In this paper, we investigate a generalized nonautonomous nonlinear equation which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber. By virtue of the generalized Darboux transformation, the first- and second-order rogue-wave solutions for the generalized nonautonomous nonlinear equation are obtained, under some variable–coefficient constraints. Properties of the first- and second-order rogue waves are graphically presented and analyzed: When the coefficients are all chosen as the constants, we can observe the some functions, the shapes of wave crests and troughs for the first- and second-order rogue waves change. Oscillating behaviors of the first- and second-order rogue waves are observed when the coefficients are the trigonometric functions.
Matter rogue waves in an F=1 spinor Bose-Einstein condensate.
Qin, Zhenyun; Mu, Gui
2012-09-01
We report new types of matter rogue waves of a spinor (three-component) model of the Bose-Einstein condensate governed by a system of three nonlinearly coupled Gross-Pitaevskii equations. The exact first-order rational solutions containing one free parameter are obtained by means of a Darboux transformation for the integrable system where the mean-field interaction is attractive and the spin-exchange interaction is ferromagnetic. For different choices of the parameter, there exists a variety of different shaped solutions including two peaks in bright rogue waves and four dips in dark rogue waves. Furthermore, by utilizing the relation between the three-component and the one-component versions of the nonlinear Schrödinger equation, we can devise higher-order rational solutions, in which three components have different shapes. In addition, it is noteworthy that dark rogue wave features disappear in the third-order rational solution.
Manipulating matter rogue waves and breathers in Bose-Einstein condensates.
Manikandan, K; Muruganandam, P; Senthilvelan, M; Lakshmanan, M
2014-12-01
We construct higher-order rogue wave solutions and breather profiles for the quasi-one-dimensional Gross-Pitaevskii equation with a time-dependent interatomic interaction and external trap through the similarity transformation technique. We consider three different forms of traps: (i) the time-independent expulsive trap, (ii) time-dependent monotonous trap, and (iii) time-dependent periodic trap. Our results show that when we change a parameter appearing in the time-independent or time-dependent trap the second- and third-order rogue waves transform into the first-order-like rogue waves. We also analyze the density profiles of breather solutions. Here we also show that the shapes of the breathers change when we tune the strength of the trap parameter. Our results may help to manage rogue waves experimentally in a BEC system.
Solutions of the vector nonlinear Schrödinger equations: evidence for deterministic rogue waves.
Baronio, Fabio; Degasperis, Antonio; Conforti, Matteo; Wabnitz, Stefan
2012-07-27
We construct and discuss a semirational, multiparametric vector solution of coupled nonlinear Schrödinger equations (Manakov system). This family of solutions includes known vector Peregrine solutions, bright- and dark-rogue solutions, and novel vector unusual freak waves. The vector rogue waves could be of great interest in a variety of complex systems, from optics and fluid dynamics to Bose-Einstein condensates and finance.
Nonlinear Schrödinger equation: generalized Darboux transformation and rogue wave solutions.
Guo, Boling; Ling, Liming; Liu, Q P
2012-02-01
In this paper, we construct a generalized Darboux transformation for the nonlinear Schrödinger equation. The associated N-fold Darboux transformation is given in terms of both a summation formula and determinants. As applications, we obtain compact representations for the Nth-order rogue wave solutions of the focusing nonlinear Schrödinger equation and Hirota equation. In particular, the dynamics of the general third-order rogue wave is discussed and shown to exhibit interesting structures.
NASA Astrophysics Data System (ADS)
Tchinang Tchameu, J. D.; Togueu Motcheyo, A. B.; Tchawoua, C.
2016-09-01
The discrete multi-rogue waves (DMRW) as solution of the discrete nonlinear Schrödinger (DNLS) equation with saturable nonlinearities is studied numerically. These biological rogue waves represent the complex probability amplitude of finding an amide-I vibrational quantum at a site. We observe that the growth in the higher order saturable nonlinearity implies the formation of DMRW including an increase in the short-living DMRW and a decrease in amplitude of the long-living DMRW.
NASA Astrophysics Data System (ADS)
Bains, A. S.; Tribeche, Mouloud; Saini, N. S.; Gill, T. S.
2017-01-01
A theoretical investigation is made to study envelope excitations and rogue wave structures of the newly predicted positron-acoustic waves (PAWs) in a plasma with nonextensive electrons and nonextensive hot positrons. The reductive perturbation technique (RPT) is used to derive a nonlinear Schrödinger equation-like (NLSE) which governs the modulational instability (MI) of the PAWs. The NLSE admits localized envelope solitary wave solutions of bright and dark type. These envelope solutions depend upon the intrinsic plasma parameters. It is found that the MI of the PAWs is significantly affected by nonextensivity and other plasma parameters. Further, the analysis is extended for the rogue wave structures of the PAWs. The findings of the present investigation should be useful in understanding the acceleration mechanism of stable electrostatic wave packets in four components nonextensive plasmas.
Rogue waves in terms of multi-point statistics and nonequilibrium thermodynamics
NASA Astrophysics Data System (ADS)
Hadjihosseini, Ali; Lind, Pedro; Mori, Nobuhito; Hoffmann, Norbert P.; Peinke, Joachim
2017-04-01
Ocean waves, which lead to rogue waves, are investigated on the background of complex systems. In contrast to deterministic approaches based on the nonlinear Schroedinger equation or focusing effects, we analyze this system in terms of a noisy stochastic system. In particular we present a statistical method that maps the complexity of multi-point data into the statistics of hierarchically ordered height increments for different time scales. We show that the stochastic cascade process with Markov properties is governed by a Fokker-Planck equation. Conditional probabilities as well as the Fokker-Planck equation itself can be estimated directly from the available observational data. This stochastic description enables us to show several new aspects of wave states. Surrogate data sets can in turn be generated allowing to work out different statistical features of the complex sea state in general and extreme rogue wave events in particular. The results also open up new perspectives for forecasting the occurrence probability of extreme rogue wave events, and even for forecasting the occurrence of individual rogue waves based on precursory dynamics. As a new outlook the ocean wave states will be considered in terms of nonequilibrium thermodynamics, for which the entropy production of different wave heights will be considered. We show evidence that rogue waves are characterized by negative entropy production. The statistics of the entropy production can be used to distinguish different wave states.
Rogue waves of the Sasa-Satsuma equation in a chaotic wave field.
Soto-Crespo, J M; Devine, N; Hoffmann, N P; Akhmediev, N
2014-09-01
We study the properties of the chaotic wave fields generated in the frame of the Sasa-Satsuma equation (SSE). Modulation instability results in a chaotic pattern of small-scale filaments with a free parameter-the propagation constant k. The average velocity of the filaments is approximately given by the group velocity calculated from the dispersion relation for the plane-wave solution. Remarkably, our results reveal the reason for the skewed profile of the exact SSE rogue-wave solutions, which was one of their distinctive unexplained features. We have also calculated the probability density functions for various values of the propagation constant k, showing that probability of appearance of rogue waves depends on k.
Reduced-order prediction of rogue waves in two-dimensional deep-water waves
NASA Astrophysics Data System (ADS)
Farazmand, Mohammad; Sapsis, Themistoklis P.
2017-07-01
We consider the problem of large wave prediction in two-dimensional water waves. Such waves form due to the synergistic effect of dispersive mixing of smaller wave groups and the action of localized nonlinear wave interactions that leads to focusing. Instead of a direct simulation approach, we rely on the decomposition of the wave field into a discrete set of localized wave groups with optimal length scales and amplitudes. Due to the short-term character of the prediction, these wave groups do not interact and therefore their dynamics can be characterized individually. Using direct numerical simulations of the governing envelope equations we precompute the expected maximum elevation for each of those wave groups. The combination of the wave field decomposition algorithm, which provides information about the statistics of the system, and the precomputed map for the expected wave group elevation, which encodes dynamical information, allows (i) for understanding of how the probability of occurrence of rogue waves changes as the spectrum parameters vary, (ii) the computation of a critical length scale characterizing wave groups with high probability of evolving to rogue waves, and (iii) the formulation of a robust and parsimonious reduced-order prediction scheme for large waves. We assess the validity of this scheme in several cases of ocean wave spectra.
Bright-dark rogue wave in mode-locked fibre laser (Conference Presentation)
NASA Astrophysics Data System (ADS)
Kbashi, Hani; Kolpakov, Stanislav; Martinez, Amós; Mou, Chengbo; Sergeyev, Sergey V.
2017-05-01
Bright-Dark Rogue Wave in Mode-Locked Fibre Laser Hani Kbashi1*, Amos Martinez1, S. A. Kolpakov1, Chengbo Mou, Alex Rozhin1, Sergey V. Sergeyev1 1Aston Institute of Photonic Technologies, School of Engineering and Applied Science Aston University, Birmingham, B4 7ET, UK kbashihj@aston.ac.uk , 0044 755 3534 388 Keywords: Optical rogue wave, Bright-Dark rogue wave, rogue wave, mode-locked fiber laser, polarization instability. Abstract: Rogue waves (RWs) are statistically rare localized waves with high amplitude that suddenly appear and disappear in oceans, water tanks, and optical systems [1]. The investigation of these events in optics, optical rogue waves, is of interest for both fundamental research and applied science. Recently, we have shown that the adjustment of the in-cavity birefringence and pump polarization leads to emerge optical RW events [2-4]. Here, we report the first experimental observation of vector bright-dark RWs in an erbium-doped stretched pulse mode-locked fiber laser. The change of induced in-cavity birefringence provides an opportunity to observe RW events at pump power is a little higher than the lasing threshold. Polarization instabilities in the laser cavity result in the coupling between two orthogonal linearly polarized components leading to the emergence of bright-dark RWs. The observed clusters belongs to the class of slow optical RWs because their lifetime is of order of a thousand of laser cavity roundtrip periods. References: 1. D. R. Solli, C. Ropers, P. Koonath,and B. Jalali, Optical rogue waves," Nature, 450, 1054-1057, 2007. 2. S. V. Sergeyev, S. A. Kolpakov, C. Mou, G. Jacobsen, S. Popov, and V. Kalashnikov, "Slow deterministic vector rogue waves," Proc. SPIE 9732, 97320K (2016). 3. S. A. Kolpakov, H. Kbashi, and S. V. Sergeyev, "Dynamics of vector rogue waves in a fiber laser with a ring cavity," Optica, 3, 8, 870, (2016). 5. S. Kolpakov, H. Kbashi, and S. Sergeyev, "Slow optical rogue waves in a unidirectional fiber laser
NASA Astrophysics Data System (ADS)
Zhang, Hai-Qiang; Yuan, Sha-Sha; Wang, Yue
2016-05-01
In this paper, the generalized Darboux transformation for the coherently-coupled nonlinear Schrödinger (CCNLS) system is constructed in terms of determinant representations. Based on the Nth-iterated formula, the vector bright soliton solution and vector rogue wave solution are systematically derived under the nonvanishing background. The general first-order vector rogue wave solution can admit many different fundamental patterns including eye-shaped and four-petaled rogue waves. It is believed that there are many more abundant patterns for high order vector rogue waves in CCNLS system.
Wave Turbulence in Superfluid {sup 4}He: Energy Cascades and Rogue Waves in the Laboratory
Efimov, V. B.; Ganshin, A. N.; McClintock, P. V. E.; Kolmakov, G. V.; Mezhov-Deglin, L. P.
2008-11-13
Recent work on second sound acoustic turbulence in superfluid {sup 4}He is reviewed. Observations of forward and inverse energy cascades are described. The onset of the inverse cascade occurs above a critical driving energy and it is accompanied by giant waves that constitute an acoustic analogue of the rogue waves that occasionally appear on the surface of the ocean. The theory of the phenomenon is outlined and shown to be in good agreement with the experiments.
Ocean rogue waves and their phase space dynamics in the limit of a linear interference model
Birkholz, Simon; Brée, Carsten; Veselić, Ivan; Demircan, Ayhan; Steinmeyer, Günter
2016-01-01
We reanalyse the probability for formation of extreme waves using the simple model of linear interference of a finite number of elementary waves with fixed amplitude and random phase fluctuations. Under these model assumptions no rogue waves appear when less than 10 elementary waves interfere with each other. Above this threshold rogue wave formation becomes increasingly likely, with appearance frequencies that may even exceed long-term observations by an order of magnitude. For estimation of the effective number of interfering waves, we suggest the Grassberger-Procaccia dimensional analysis of individual time series. For the ocean system, it is further shown that the resulting phase space dimension may vary, such that the threshold for rogue wave formation is not always reached. Time series analysis as well as the appearance of particular focusing wind conditions may enable an effective forecast of such rogue-wave prone situations. In particular, extracting the dimension from ocean time series allows much more specific estimation of the rogue wave probability. PMID:27731411
Ocean rogue waves and their phase space dynamics in the limit of a linear interference model.
Birkholz, Simon; Brée, Carsten; Veselić, Ivan; Demircan, Ayhan; Steinmeyer, Günter
2016-10-12
We reanalyse the probability for formation of extreme waves using the simple model of linear interference of a finite number of elementary waves with fixed amplitude and random phase fluctuations. Under these model assumptions no rogue waves appear when less than 10 elementary waves interfere with each other. Above this threshold rogue wave formation becomes increasingly likely, with appearance frequencies that may even exceed long-term observations by an order of magnitude. For estimation of the effective number of interfering waves, we suggest the Grassberger-Procaccia dimensional analysis of individual time series. For the ocean system, it is further shown that the resulting phase space dimension may vary, such that the threshold for rogue wave formation is not always reached. Time series analysis as well as the appearance of particular focusing wind conditions may enable an effective forecast of such rogue-wave prone situations. In particular, extracting the dimension from ocean time series allows much more specific estimation of the rogue wave probability.
Ocean rogue waves and their phase space dynamics in the limit of a linear interference model
NASA Astrophysics Data System (ADS)
Birkholz, Simon; Brée, Carsten; Veselić, Ivan; Demircan, Ayhan; Steinmeyer, Günter
2016-10-01
We reanalyse the probability for formation of extreme waves using the simple model of linear interference of a finite number of elementary waves with fixed amplitude and random phase fluctuations. Under these model assumptions no rogue waves appear when less than 10 elementary waves interfere with each other. Above this threshold rogue wave formation becomes increasingly likely, with appearance frequencies that may even exceed long-term observations by an order of magnitude. For estimation of the effective number of interfering waves, we suggest the Grassberger-Procaccia dimensional analysis of individual time series. For the ocean system, it is further shown that the resulting phase space dimension may vary, such that the threshold for rogue wave formation is not always reached. Time series analysis as well as the appearance of particular focusing wind conditions may enable an effective forecast of such rogue-wave prone situations. In particular, extracting the dimension from ocean time series allows much more specific estimation of the rogue wave probability.
Ion-acoustic super rogue waves in ultracold neutral plasmas with nonthermal electrons
El-Tantawy, S. A.; El-Bedwehy, N. A.; El-Labany, S. K.
2013-07-15
The ion-acoustic rogue waves in ultracold neutral plasmas consisting of ion fluid and nonthermal electrons are reported. A reductive perturbation method is used to obtain a nonlinear Schrödinger equation for describing the system and the modulation instability of the ion-acoustic wave is analyzed. The critical wave number k{sub c}, which indicates where the modulational instability sets in, has been determined. Moreover, the possible region for the ion-acoustic rogue waves to exist is defined precisely. The effects of the nonthermal parameter β and the ions effective temperature ratio σ{sub *} on the critical wave number k{sub c} are studied. It is found that there are two critical wave numbers in our plasma system. For low wave number, increasing β would lead to cringe k{sub c} until β approaches to its critical value β{sub c}, then further increase of β beyond β{sub c} would enhance the values of k{sub c}. For large wave numbers, the increase of β would lead to a decrease of k{sub c}. However, increasing σ{sub *} would lead to the reduction of k{sub c} for all values of the wave number. The dependence of the rogue waves profile on the plasma parameters is numerically examined. It is found that the rogue wave amplitudes have complex behavior with increasing β. Furthermore, the enhancement of σ{sub *} and the carrier wave number k reduces the rogue wave amplitude. It is noticed that near to the critical wave number, the rogue wave amplitude becomes high, but it shrinks whenever we stepped away from k{sub c}. The implications of our results in laboratory ultracold neutral plasma experiments are briefly discussed.
NASA Astrophysics Data System (ADS)
Sun, Wen-Rong; Tian, Bo; Xie, Xi-Yang; Chai, Jun; Jiang, Yan
2016-10-01
High-order rogue waves of the coupled nonlinear Schrödinger equations with negative coherent coupling, which describe the propagation of orthogonally polarized optical waves in an isotropic medium, are reported in this paper. Key point lies in the introduction of a limit process in the Darboux transformation, with which we obtain a family of the first- and second-order rational solutions for the purpose of modelling the rogue waves. We observe that the double-hump rogue wave in the course of evolution turns into the one-hump rogue wave, and that the dark rogue wave with four valleys in the course of evolution turns into the bright rogue wave. It is found that the second-order rogue wave can split up, giving birth to the multiple rogue waves.
Dust ion-acoustic rogue waves in a three-species ultracold quantum dusty plasmas
Sun, Wen-Rong; Tian, Bo Liu, Rong-Xiang; Liu, De-Yin
2014-10-15
Dust ion-acoustic (DIA) rogue waves are reported for a three-component ultracold quantum dusty plasma comprised of inertialess electrons, inertial ions, and negatively charged immobile dust particles. The nonlinear Schrödinger (NLS) equation appears for the low frequency limit. Modulation instability (MI) of the DIA waves is analyzed. Influence of the modulation wave number, ion-to-electron Fermi temperature ratio ρ and dust-to-ion background density ratio N{sub d} on the MI growth rate is discussed. The first- and second-order DIA rogue-wave solutions of the NLS equation are examined numerically. It is found that the enhancement of N{sub d} and carrier wave number can increase the envelope rogue-wave amplitudes. However, the increase of ρ reduces the envelope rogue-wave amplitudes. - Highlights: • The nonlinear Schrödinger equation is derived for the low frequency limit. • Modulational instability growth rate is discussed. • The first- and second-order dust ion-acoustic rogue waves are examined numerically.
Rogue-wave bullets in a composite (2+1)D nonlinear medium.
Chen, Shihua; Soto-Crespo, Jose M; Baronio, Fabio; Grelu, Philippe; Mihalache, Dumitru
2016-07-11
We show that nonlinear wave packets localized in two dimensions with characteristic rogue wave profiles can propagate in a third dimension with significant stability. This unique behavior makes these waves analogous to light bullets, with the additional feature that they propagate on a finite background. Bulletlike rogue-wave singlet and triplet are derived analytically from a composite (2+1)D nonlinear wave equation. The latter can be interpreted as the combination of two integrable (1+1)D models expressed in different dimensions, namely, the Hirota equation and the complex modified Korteweg-de Vries equation. Numerical simulations confirm that the generation of rogue-wave bullets can be observed in the presence of spontaneous modulation instability activated by quantum noise.
On a plasma having nonextensive electrons and positrons: Rogue and solitary wave propagation
El-Awady, E. I.; Moslem, W. M.
2011-08-15
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 Schroedinger 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.
Harnessing rogue wave for supercontinuum generation in cascaded photonic crystal fiber.
Zhao, Saili; Yang, Hua; Zhao, Chujun; Xiao, Yuzhe
2017-04-03
Based on induced modulation instability, we present a numerical study on harnessing rogue wave for supercontinuum generation in cascaded photonic crystal fibers. By selecting optimum modulation frequency, we achieve supercontinuum with a great improvement on spectrum stability when long-pulse is used as the pump. In this case, rogue wave can be obtained in the first segmented photonic crystal fiber with one zero dispersion wavelength in a controllable manner. Numerical simulations show that spectral range and flatness can be regulated in an extensive range by cascading a photonic crystal fiber with two zero dispersion wavelengths. Some novel phenomena are observed in the second segmented photonic crystal fiber. When the second zero dispersion wavelength is close to the first one, rogue wave is directly translated into dispersion waves, which is conducive to the generation of smoother supercontinuum. When the second zero dispersion wavelength is far away from the first one, rogue wave is translated into the form of fundamental soliton steadily propagating in the vicinity of the second zero dispersion wavelength. Meanwhile, the corresponding red-shifted dispersion wave is generated when the phase matching condition is met, which is beneficial to the generation of wider supercontinuum. The results presented in this work provide a better application of optical rogue wave to generate flat and broadband supercontinuum in cascaded photonic crystal fibers.
Ion-acoustic rogue waves in magnetized solar wind plasma with nonextensive electrons
NASA Astrophysics Data System (ADS)
Bacha, Mustapha; Gougam, Leila Ait; Tribeche, Mouloud
2017-01-01
Ion-acoustic rogue waves are investigated in a two-component magnetized solar wind plasma, composed of positively charged fluid ions, as well as nonextensive electrons. Typical solar wind plasmas parameters are used. It is shown that the wave number domain for the onset of ion-acoustic modulational instability enlarges as the electrons evolve towards their thermal equilibrium. Interestingly, we show that as the solar wind plasma expands far out from the sun, the wave amplitude increases and the IA rogue wave concentrates therefore a significant amount of energy. Our investigation may be of wide relevance to astronomers and space scientists working on the solar wind and interstellar plasmas.
Rogue wave triplets in an ion-beam dusty plasma with superthermal electrons and negative ions
NASA Astrophysics Data System (ADS)
Guo, Shimin; Mei, Liquan; Shi, Weijuan
2013-11-01
A new dust ion-acoustic wave structure called ‘Rogue wave triplets’ is investigated in an unmagnetized plasma consisting of stationary negatively charged dust grains, charged positive and negative ions, and electrons obeying kappa distribution, which is penetrated by an ion beam. The reductive perturbation theory is used to derive the nonlinear Schrödinger equation governing the dynamics as well as the modulation of wave packets. The rogue wave triplets which are composed of three separate Peregrine breathers can be generated in the modulation instability region. It has been suggested that a laboratory experiment be performed to test the theory presented here.
Ion acoustic kinetic Alfvén rogue waves in two temperature electrons superthermal plasmas
NASA Astrophysics Data System (ADS)
Kaur, Nimardeep; Saini, N. S.
2016-10-01
The propagation properties of ion acoustic kinetic Alfvén (IAKA) solitary and rogue waves have been investigated in two temperature electrons magnetized superthermal plasma in the presence of dust impurity. A nonlinear analysis is carried out to derive the Korteweg-de Vries (KdV) equation using the reductive perturbation method (RPM) describing the evolution of solitary waves. The effect of various plasma parameters on the characteristics of the IAKA solitary waves is studied. The dynamics of ion acoustic kinetic Alfvén rogue waves (IAKARWs) are also studied by transforming the KdV equation into nonlinear Schrödinger (NLS) equation. The characteristics of rogue wave profile under the influence of various plasma parameters (κc, μc, σ , θ) are examined numerically by using the data of Saturn's magnetosphere (Schippers et al. 2008; Sakai et al. 2013).
Decay of capillary wave turbulence.
Deike, Luc; Berhanu, Michael; Falcon, Eric
2012-06-01
We report on the observation of freely decaying capillary wave turbulence on the surface of a fluid. The capillary wave turbulence spectrum decay is found to be self-similar in time with the same power law exponent as the one found in the stationary regime, in agreement with weak turbulence predictions. The amplitude of all Fourier modes are found to decrease exponentially with time at the same damping rate. The longest wavelengths involved in the system are shown to be damped by a viscous surface boundary layer. These long waves play the role of an energy source during the decay that sustains nonlinear interactions to keep capillary waves in a wave turbulent state.
New Patterns of the Two-Dimensional Rogue Waves: (2+1)-Dimensional Maccari System
NASA Astrophysics Data System (ADS)
Wang, Gai-Hua; Wang, Li-Hong; Rao, Ji-Guang; He, Jing-Song
2017-06-01
The ocean rogue wave is one kind of puzzled destructive phenomenon that has not been understood thoroughly so far. The two-dimensional nature of this wave has inspired the vast endeavors on the recognizing new patterns of the rogue waves based on the dynamical equations with two-spatial variables and one-temporal variable, which is a very crucial step to prevent this disaster event at the earliest stage. Along this issue, we present twelve new patterns of the two-dimensional rogue waves, which are reduced from a rational and explicit formula of the solutions for a (2+1)-dimensional Maccari system. The extreme points (lines) of the first-order lumps (rogue waves) are discussed according to their analytical formulas. For the lower-order rogue waves, we show clearly in formula that parameter b 2 plays a significant role to control these patterns. Supported by the National Natural Science Foundation of China under Grant No. 11671219, the K. C. Wong Magna Fund in Ningbo University, Gai-Hua Wang is also supported by the Scientific Research Foundation of Graduate School of Ningbo University
Rogue wave variational modelling through the interaction of two solitary waves
NASA Astrophysics Data System (ADS)
Gidel, Floriane; Bokhove, Onno
2016-04-01
The extreme and unexpected characteristics of Rogue waves have made them legendary for centuries. It is only on the 1st of January 1995 that these mariners' tales started to raise scientist's curiosity, when such a wave was recorded in the North Sea; a sudden wall of water hit the Draupner offshore platform, more than twice higher than the other waves, providing evidence of the existence of rogue or freak waves. Since then, studies have shown that these surface gravity waves of high amplitude (at least twice the height of the other sea waves [Dyste et al., 2008]) appear in non-linear dispersive water motion [Drazin and Johnson, 1989], at any depth, and have caused a lot of damage in recent years [Nikolkina and Didenkulova, 2011 ]. So far, most of the studies have tried to determine their probability of occurrence, but no conclusion has been achieved yet, which means that we are currently unenable to predict or avoid these monster waves. An accurate mathematical and numerical water-wave model would enable simulation and observation of this external forcing on boats and offshore structures and hence reduce their threat. In this work, we aim to model rogue waves through a soliton splash generated by the interaction of two solitons coming from different channels at a specific angle. Kodama indeed showed that one way to produce extreme waves is through the intersection of two solitary waves, or one solitary wave and its oblique reflection on a vertical wall [Yeh, Li and Kodama, 2010 ]. While he modelled Mach reflection from Kadomtsev-Petviashvili (KP) theory, we aim to model rogue waves from the three-dimensional potential flow equations and/or their asymptotic equivalent described by Benney and Luke [Benney and Luke, 1964]. These theories have the advantage to allow wave propagation in several directions, which is not the case with KP equations. The initial solitary waves are generated by removing a sluice gate in each channel. The equations are derived through a
Dudley, J. M.; Sarano, V.; Dias, F.
2013-01-01
The Hokusai woodcut entitled The great wave off Kanagawa has been interpreted as an unusually large storm wave, likely to be classed as a rogue wave, and possibly generated from nonlinear wave dynamics (J. H. E. Cartwright and H. Nakamura, Notes Rec. R. Soc. 63, 119–135 (2009)). In this paper, we present a complementary discussion of this hypothesis, discussing in particular how linear and nonlinear mechanisms can both contribute to the emergence of rogue wave events. By making reference to the Great wave's simultaneous transverse and longitudinal localization, we show that the purely linear mechanism of directional focusing also predicts characteristics consistent with those of the Great wave. In addition, we discuss the properties of a particular rogue wave photographed on the open ocean in sub-Antarctic waters, which shows two-dimensional localization and breaking dynamics remarkably similar to Hokusai's depiction in the woodcut. PMID:24687148
Dudley, J M; Sarano, V; Dias, F
2013-06-20
The Hokusai woodcut entitled The great wave off Kanagawa has been interpreted as an unusually large storm wave, likely to be classed as a rogue wave, and possibly generated from nonlinear wave dynamics (J. H. E. Cartwright and H. Nakamura, Notes Rec. R. Soc.63, 119-135 (2009)). In this paper, we present a complementary discussion of this hypothesis, discussing in particular how linear and nonlinear mechanisms can both contribute to the emergence of rogue wave events. By making reference to the Great wave's simultaneous transverse and longitudinal localization, we show that the purely linear mechanism of directional focusing also predicts characteristics consistent with those of the Great wave. In addition, we discuss the properties of a particular rogue wave photographed on the open ocean in sub-Antarctic waters, which shows two-dimensional localization and breaking dynamics remarkably similar to Hokusai's depiction in the woodcut.
Magnetic rogue wave in a perpendicular anisotropic ferromagnetic nanowire with spin-transfer torque
NASA Astrophysics Data System (ADS)
Zhao, Fei; Li, Zai-Dong; Li, Qiu-Yan; Wen, Lin; Fu, Guangsheng; Liu, W. M.
2012-09-01
We present the current controlled motion of a dynamic soliton embedded in spin wave background in ferromagnetic nanowire. With the stronger breather character we get the novel magnetic rogue wave and clarify its formation mechanism. The generation of magnetic rogue wave mainly arises from the accumulation of energy and magnons toward to its central part. We also observe that the spin-polarized current can control the exchange rate of magnons between the envelope soliton and the background, and the critical current condition is obtained analytically. Even more interesting is that the spin-transfer torque plays the completely opposite role for the cases below and above the critical value.
NASA Astrophysics Data System (ADS)
Tsai, Ya-Yi; Tsai, Jun-Yi; I, Lin
2016-06-01
Rogue waves--rare uncertainly emerging localized events with large amplitudes--have been experimentally observed in many nonlinear wave phenomena, such as water waves, optical waves, second sound in superfluid He II (ref. ) and ion acoustic waves in plasmas. Past studies have mainly focused on one-dimensional (1D) wave behaviour through modulation instabilities, and to a lesser extent on higher-dimensional behaviour. The question whether rogue waves also exist in nonlinear 3D acoustic-type plasma waves, the kinetic origin of their formation and their correlation with surrounding 3D waveforms are unexplored fundamental issues. Here we report the direct experimental observation of dust acoustic rogue waves in dusty plasmas and construct a picture of 3D particle focusing by the surrounding tilted and ruptured wave crests, associated with the higher probability of low-amplitude holes for rogue-wave generation.
On the rogue waves propagation in non-Maxwellian complex space plasmas
NASA Astrophysics Data System (ADS)
El-Tantawy, S. A.; El-Awady, E. I.; Tribeche, M.
2015-11-01
The implications of the non-Maxwellian electron distributions (nonthermal/or suprathermal/or nonextensive distributions) are examined on the dust-ion acoustic (DIA) rogue/freak waves in a dusty warm plasma. Using a reductive perturbation technique, the basic set of fluid equations is reduced to a nonlinear Schrödinger equation. The latter is used to study the nonlinear evolution of modulationally unstable DIA wavepackets and to describe the rogue waves (RWs) propagation. Rogue waves are large-amplitude short-lived wave groups, routinely observed in space plasmas. The possible region for the rogue waves to exist is defined precisely for typical parameters of space plasmas. It is shown that the RWs strengthen for decreasing plasma nonthermality and increasing superthermality. For nonextensive electrons, the RWs amplitude exhibits a bit more complex behavior, depending on the entropic index q. Moreover, our numerical results reveal that the RWs exist with all values of the ion-to-electron temperature ratio σ for nonthermal and superthermal distributions and there is no limitation for the freak waves to propagate in both two distributions in the present plasma system. But, for nonextensive electron distribution, the bright- and dark-type waves can propagate in this case, which means that there is a limitation for the existence of freak waves. Our systematic investigation should be useful in understanding the properties of DIA solitary waves that may occur in non-Maxwellian space plasmas.
On the rogue waves propagation in non-Maxwellian complex space plasmas
El-Tantawy, S. A. El-Awady, E. I.; Tribeche, M. E-mail: mtribeche@usthb.dz
2015-11-15
The implications of the non-Maxwellian electron distributions (nonthermal/or suprathermal/or nonextensive distributions) are examined on the dust-ion acoustic (DIA) rogue/freak waves in a dusty warm plasma. Using a reductive perturbation technique, the basic set of fluid equations is reduced to a nonlinear Schrödinger equation. The latter is used to study the nonlinear evolution of modulationally unstable DIA wavepackets and to describe the rogue waves (RWs) propagation. Rogue waves are large-amplitude short-lived wave groups, routinely observed in space plasmas. The possible region for the rogue waves to exist is defined precisely for typical parameters of space plasmas. It is shown that the RWs strengthen for decreasing plasma nonthermality and increasing superthermality. For nonextensive electrons, the RWs amplitude exhibits a bit more complex behavior, depending on the entropic index q. Moreover, our numerical results reveal that the RWs exist with all values of the ion-to-electron temperature ratio σ for nonthermal and superthermal distributions and there is no limitation for the freak waves to propagate in both two distributions in the present plasma system. But, for nonextensive electron distribution, the bright- and dark-type waves can propagate in this case, which means that there is a limitation for the existence of freak waves. Our systematic investigation should be useful in understanding the properties of DIA solitary waves that may occur in non-Maxwellian space plasmas.
NASA Astrophysics Data System (ADS)
Wang, Yue-Yue; Dai, Chao-Qing
2012-08-01
With the help of the similarity transformation connected the variable-coefficient (3+1)-dimensional nonlinear Schrödinger equation with the standard nonlinear Schrödinger equation, we firstly obtain first-order and second-order rogue wave solutions. Then, we investigate the controllable behaviors of these rogue waves in the hyperbolic dispersion decreasing profile. Our results indicate that the integral relation between the accumulated time T and the real time t is the basis to realize the control and manipulation of propagation behaviors of rogue waves, such as sustainment and restraint. We can modulate the value To to achieve the sustained and restrained spatiotemporal rogue waves. Moreover, the controllability for position of sustainment and restraint for spatiotemporal rogue waves can also be realized by setting different values of X0.
NASA Astrophysics Data System (ADS)
Ling, Liming; Feng, Bao-Feng; Zhu, Zuonong
2016-07-01
In the present paper, we are concerned with the general analytic solutions to the complex short pulse (CSP) equation including soliton, breather and rogue wave solutions. With the aid of a generalized Darboux transformation, we construct the N-bright soliton solution in a compact determinant form, the N-breather solution including the Akhmediev breather and a general higher order rogue wave solution. The first and second order rogue wave solutions are given explicitly and analyzed. The asymptotic analysis is performed rigorously for both the N-soliton and the N-breather solutions. All three forms of the analytical solutions admit either smoothed-, cusped- or looped-type ones for the CSP equation depending on the parameters. It is noted that, due to the reciprocal (hodograph) transformation, the rogue wave solution to the CSP equation can be a smoothed, cusponed or a looped one, which is different from the rogue wave solution found so far.
Amplification of matter rogue waves and breathers in quasi-two-dimensional Bose-Einstein condensates
NASA Astrophysics Data System (ADS)
Manikandan, K.; Senthilvelan, M.; Kraenkel, R. A.
2016-02-01
We construct rogue wave and breather solutions of a quasi-two-dimensional Gross-Pitaevskii equation with a time-dependent interatomic interaction and external trap. We show that the trapping potential and an arbitrary functional parameter that present in the similarity transformation should satisfy a constraint for the considered equation to be integrable and yield the desired solutions. We consider two different forms of functional parameters and investigate how the density of the rogue wave and breather profiles vary with respect to these functional parameters. We also construct vector localized solutions of a two coupled quasi-two-dimensional Bose-Einstein condensate system. We then investigate how the vector localized density profiles modify in the constant density background with respect to the functional parameters. Our results may help to manipulate matter rogue waves experimentally in the two-dimensional Bose-Einstein condensate systems.
Classifying the hierarchy of nonlinear-Schrödinger-equation rogue-wave solutions.
Kedziora, David J; Ankiewicz, Adrian; Akhmediev, Nail
2013-07-01
We present a systematic classification for higher-order rogue-wave solutions of the nonlinear Schrödinger equation, constructed as the nonlinear superposition of first-order breathers via the recursive Darboux transformation scheme. This hierarchy is subdivided into structures that exhibit varying degrees of radial symmetry, all arising from independent degrees of freedom associated with physical translations of component breathers. We reveal the general rules required to produce these fundamental patterns. Consequently, we are able to extrapolate the general shape for rogue-wave solutions beyond order 6, at which point accuracy limitations due to current standards of numerical generation become non-negligible. Furthermore, we indicate how a large set of irregular rogue-wave solutions can be produced by hybridizing these fundamental structures.
NASA Astrophysics Data System (ADS)
Tsai, Ya-Yi; Chang, Mei-Chu; Tsai, Jun-Yi; I, Lin
2017-05-01
In this work, we briefly review our recent experimental studies on the observations and waveform dynamics of spontaneous excitations of low and high amplitude singular objects: low amplitude hole filaments coinciding with the wiggling trajectories of topological defects surrounded by acoustic vortices with helical waveforms, and uncertain rogue wave events, in self-excited weakly disordered dust acoustic waves. The changes of waveform topology, caused by kinking, rupturing and reconnection of sequential wave crests surfaces, and the reversed process, are responsible for the chaotic creation, propagation, and annihilation of acoustic vortex pairs with opposite helicities winding around low amplitude hole filaments. The observed rogue wave events are preceded by a higher probability of surrounding defects. Particle focusing by the transverse electric forces from ruptured and tilted wave crests nearby defects are identified as the major cause for rogue wave generation.
Rogue wave modes for a derivative nonlinear Schrödinger model.
Chan, Hiu Ning; Chow, Kwok Wing; Kedziora, David Jacob; Grimshaw, Roger Hamilton James; Ding, Edwin
2014-03-01
Rogue waves in fluid dynamics and optical waveguides are unexpectedly large displacements from a background state, and occur in the nonlinear Schrödinger equation with positive linear dispersion in the regime of positive cubic nonlinearity. Rogue waves of a derivative nonlinear Schrödinger equation are calculated in this work as a long-wave limit of a breather (a pulsating mode), and can occur in the regime of negative cubic nonlinearity if a sufficiently strong self-steepening nonlinearity is also present. This critical magnitude is shown to be precisely the threshold for the onset of modulation instabilities of the background plane wave, providing a strong piece of evidence regarding the connection between a rogue wave and modulation instability. The maximum amplitude of the rogue wave is three times that of the background plane wave, a result identical to that of the Peregrine breather in the classical nonlinear Schrödinger equation model. This amplification ratio and the resulting spectral broadening arising from modulation instability correlate with recent experimental results of water waves. Numerical simulations in the regime of marginal stability are described.
Rogue waves for a system of coupled derivative nonlinear Schrödinger equations
NASA Astrophysics Data System (ADS)
Chan, Hiu Ning; Malomed, Boris; Chow, Kwok Wing
2015-11-01
Previous works in the literature on water waves have demonstrated that the fourth-order evolution of gravity waves in deep water will be governed by a higher order nonlinear Schrödinger equation. In the presence of two wave trains, the system is described by a higher order coupled nonlinear Schrödinger system. Through a gauge transformation, these evolution equations are reduced to a coupled derivative nonlinear Schrödinger system. The goal here is to study rogue waves, unexpectedly large displacements from an equilibrium position, through the Hirota bilinear transformation theoretically. The connections between the onset of rogue waves and modulation instability are investigated. The range of cubic nonlinearity allowing rogue wave formation is elucidated. Under a finite group velocity mismatch between the two components, the existence regime for rogue waves is extended as compared to the case with a single wave train. The amplification ratio of the amplitude can be higher than that of the single component nonlinear Schrödinger equation. Partial financial support has been provided by the Research Grants Council through contracts HKU711713E and HKU17200815.
Capillary waves and ellipsometry experiments
NASA Astrophysics Data System (ADS)
Bonn, D.; Wegdam, G. H.
1992-09-01
The inclusion of higher-order terms in the capillary-wave Hamiltonian may reduce the contributions of these fluctuations to the ellipsometric coefficients. We show that the renormalization of capillary waves at a fluid-fluid interface by Sengers and van Leeuwen [Phys. Rev. A 39 (1989) 6346] using the wave vector-dependent surface tension that follows from the coupled mode theory by Meunier [Phys. France 48 (1987)1819] yields a satisfactory agreement with recent ellipsometry measurements by Schmidt [Phys. Rev. A 38 (1988) 567]. The interface is viewed upon as an intrinsic interface broadened by capillary waves. We suppose that the cutoff wave vector q_{max} that follows from mode-coupling theory marks the transition from the short-wavelength bulk-like fluctuations that contribute to the bare surface tension to the long-wavelength capillary wave-like fluctuations that contribute to the full surface tension. This enables us to calculate, without any adjustable parameters, both the ratio of the bare and experimental surface tension and the universal constant for the elliptical thickness of the interface. Both agree remarkably well with experimental values.
Amplitude modulation of hydromagnetic waves and associated rogue waves in magnetoplasmas.
Sabry, R; Moslem, W M; Shukla, P K
2012-09-01
It is shown that the dynamics of amplitude-modulated compressional dispersive Alfvénic (CDA) waves in a collisional megnetoplasma is governed by a complex Ginzburg-Landau (CGL) equation. The nonlinear dispersion relation for the modulational instability of the CDA waves is derived and investigated numerically. It is found that the growth rate of the modulational instability decreases (increases) with the increase of the normalized electron-ion collision frequency α (the plasma β). The modulational instability criterion for the CGL equation is defined precisely and investigated numerically. The region of the modulational instability becomes narrower with the increase of α and β, indicating that the system dissipates the wave energy by collisions, and a stable CDA wave envelope packet in the form of a hole will be a dominant localized pulse. For a collisionless plasma, i.e., α=0, the CGL equation reduces to the standard nonlinear Schrödinger (NLS) equation. The latter is used to investigate the modulational (in)stability region for the CDA waves in a collisionless magnetoplasma. It is shown that, within unstable regions, a random set of nonlinearly interacting CDA perturbations leads to the formation of CDA rogue waves. In order to demonstrate that the characteristics of the CDA rogue waves are influenced by the plasma β, the relevant numerical analysis of the appropriate nonlinear solution of the NLS equation is presented. The application of our investigation to space and laboratory magnetoplasmas is discussed.
Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents
Kundu, Anjan; Mukherjee, Abhik; Naskar, Tapan
2014-01-01
Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves. PMID:24711719
Electron-acoustic rogue waves in a plasma with Tribeche-Tsallis-Cairns distributed electrons
NASA Astrophysics Data System (ADS)
Merriche, Abderrzak; Tribeche, Mouloud
2017-01-01
The problem of electron-acoustic (EA) rogue waves in a plasma consisting of fluid cold electrons, nonthermal nonextensive electrons and stationary ions, is addressed. A standard multiple scale method has been carried out to derive a nonlinear Schrödinger-like equation. The coefficients of dispersion and nonlinearity depend on the nonextensive and nonthermal parameters. The EA wave stability is analyzed. Interestingly, it is found that the wave number threshold, above which the EA wave modulational instability (MI) sets in, increases as the nonextensive parameter increases. As the nonthermal character of the electrons increases, the MI occurs at large wavelength. Moreover, it is shown that as the nonextensive parameter increases, the EA rogue wave pulse grows while its width is narrowed. The amplitude of the EA rogue wave decreases with an increase of the number of energetic electrons. In the absence of nonthermal electrons, the nonextensive effects are more perceptible and more noticeable. In view of the crucial importance of rogue waves, our results can contribute to the understanding of localized electrostatic envelope excitations and underlying physical processes, that may occur in space as well as in laboratory plasmas.
Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents.
Kundu, Anjan; Mukherjee, Abhik; Naskar, Tapan
2014-04-08
Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves.
Rogue wave solutions to the generalized nonlinear Schrödinger equation with variable coefficients.
Zhong, Wei-Ping; Belić, Milivoj R; Huang, Tingwen
2013-06-01
A similarity transformation is utilized to reduce the generalized nonlinear Schrödinger (NLS) equation with variable coefficients to the standard NLS equation with constant coefficients, whose rogue wave solutions are then transformed back into the solutions of the original equation. In this way, Ma breathers, the first- and second-order rogue wave solutions of the generalized equation, are constructed. Properties of a few specific solutions and controllability of their characteristics are discussed. The results obtained may raise the possibility of performing relevant experiments and achieving potential applications.
Breather and rogue wave solutions of a generalized nonlinear Schrödinger equation.
Wang, L H; Porsezian, K; He, J S
2013-05-01
In this paper, using the Darboux transformation, we demonstrate the generation of first-order breather and higher-order rogue waves from a generalized nonlinear Schrödinger equation with several higher-order nonlinear effects representing femtosecond pulse propagation through nonlinear silica fiber. The same nonlinear evolution equation can also describe the soliton-type nonlinear excitations in classical Heisenberg spin chain. Such solutions have a parameter γ(1), denoting the strength of the higher-order effects. From the numerical plots of the rational solutions, the compression effects of the breather and rogue waves produced by γ(1) are discussed in detail.
Rogue-wave-like statistics in ultrafast white-light continuum generation in sapphire.
Majus, D; Jukna, V; Pileckis, E; Valiulis, G; Dubietis, A
2011-08-15
We experimentally study the statistics of the white-light continuum generated by focusing of 130 fs, 800 nm pulses in a sapphire plate and show that the statistical distributions of the spectral intensity of the blue-shifted continuum components obey the extreme-value statistics. This rogue-wave-like behavior is detected only within a narrow input-pulse energy interval. By the use of numerical simulations, we show that the observed rogue-wave-like behavior is associated with pulse splitting and build-up of intense trailing pulse. The extreme events are thereafter suppressed by the intensity clamping.
Rogue wave triggered at a critical frequency of a nonlinear resonant medium
NASA Astrophysics Data System (ADS)
He, Jingsong; Xu, Shuwei; Porsezian, K.; Cheng, Yi; Dinda, P. Tchofo
2016-06-01
We consider a two-level atomic system interacting with an electromagnetic field controlled in amplitude and frequency by a high intensity laser. We show that the amplitude of the induced electric field admits an envelope profile corresponding to a breather soliton. We demonstrate that this soliton can propagate with any frequency shift with respect to that of the control laser, except a critical frequency, at which the system undergoes a structural discontinuity that transforms the breather in a rogue wave. A mechanism of generation of rogue waves by means of an intense laser field is thus revealed.
Rogue wave triggered at a critical frequency of a nonlinear resonant medium.
He, Jingsong; Xu, Shuwei; Porsezian, K; Cheng, Yi; Dinda, P Tchofo
2016-06-01
We consider a two-level atomic system interacting with an electromagnetic field controlled in amplitude and frequency by a high intensity laser. We show that the amplitude of the induced electric field admits an envelope profile corresponding to a breather soliton. We demonstrate that this soliton can propagate with any frequency shift with respect to that of the control laser, except a critical frequency, at which the system undergoes a structural discontinuity that transforms the breather in a rogue wave. A mechanism of generation of rogue waves by means of an intense laser field is thus revealed.
Rogue-wave solutions of a three-component coupled nonlinear Schrödinger equation.
Zhao, Li-Chen; Liu, Jie
2013-01-01
We investigate rogue-wave solutions in a three-component coupled nonlinear Schrödinger equation. With certain requirements on the backgrounds of components, we construct a multi-rogue-wave solution that exhibits a structure like a four-petaled flower in temporal-spatial distribution, in contrast to the eye-shaped structure in one-component or two-component systems. The results could be of interest in such diverse fields as Bose-Einstein condensates, nonlinear fibers, and superfluids.
Dark three-sister rogue waves in normally dispersive optical fibers with random birefringence.
Chen, Shihua; Soto-Crespo, Jose M; Grelu, Philippe
2014-11-03
We investigate dark rogue wave dynamics in normally dispersive birefringent optical fibers, based on the exact rational solutions of the coupled nonlinear Schrödinger equations. Analytical solutions are derived up to the second order via a nonrecursive Darboux transformation method. Vector dark "three-sister" rogue waves as well as their existence conditions are demonstrated. The robustness against small perturbations is numerically confirmed in spite of the onset of modulational instability, offering the possibility to observe such extreme events in normal optical fibers with random birefringence, or in other Manakov-type vector nonlinear media.
An adaptive filter for studying the life cycle of optical rogue waves.
Liu, Chu; Rees, Eric J; Laurila, Toni; Jian, Shuisheng; Kaminski, Clemens F
2010-12-06
We present an adaptive numerical filter for analyzing fiber-length dependent properties of optical rogue waves, which are highly intense and extremely red-shifted solitons that arise during supercontinuum generation in photonic crystal fiber. We use this filter to study a data set of 1000 simulated supercontinuum pulses, produced from 5 ps pump pulses containing random noise. Optical rogue waves arise in different supercontinuum pulses at various positions along the fiber, and exhibit a lifecycle: their intensity peaks over a finite range of fiber length before declining slowly.
Raman rogue waves in a partially mode-locked fiber laser.
Runge, Antoine F J; Aguergaray, Claude; Broderick, Neil G R; Erkintalo, Miro
2014-01-15
We report on an experimental study of spectral fluctuations induced by intracavity Raman conversion in a passively partially mode-locked, all-normal dispersion fiber laser. Specifically, we use dispersive Fourier transformation to measure single-shot spectra of Raman-induced noise-like pulses, demonstrating that for low cavity gain values Raman emission is sporadic and follows rogue-wave-like probability distributions, while a saturated regime with Gaussian statistics is obtained for high pump powers. Our experiments further reveal intracavity rogue waves originating from cascaded Raman dynamics.
NASA Astrophysics Data System (ADS)
Su, Chuan-Qi; Gao, Yi-Tian; Xue, Long; Yu, Xin
2015-10-01
Under investigation in this article is a higher-order nonlinear Schrödinger-Maxwell-Bloch (HNLS-MB) system for the optical pulse propagation in an erbium-doped fiber. Lax pair, Darboux transformation (DT), and generalised DT for the HNLS-MB system are constructed. Soliton solutions and rogue wave solutions are derived based on the DT and generalised DT, respectively. Properties of the solitons and rogue waves are graphically presented. The third-order dispersion parameter, fourth-order dispersion parameter, and frequency detuning all influence the characteristic lines and velocities of the solitons. The frequency detuning also affects the amplitudes of solitons. The separating function has no effect on the properties of the first-order rogue waves, except for the locations where the first-order rogue waves appear. The third-order dispersion parameter affects the propagation directions and shapes of the rogue waves. The frequency detuning influences the rogue-wave types of the module for the measure of polarization of resonant medium and the extant population inversion. The fourth-order dispersion parameter impacts the rogue-wave interaction range and also has an effect on the rogue-wave type of the extant population inversion. The value of separating function affects the spatial-temporal separation of constituting elementary rogue waves for the second-order and third-order rogue waves. The second-order and third-order rogue waves can exhibit the triangular and pentagon patterns under different choices of separating functions.
Vector rogue waves and dark-bright boomeronic solitons in autonomous and nonautonomous settings.
Mareeswaran, R Babu; Charalampidis, E G; Kanna, T; Kevrekidis, P G; Frantzeskakis, D J
2014-10-01
In this work we consider the dynamics of vector rogue waves and dark-bright solitons in two-component nonlinear Schrödinger equations with various physically motivated time-dependent nonlinearity coefficients, as well as spatiotemporally dependent potentials. A similarity transformation is utilized to convert the system into the integrable Manakov system and subsequently the vector rogue and dark-bright boomeronlike soliton solutions of the latter are converted back into ones of the original nonautonomous model. Using direct numerical simulations we find that, in most cases, the rogue wave formation is rapidly followed by a modulational instability that leads to the emergence of an expanding soliton train. Scenarios different than this generic phenomenology are also reported.
Magnetic rogue wave in a perpendicular anisotropic ferromagnetic nanowire with spin-transfer torque
Zhao, Fei; Li, Zai-Dong; Li, Qiu-Yan; Wen, Lin; Fu, Guangsheng; Liu, W.M.
2012-09-15
We present the current controlled motion of a dynamic soliton embedded in spin wave background in ferromagnetic nanowire. With the stronger breather character we get the novel magnetic rogue wave and clarify its formation mechanism. The generation of magnetic rogue wave mainly arises from the accumulation of energy and magnons toward to its central part. We also observe that the spin-polarized current can control the exchange rate of magnons between the envelope soliton and the background, and the critical current condition is obtained analytically. Even more interesting is that the spin-transfer torque plays the completely opposite role for the cases below and above the critical value. - Highlights: Black-Right-Pointing-Pointer We get the current controlled motion of a dynamic soliton embedded in spin wave background. Black-Right-Pointing-Pointer We get the novel magnetic rogue wave and clarify its formation mechanism. Black-Right-Pointing-Pointer The generation of magnetic rogue wave arises from the accumulation of energy and magnons. Black-Right-Pointing-Pointer The spin-polarized current controls exchange rate of magnons between the envelope soliton and the background. Black-Right-Pointing-Pointer The spin-transfer torque plays the completely opposite role below and above the critical value.
Observation of a hierarchy of up to fifth-order rogue waves in a water tank.
Chabchoub, A; Hoffmann, N; Onorato, M; Slunyaev, A; Sergeeva, A; Pelinovsky, E; Akhmediev, N
2012-11-01
We present experimental observations of the hierarchy of rational breather solutions of the nonlinear Schrödinger equation (NLS) generated in a water wave tank. First, five breathers of the infinite hierarchy have been successfully generated, thus confirming the theoretical predictions of their existence. Breathers of orders higher than five appeared to be unstable relative to the wave-breaking effect of water waves. Due to the strong influence of the wave breaking and relatively small carrier steepness values of the experiment these results for the higher-order solutions do not directly explain the formation of giant oceanic rogue waves. However, our results are important in understanding the dynamics of rogue water waves and may initiate similar experiments in other nonlinear dispersive media such as fiber optics and plasma physics, where the wave propagation is governed by the NLS.
Nonlinear random optical waves: Integrable turbulence, rogue waves and intermittency
NASA Astrophysics Data System (ADS)
Randoux, Stéphane; Walczak, Pierre; Onorato, Miguel; Suret, Pierre
2016-10-01
We examine the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations. In our study that enters within the framework of integrable turbulence, we specifically focus on optical fiber systems accurately described by the integrable one-dimensional nonlinear Schrödinger equation. We consider random complex fields having a Gaussian statistics and an infinite extension at initial stage. We use numerical simulations with periodic boundary conditions and optical fiber experiments to investigate spectral and statistical changes experienced by nonlinear waves in focusing and in defocusing propagation regimes. As a result of nonlinear propagation, the power spectrum of the random wave broadens and takes exponential wings both in focusing and in defocusing regimes. Heavy-tailed deviations from Gaussian statistics are observed in focusing regime while low-tailed deviations from Gaussian statistics are observed in defocusing regime. After some transient evolution, the wave system is found to exhibit a statistically stationary state in which neither the probability density function of the wave field nor the spectrum changes with the evolution variable. Separating fluctuations of small scale from fluctuations of large scale both in focusing and defocusing regimes, we reveal the phenomenon of intermittency; i.e., small scales are characterized by large heavy-tailed deviations from Gaussian statistics, while the large ones are almost Gaussian.
Influence of optical activity on rogue waves propagating in chiral optical fibers
NASA Astrophysics Data System (ADS)
Temgoua, D. D. Estelle; Kofane, T. C.
2016-06-01
We derive the nonlinear Schrödinger (NLS) equation in chiral optical fiber with right- and left-hand nonlinear polarization. We use the similarity transformation to reduce the generalized chiral NLS equation to the higher-order integrable Hirota equation. We present the first- and second-order rational solutions of the chiral NLS equation with variable and constant coefficients, based on the modified Darboux transformation method. For some specific set of parameters, the features of chiral optical rogue waves are analyzed from analytical results, showing the influence of optical activity on waves. We also generate the exact solutions of the two-component coupled nonlinear Schrödinger equations, which describe optical activity effects on the propagation of rogue waves, and their properties in linear and nonlinear coupling cases are investigated. The condition of modulation instability of the background reveals the existence of vector rogue waves and the number of stable and unstable branches. Controllability of chiral optical rogue waves is examined by numerical simulations and may bring potential applications in optical fibers and in many other physical systems.
Influence of optical activity on rogue waves propagating in chiral optical fibers.
Temgoua, D D Estelle; Kofane, T C
2016-06-01
We derive the nonlinear Schrödinger (NLS) equation in chiral optical fiber with right- and left-hand nonlinear polarization. We use the similarity transformation to reduce the generalized chiral NLS equation to the higher-order integrable Hirota equation. We present the first- and second-order rational solutions of the chiral NLS equation with variable and constant coefficients, based on the modified Darboux transformation method. For some specific set of parameters, the features of chiral optical rogue waves are analyzed from analytical results, showing the influence of optical activity on waves. We also generate the exact solutions of the two-component coupled nonlinear Schrödinger equations, which describe optical activity effects on the propagation of rogue waves, and their properties in linear and nonlinear coupling cases are investigated. The condition of modulation instability of the background reveals the existence of vector rogue waves and the number of stable and unstable branches. Controllability of chiral optical rogue waves is examined by numerical simulations and may bring potential applications in optical fibers and in many other physical systems.
Rogue wave formation under the action of quasi-stationary pressure
NASA Astrophysics Data System (ADS)
Abrashkin, A. A.; Oshmarina, O. E.
2016-05-01
The process of rogue wave formation on deep water is considered. A wave of extreme amplitude is born against the background of uniform waves (Gerstner waves) under the action of external pressure on free surface. The pressure distribution has a form of a quasi-stationary "pit". The fluid motion is supposed to be a vortex one and is described by an exact solution of equations of 2D hydrodynamics for an ideal fluid in Lagrangian coordinates. Liquid particles are moving around circumferences of different radii in the absence of drift flow. Values of amplitude and wave steepness optimal for rogue wave formation are found numerically. The influence of vorticity distribution and pressure drop on parameters of the fluid is investigated.
Kinetic Alfvén solitary and rogue waves in superthermal plasmas
Bains, A. S.; Li, Bo Xia, Li-Dong
2014-03-15
We investigate the small but finite amplitude solitary Kinetic Alfvén waves (KAWs) in low β plasmas with superthermal electrons modeled by a kappa-type distribution. A nonlinear Korteweg-de Vries (KdV) equation describing the evolution of KAWs is derived by using the standard reductive perturbation method. Examining the dependence of the nonlinear and dispersion coefficients of the KdV equation on the superthermal parameter κ, plasma β, and obliqueness of propagation, we show that these parameters may change substantially the shape and size of solitary KAW pulses. Only sub-Alfvénic, compressive solitons are supported. We then extend the study to examine kinetic Alfvén rogue waves by deriving a nonlinear Schrödinger equation from the KdV equation. Rational solutions that form rogue wave envelopes are obtained. We examine how the behavior of rogue waves depends on the plasma parameters in question, finding that the rogue envelopes are lowered with increasing electron superthermality whereas the opposite is true when the plasma β increases. The findings of this study may find applications to low β plasmas in astrophysical environments where particles are superthermally distributed.
Two-dimensional linear and nonlinear Talbot effect from rogue waves.
Zhang, Yiqi; Belić, Milivoj R; Petrović, Milan S; Zheng, Huaibin; Chen, Haixia; Li, Changbiao; Lu, Keqing; Zhang, Yanpeng
2015-03-01
We introduce two-dimensional (2D) linear and nonlinear Talbot effects. They are produced by propagating periodic 2D diffraction patterns and can be visualized as 3D stacks of Talbot carpets. The nonlinear Talbot effect originates from 2D rogue waves and forms in a bulk 3D nonlinear medium. The recurrences of an input rogue wave are observed at the Talbot length and at the half-Talbot length, with a π phase shift; no other recurrences are observed. Differing from the nonlinear Talbot effect, the linear effect displays the usual fractional Talbot images as well. We also find that the smaller the period of incident rogue waves, the shorter the Talbot length. Increasing the beam intensity increases the Talbot length, but above a threshold this leads to a catastrophic self-focusing phenomenon which destroys the effect. We also find that the Talbot recurrence can be viewed as a self-Fourier transform of the initial periodic beam that is automatically performed during propagation. In particular, linear Talbot effect can be viewed as a fractional self-Fourier transform, whereas the nonlinear Talbot effect can be viewed as the regular self-Fourier transform. Numerical simulations demonstrate that the rogue-wave initial condition is sufficient but not necessary for the observation of the effect. It may also be observed from other periodic inputs, provided they are set on a finite background. The 2D effect may find utility in the production of 3D photonic crystals.
Ankiewicz, Adrian; Wang, Yan; Wabnitz, Stefan; Akhmediev, Nail
2014-01-01
We consider an extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms with variable coefficients. The resulting equation has soliton solutions and approximate rogue wave solutions. We present these solutions up to second order. Moreover, specific constraints on the parameters of higher-order terms provide integrability of the resulting equation, providing a corresponding Lax pair. Particular cases of this equation are the Hirota and the Lakshmanan-Porsezian-Daniel equations. The resulting integrable equation admits exact rogue wave solutions. In particular cases, mentioned above, these solutions are reduced to the rogue wave solutions of the corresponding equations.
Mechanical energy fluctuations in granular chains: the possibility of rogue fluctuations or waves.
Han, Ding; Westley, Matthew; Sen, Surajit
2014-09-01
The existence of rogue or freak waves in the ocean has been known for some time. They have been reported in the context of optical lattices and the financial market. We ask whether such waves are generic to late time behavior in nonlinear systems. In that vein, we examine the dynamics of an alignment of spherical elastic beads held within fixed, rigid walls at zero precompression when they are subjected to sufficiently rich initial conditions. Here we define such waves generically as unusually large energy fluctuations that sustain for short periods of time. Our simulations suggest that such unusually large fluctuations ("hot spots") and occasional series of such fluctuations through space and time ("rogue fluctuations") are likely to exist in the late time dynamics of the granular chain system at zero dissipation. We show that while hot spots are common in late time evolution, rogue fluctuations are seen in purely nonlinear systems (i.e., no precompression) at late enough times. We next show that the number of such fluctuations grows exponentially with increasing nonlinearity whereas rogue fluctuations decrease superexponentially with increasing precompression. Dissipation-free granular alignment systems may be possible to realize as integrated circuits and hence our observations may potentially be testable in the laboratory.
Mechanical energy fluctuations in granular chains: The possibility of rogue fluctuations or waves
NASA Astrophysics Data System (ADS)
Han, Ding; Westley, Matthew; Sen, Surajit
2014-09-01
The existence of rogue or freak waves in the ocean has been known for some time. They have been reported in the context of optical lattices and the financial market. We ask whether such waves are generic to late time behavior in nonlinear systems. In that vein, we examine the dynamics of an alignment of spherical elastic beads held within fixed, rigid walls at zero precompression when they are subjected to sufficiently rich initial conditions. Here we define such waves generically as unusually large energy fluctuations that sustain for short periods of time. Our simulations suggest that such unusually large fluctuations ("hot spots") and occasional series of such fluctuations through space and time ("rogue fluctuations") are likely to exist in the late time dynamics of the granular chain system at zero dissipation. We show that while hot spots are common in late time evolution, rogue fluctuations are seen in purely nonlinear systems (i.e., no precompression) at late enough times. We next show that the number of such fluctuations grows exponentially with increasing nonlinearity whereas rogue fluctuations decrease superexponentially with increasing precompression. Dissipation-free granular alignment systems may be possible to realize as integrated circuits and hence our observations may potentially be testable in the laboratory.
Semirational and symbiotic self-similar rogue waves in a (2+1)-dimensional graded-index waveguide
NASA Astrophysics Data System (ADS)
De, Kanchan Kumar; Soloman Raju, Thokala; Kumar, C. N.; Panigrahi, Prasanta K.
2016-07-01
We have investigated the (?)-dimensional variable coefficient-coupled nonlinear Schrödinger equation (vc-CNLSE) in a graded-index waveguide. Similarity transformations are used to convert the vc-CNLSE into constant coefficient CNLSE. Under certain functional constraints we could extract semirational, multi-parametric solution of the associated Manakov system. This family of solutions include known Peregrine soliton, mixture of either bright soliton and rogue wave or dark soliton and rogue wave or breather and rogue wave. Under a distinct set of self-phase modulation and cross-phase modulation coefficients we could establish symbiotic existence of different soliton pairs as solutions. These soliton pairs may constitute of one bright and a dark soliton, two bright solitons or two dark solitons. Finally, when two wave components are directly proportional, we find bright and dark similaritons, self-similar breathers, and rogue waves as different solutions.
Rogue waves for a coupled nonlinear Schrödinger system in a multi-mode fibre
NASA Astrophysics Data System (ADS)
Li, Hui-Min; Tian, Bo; Wang, Deng-Shan; Sun, Wen-Rong; Xie, Xi-Yang; Liu, Lei
2016-10-01
In this paper, we investigate the rogue waves for an integrable coupled nonlinear Schrödinger (CNLS) system with the self-phase modulation, cross-phase modulation and four-wave mixing term, which can describe the propagation of optical waves in a multi-mode fibre. We construct a generalized Darboux transformation (GDT) for the CNLS system and find a gauge transformation which converts the Lax pair into the constant-coefficient differential equations. Solving those equations, we can obtain the vector solutions of the Lax pair. Using the GDT, we derive an iterative formula for the nth-order rogue-wave solutions for the CNLS system. We derive the first- and second-order rogue-wave solutions for the CNLS system and analyse the profiles for the rogue waves with respect to the self-phase modulation term a, cross-phase modulation term c and four-wave mixing term b, respectively. The rogue waves become thinner with the increase in the value for the real part of b and that the effect of a or c on the rogue waves is the same as the one of the real part of b.
NASA Astrophysics Data System (ADS)
Li, Jin Hua; Chan, Hiu Ning; Chiang, Kin Seng; Chow, Kwok Wing
2015-11-01
Breathers and rogue waves of special coupled nonlinear Schrödinger systems (the Manakov equations) are studied analytically. These systems model the orthogonal polarization modes in an optical fiber with randomly varying birefringence. Studies earlier in the literature had shown that rogue waves can occur in these Manakov systems with dispersion and nonlinearity of opposite signs, and that the criterion for the existence of rogue waves correlates closely with the onset of modulation instability. In the present work the Hirota bilinear transform is employed to calculate the breathers (pulsating modes), and rogue waves are obtained as a long wave limit of such breathers. In terms of wave profiles, a 'black' rogue wave (intensity dropping to zero) and the transition to a four-petal configuration are elucidated analytically. Sufficiently strong modulation instabilities of the background may overwhelm or mask the development of the rogue waves, and such thresholds are correlated to actual physical properties of optical fibers. Numerical simulations on the evolution of breathers are performed to verify the prediction of the analytical formulations.
Capillary wave spectroscopy on ferrofluids
NASA Astrophysics Data System (ADS)
Patzke, J.; Rathke, B.; Will, S.
2007-12-01
We investigate the magnetoviscous effect in ferrofluids by Capillary Wave Spectroscopy (CWS, Surface Light Scattering). This technique probes a specific mode of thermally excited surface waves giving information on surface tension and viscosity. In ferrofluids we detect a transition from propagating surface modes to overdamped ones depending on the particle concentration and strength and the orientation of an externally applied magnetic field. We interprete this effect as caused by an increase of the liquid viscosity with an increasing particle concentration and field-strength. Changing the relative orientation of the scattering vector and magnetic field shows that the viscous properties of ferrofluids in a magnetic field are anisotropic. Figs 8, Refs 12.
Two-dimensional cylindrical ion-acoustic solitary and rogue waves in ultrarelativistic plasmas
Ata-ur-Rahman; Ali, S.; Moslem, W. M.; Mushtaq, A.
2013-07-15
The propagation of ion-acoustic (IA) solitary and rogue waves is investigated in a two-dimensional ultrarelativistic degenerate warm dense plasma. By using the reductive perturbation technique, the cylindrical Kadomtsev–Petviashvili (KP) equation is derived, which can be further transformed into a Korteweg–de Vries (KdV) equation. The latter admits a solitary wave solution. However, when the frequency of the carrier wave is much smaller than the ion plasma frequency, the KdV equation can be transferred to a nonlinear Schrödinger equation to study the nonlinear evolution of modulationally unstable modified IA wavepackets. The propagation characteristics of the IA solitary and rogue waves are strongly influenced by the variation of different plasma parameters in an ultrarelativistic degenerate dense plasma. The present results might be helpful to understand the nonlinear electrostatic excitations in astrophysical degenerate dense plasmas.
NASA Astrophysics Data System (ADS)
Gupta, Samit Kumar; Sarma, Amarendra K.
2016-07-01
In this work, we have studied the peregrine rogue wave dynamics, with a solitons on finite background (SFB) ansatz, in the recently proposed (Ablowitz and Musslimani, (2013) [31]) continuous nonlinear Schrödinger system with parity-time symmetric Kerr nonlinearity. We have found that the continuous nonlinear Schrödinger system with PT-symmetric nonlinearity also admits Peregrine soliton solution. Motivated by the fact that Peregrine solitons are regarded as prototypical solutions of rogue waves, we have studied Peregrine rogue wave dynamics in the c-PTNLSE model. Upon numerical computation, we observe the appearance of low-intense Kuznetsov-Ma (KM) soliton trains in the absence of transverse shift (unbroken PT-symmetry) and well-localized high-intense Peregrine rogue waves in the presence of transverse shift (broken PT-symmetry) in a definite parametric regime.
Analytical solutions and rogue waves in (3+1)-dimensional nonlinear Schrödinger equation
NASA Astrophysics Data System (ADS)
Ma, Zheng-Yi; Ma, Song-Hua
2012-03-01
Analytical solutions in terms of rational-like functions are presented for a (3+1)-dimensional nonlinear Schrödinger equation with time-varying coefficients and a harmonica potential using the similarity transformation and a direct ansatz. Several free functions of time t are involved to generate abundant wave structures. Three types of elementary functions are chosen to exhibit the corresponding nonlinear rogue wave propagations.
Solitons and rogue waves for a nonlinear system in the geophysical fluid
NASA Astrophysics Data System (ADS)
Xie, Xi-Yang; Tian, Bo; Liu, Lei; Wu, Xiao-Yu; Jiang, Yan
2016-12-01
In this paper, we investigate a nonlinear system, which describes the marginally unstable baroclinic wave packets in the geophysical fluid. Based on the symbolic computation and Hirota method, bright one- and two-soliton solutions for such a system are derived. Propagation and collisions of the solitons are graphically shown and discussed with β, which reflects the collision between the wave packet and mean flow, α, which measures the state of the basic flow, and group velocity γ. γ is observed to affect the amplitudes of the solitons, and α can influence the solitons’ traveling directions. By virtue of the generalized Darboux transformation, the first- and second-order rogue-wave solutions are derived. Properties of the first- and second-order rogue waves are graphically presented and analyzed: The first-order rogue waves are shown in the figures. α has no effects on A, which is the amplitude of the wave packet, but with the increase of α, amplitude of B, which is a quantity measuring the correction of the basic flow, decreases. When β is chosen differently, A and B do not keep their shapes invariant. With the value of γ increasing, amplitudes of A and B become larger. The second-order rogue wave is presented, from which we observe that with α increasing, amplitude of B decreases, but α has no effects on A. Collision features of A and B alter with the value of β changing. When we make the value of γ larger, amplitudes of A and B increase.
Rogue waves: from nonlinear Schrödinger breather solutions to sea-keeping test.
Onorato, Miguel; Proment, Davide; Clauss, Günther; Klein, Marco
2013-01-01
Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during extreme ocean conditions using such breather solutions. In particular, we discuss a state of the art sea-keeping test in a 90-meter long wave tank by creating a Peregrine breather solution hitting a scaled chemical tanker and we discuss its potential devastating effects on the ship.
Rogue Waves: From Nonlinear Schrödinger Breather Solutions to Sea-Keeping Test
Onorato, Miguel; Proment, Davide; Clauss, Günther; Klein, Marco
2013-01-01
Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during extreme ocean conditions using such breather solutions. In particular, we discuss a state of the art sea-keeping test in a 90-meter long wave tank by creating a Peregrine breather solution hitting a scaled chemical tanker and we discuss its potential devastating effects on the ship. PMID:23405086
N-order bright and dark rogue waves in a resonant erbium-doped fiber system.
He, Jingsong; Xu, Shuwei; Porsezian, K; Porseizan, K
2012-12-01
The rogue waves in a resonant erbium-doped fiber system governed by a coupled system of the nonlinear Schrödinger equation and the Maxwell-Bloch equation (NLS-MB equations) are given explicitly by a Taylor series expansion about the breather solutions of the normalized slowly varying amplitude of the complex field envelope E, polarization p, and population inversion η. The n-order breather solutions of the three fields are constructed using a Darboux transformation (DT) by assuming periodic seed solutions. Moreover, the n-order rogue waves are given by determinant forms with n+3 free parameters. Furthermore, the possible connection between our rouge waves and the generation of supercontinuum generation is discussed.
N-order bright and dark rogue waves in a resonant erbium-doped fiber system
NASA Astrophysics Data System (ADS)
He, Jingsong; Xu, Shuwei; Porseizan, K.
2012-12-01
The rogue waves in a resonant erbium-doped fiber system governed by a coupled system of the nonlinear Schrödinger equation and the Maxwell-Bloch equation (NLS-MB equations) are given explicitly by a Taylor series expansion about the breather solutions of the normalized slowly varying amplitude of the complex field envelope E, polarization p, and population inversion η. The n-order breather solutions of the three fields are constructed using a Darboux transformation (DT) by assuming periodic seed solutions. Moreover, the n-order rogue waves are given by determinant forms with n+3 free parameters. Furthermore, the possible connection between our rouge waves and the generation of supercontinuum generation is discussed.
Dissipative rogue waves induced by soliton explosions in an ultrafast fiber laser.
Liu, Meng; Luo, Ai-Ping; Xu, Wen-Cheng; Luo, Zhi-Chao
2016-09-01
We reported on the observation of dissipative rogue waves (DRWs) induced by soliton explosions in an ultrafast fiber laser. It was found that the soliton explosions could be obtained in the fiber laser at a critical pump power level. During the process of the soliton explosion, the high-amplitude waves that fulfill the rogue wave criteria could be detected. The appearance of the DRWs was identified by characterizing the intensity statistics of the time-stretched soliton profile based on the dispersive Fourier-transform method. Our findings provide the first experimental demonstration that the DRWs could be observed in the soliton explosion regime and further enhance the understanding of the physical mechanism of optical RW generation.
Classification of homoclinic rogue wave solutions of the nonlinear Schrödinger equation
NASA Astrophysics Data System (ADS)
Osborne, A. R.
2014-01-01
Certain homoclinic solutions of the nonlinear Schrödinger (NLS) equation, with spatially periodic boundary conditions, are the most common unstable wave packets associated with the phenomenon of oceanic rogue waves. Indeed the homoclinic solutions due to Akhmediev, Peregrine and Kuznetsov-Ma are almost exclusively used in scientific and engineering applications. Herein I investigate an infinite number of other homoclinic solutions of NLS and show that they reduce to the above three classical homoclinic solutions for particular spectral values in the periodic inverse scattering transform. Furthermore, I discuss another infinity of solutions to the NLS equation that are not classifiable as homoclinic solutions. These latter are the genus-2N theta function solutions of the NLS equation: they are the most general unstable spectral solutions for periodic boundary conditions. I further describe how the homoclinic solutions of the NLS equation, for N = 1, can be derived directly from the theta functions in a particular limit. The solutions I address herein are actual spectral components in the nonlinear Fourier transform theory for the NLS equation: The periodic inverse scattering transform. The main purpose of this paper is to discuss a broader class of rogue wave packets1 for ship design, as defined in the Extreme Seas program. The spirit of this research came from D. Faulkner (2000) who many years ago suggested that ship design procedures, in order to take rogue waves into account, should progress beyond the use of simple sine waves. 1An overview of other work in the field of rogue waves is given elsewhere: Osborne 2010, 2012 and 2013. See the books by Olagnon and colleagues 2000, 2004 and 2008 for the Brest meetings. The books by Kharif et al. (2008) and Pelinovsky et al. (2010) are excellent references.
The low probability but increased hazard of a "rogue wave" from an unexpected direction
NASA Astrophysics Data System (ADS)
Gemmrich, Johannes; Baschek, Burkard; Garrett, Chris
2013-04-01
According to reports by the Captain and crew, the crab fishing vessel Early Dawn, while fishing near St. Paul, Alaska, on 14 January 2010, was hit by a wave "at least twice as high as the rest of the waves, if not 2.5 times as high" and propagating at an angle of 45o relative to the predominant waves. The significant wave height at the time of the incident was estimated as Hs = 4.5 - 5.5m. The Captain first saw the wave at a distance of approximately 100 metres and issued a warning. Three crew members were able to get to safety, while one crew member working at the stern of the vessel was injured. Simple models of "rogue waves" that do not specify directionality predict that a wave of the observed height or more could have been expected roughly once every 30 hours. However, the directionality of this wave clearly made it more unusual as well as increasing the potential for injuries and damage to the ship. Here we combine models of rogue wave directionality with the analysis of wave buoy observations and marine weather forecasts to argue that the chance of a wave of at least the observed height and at least the observed deviation from the main direction of the waves had a probability of only 1 in 500 of occurring in a 6 hour period.
Breathers and rogue waves excited by all-magnonic spin-transfer torque.
Li, Zai-Dong; Li, Qiu-Yan; Xu, Tian-Fu; He, Peng-Bin
2016-10-01
In terms of Darboux transformation we investigate the dynamic process of spin wave passing through a magnetic soliton. It causes nonlinear excitations, such as Akhmediev breathers solution and Kuznetsov-Ma soliton. The former case demonstrates a spatial periodic process of a magnetic soliton forming the petal with four pieces. The spatial separation of adjacent magnetic petals increases rapidly, while one valley splits into two and the amplitude of valley increases gradually with the increasing amplitude of spin wave. The other case shows a localized process of the spin-wave background. In the limit case, we get rogue waves and clarify its formation mechanism.
Breathers and rogue waves excited by all-magnonic spin-transfer torque
NASA Astrophysics Data System (ADS)
Li, Zai-Dong; Li, Qiu-Yan; Xu, Tian-Fu; He, Peng-Bin
2016-10-01
In terms of Darboux transformation we investigate the dynamic process of spin wave passing through a magnetic soliton. It causes nonlinear excitations, such as Akhmediev breathers solution and Kuznetsov-Ma soliton. The former case demonstrates a spatial periodic process of a magnetic soliton forming the petal with four pieces. The spatial separation of adjacent magnetic petals increases rapidly, while one valley splits into two and the amplitude of valley increases gradually with the increasing amplitude of spin wave. The other case shows a localized process of the spin-wave background. In the limit case, we get rogue waves and clarify its formation mechanism.
Multi-rogue waves solutions: from the NLS to the KP-I equation
NASA Astrophysics Data System (ADS)
Dubard, P.; Matveev, V. B.
2013-12-01
Our discovery of multi-rogue wave (MRW) solutions in 2010 completely changed the viewpoint on the links between the theory of rogue waves and integrable systems, and helped explain many phenomena which were never understood before. It is enough to mention the famous Three Sister waves observed in oceans, the creation of a regular approach to studying higher Peregrine breathers, and the new understanding of 2 + 1 dimensional rogue waves via the NLS-KP correspondence. This article continues the study of the MRW solutions of the NLS equation and their links with the KP-I equation started in a previous series of articles (Dubard et al 2010 Eur. Phys. J. 185 247-58, Dubard and Matveev 2011 Natural Hazards Earth Syst. Sci. 11 667-72, Matveev and Dubard 2010 Proc. Int. Conf. FNP-2010 (Novgorod, St Petersburg) pp 100-101, Dubard 2010 PhD Thesis). In particular, it contains a discussion of the large parametric asymptotics of these solutions, which has never been studied before.
NASA Astrophysics Data System (ADS)
Rodin, Artem; Rodina, Natalia
2016-04-01
Every year marine natural disasters claim thousands of lives. Only rogue waves during the last 10 years caused the death of 125 and injury of 169 people. In addition to studying the physical mechanisms of generation of rogue waves is important to study the mechanisms of human behavior in such extreme situations. The impact as large-scale natural disasters, as well as less severe (in its consequences) disaster strikes must be assessed on the basis of the entire set of conditions, in whose framework the community of people appears to be, taking into account both the power of the elements, and the available resources at their disposal to restore an acceptable level of life, including social and psychological context. Here particular relevance acquire interdisciplinary researches. This interaction is extremely important not only for sociologists and psychologists, but also for the representatives of the natural sciences (physics, chemistry, mathematics) since the ultimate goal of all efforts is to minimize the harm produced by any element or negative influence of technological progress.This also work contains statistical analysis of the appearance of rogue waves on the wind wave background in the shallow bay, obtained during the experiment in the Baltic Sea.
NASA Astrophysics Data System (ADS)
Weerasekara, Gihan; Maruta, Akihiro
2017-01-01
The dynamics of the optical rogue wave phenomenon in the framework of integrable higher-order nonlinear Schrödinger equation (HNLSE) including the third order dispersion term is presented in this paper. When rogue waves generate through soliton collision, the colliding solitons' eigenvalues of the associated equation of HNLSE should be constant in the vicinity of rogue wave generation. Our results reveal that soliton collision is one of the generation mechanisms of optical rogue waves in anomalous dispersion fiber by taking the third order dispersion into consideration in the HNLSE based model.
Lee, Min Won; Baladi, Fadwa; Burie, Jean-René; Bettiati, Mauro A; Boudrioua, Azzedine; Fischer, Alexis P A
2016-10-01
Rogue waves are observed for the first time, to the best of our knowledge, in a 980 nm laser diode subject to filtered optical feedback via a fiber Bragg grating. By counting the number of rogue waves in a fixed time window, a rogue wave map is established experimentally as a function of both the optical feedback ratio and the laser current. The comparison with low frequency fluctuations (LFFs) reveals that the rogue waves observed in our system are, in fact, LFF jump-ups.
Non-Gaussian statistics and optical rogue waves in stimulated Raman scattering.
Monfared, Yashar E; Ponomarenko, Sergey A
2017-03-20
We explore theoretically and numerically optical rogue wave formation in stimulated Raman scattering inside a hydrogen filled hollow core photonic crystal fiber. We assume a weak noisy Stokes pulse input and explicitly construct the input Stokes pulse ensemble using the coherent mode representation of optical coherence theory, thereby providing a link between optical coherence and rogue wave theories. We show that the Stokes pulse peak power probability distribution function (PDF) acquires a long tail in the limit of nearly incoherent input Stokes pulses. We demonstrate a clear link between the PDF tail magnitude and the source coherence time. Thus, the latter can serve as a convenient parameter to control the former. We explain our findings qualitatively using the concepts of statistical granularity and global degree of coherence.
Reply to ''Comment on 'Optical rogue waves in telecommunication data streams'''
Vergeles, Sergey; Turitsyn, Sergei K.
2011-12-15
We feel that the main claim made in the abstract of the preceding Comment [Phys. Rev. A 84, 067801 (2011)] is wrong. Using results obtained in our paper [Phys. Rev. A 83, 061801 (2011)], we prove that rogue waves with amplitudes much larger than the average level can be observed during a short period of time in purely linear propagation regimes in optical fiber systems.
Rogue waves of the Hirota and the Maxwell-Bloch equations.
Li, Chuanzhong; He, Jingsong; Porsezian, K; Porseizan, K
2013-01-01
In this paper, we derive a Darboux transformation of the Hirota and the Maxwell-Bloch (H-MB) system which is governed by femtosecond pulse propagation through an erbium doped fiber and further generalize it to the matrix form of the n-fold Darboux transformation of this system. This n-fold Darboux transformation implies the determinant representation of nth solutions of (E([n]),p([n]),η([n])) generated from the known solution of (E,p,η). The determinant representation of (E([n]),p([n]),η([n])) provides soliton solutions, positon solutions, and breather solutions (both bright and dark breathers) of the H-MB system. From the breather solutions, we also construct a bright and dark rogue wave solution for the H-MB system, which is currently one of the hottest topics in mathematics and physics. Surprisingly, the rogue wave solution for p and η has two peaks because of the order of the numerator and denominator of them. Meanwhile, after fixing the time and spatial parameters and changing two other unknown parameters α and β, we generate a rogue wave shape.
NASA Astrophysics Data System (ADS)
Guo, Shimin; Mei, Liquan; He, Yaling; Li, Ying
2016-02-01
The nonlinear propagation of ion-acoustic waves is theoretically reported in a collisional plasma containing strongly coupled ions and nonthermal electrons featuring Tsallis distribution. For this purpose, the nonlinear integro-differential form of the generalized hydrodynamic model is used to investigate the strong-coupling effect. The modified complex Ginzburg-Landau equation with a linear dissipative term is derived for the potential wave amplitude in the hydrodynamic regime, and the modulation instability of ion-acoustic waves is examined. When the dissipative effect is neglected, the modified complex Ginzburg-Landau equation reduces to the nonlinear Schrödinger equation. Within the unstable region, two different types of second-order ion-acoustic rogue waves including single peak type and rogue wave triplets are discussed. The effect of the plasma parameters on the rogue waves is also presented.
Effect of capillary waves on surface tension
NASA Technical Reports Server (NTRS)
Kayser, R. F.
1986-01-01
The present study is concerned with the effect which a cutting off of the capillary waves has on surface tension, taking into account a calculation based on capillary-wave theory. For simplicity, three-dimensional systems are considered, and capillary-wave theory is used to calculate sigma-k, the surface tension of an interface where only those modes with at least one wave-vector component greater than k are allowed. Attention is given to a review of capillary-wave theory, the calculation of surface tensions, a determination of the range of validity of capillary-wave theory, and some numerical examples. The quantitative behavior of sigma-k and its relation to the surface tension of a finite-size system are considered. The most surprising result is that sigma-k can be significantly larger than the unconstrained surface tension.
Akhmediev, N; Soto-Crespo, J M; Devine, N
2016-08-01
Turbulence in integrable systems exhibits a noticeable scientific advantage: it can be expressed in terms of the nonlinear modes of these systems. Whether the majority of the excitations in the system are breathers or solitons defines the properties of the turbulent state. In the two extreme cases we can call such states "breather turbulence" or "soliton turbulence." The number of rogue waves, the probability density functions of the chaotic wave fields, and their physical spectra are all specific for each of these two situations. Understanding these extreme cases also helps in studies of mixed turbulent states when the wave field contains both solitons and breathers, thus revealing intermediate characteristics.
NASA Astrophysics Data System (ADS)
Akhmediev, N.; Soto-Crespo, J. M.; Devine, N.
2016-08-01
Turbulence in integrable systems exhibits a noticeable scientific advantage: it can be expressed in terms of the nonlinear modes of these systems. Whether the majority of the excitations in the system are breathers or solitons defines the properties of the turbulent state. In the two extreme cases we can call such states "breather turbulence" or "soliton turbulence." The number of rogue waves, the probability density functions of the chaotic wave fields, and their physical spectra are all specific for each of these two situations. Understanding these extreme cases also helps in studies of mixed turbulent states when the wave field contains both solitons and breathers, thus revealing intermediate characteristics.
NASA Astrophysics Data System (ADS)
Wang, Xiu-Bin; Tian, Shou-Fu; Qin, Chun-Yan; Zhang, Tian-Tian
2016-07-01
Under investigation in this work is a generalized (2+1)-dimensional Boussinesq equation, which can be used to describe the propagation of small-amplitude, long wave in shallow water. By virtue of Bell's polynomials, an effective way is presented to succinctly construct its bilinear form. Furthermore, based on the bilinear formalism and the extended homoclinic test method, the breather wave solution, rogue-wave solution and solitary-wave solution of the equation are well constructed. Our results can be used to enrich the dynamical behavior of the generalized (2+1)-dimensional nonlinear wave fields.
Brillouin scattering-induced rogue waves in self-pulsing fiber lasers
Hanzard, Pierre-Henry; Talbi, Mohamed; Mallek, Djouher; Kellou, Abdelhamid; Leblond, Hervé; Sanchez, François; Godin, Thomas; Hideur, Ammar
2017-01-01
We report the experimental observation of extreme instabilities in a self-pulsing fiber laser under the influence of stimulated Brillouin scattering (SBS). Specifically, we observe temporally localized structures with high intensities that can be referred to as rogue events through their statistical behaviour with highly-skewed intensity distributions. The emergence of these SBS-induced rogue waves is attributed to the interplay between laser operation and resonant Stokes orders. As this behaviour is not accounted for by existing models, we also present numerical simulations showing that such instabilities can be observed in chaotic laser operation. This study opens up new possibilities towards harnessing extreme events in highly-dissipative systems through adapted laser cavity configurations. PMID:28374840
NASA Astrophysics Data System (ADS)
Su, Chuan-Qi; Gao, Yi-Tian; Xue, Long; Wang, Qi-Min
2016-07-01
Under investigation in this paper is the Gross-Pitaevskii equation which describes the dynamics of the Bose-Einstein condensate. Lax pair, conservation laws and Darboux transformation (DT) are constructed. Nonautonomous solitons and breathers are derived based on the DT obtained. A kind of modulation instability process is generated. Nonautonomous rogue waves are obtained via the generalized DT. Influence of the nonlinearity, linear external potential, harmonic external potential, and spectral parameter on the propagation and interaction of the nonautonomous solitons, breathers and rogue waves is also discussed. Amplitude of the first-order nonautonomous soliton is proportional to the imaginary part of the spectral parameter and inversely proportional to the nonlinearity parameter. Linear external potential parameter affects the location of the first-order nonautonomous soliton. Head-on interaction, overtaking interaction and bound-state-like nonautonomous solitons can be formed based on the signs of the real parts of the spectral parameters. Quasi-periodic behaviors are exhibited for the nonautonomous breathers. If the harmonic external potential parameter is negative, quasi-period decreases along the positive time axis, with an increase in the amplitude and a compression in the width. Quasi-period decreases with the increase of the nonlinearity parameter. The second-order nonautonomous rogue wave can split into three first-order ones. Nonlinearity parameter has an effect on the amplitude of the rogue wave. Linear external potential parameter influences the location of the rogue wave, while harmonic external potential parameter affects the curved direction of the background.
NASA Astrophysics Data System (ADS)
Wen, Xiao-Yong; Yan, Zhenya
2017-02-01
The novel generalized perturbation (n, M)-fold Darboux transformations (DTs) are reported for the (2 + 1)-dimensional Kadomtsev-Petviashvili (KP) equation and its extension by using the Taylor expansion of the Darboux matrix. The generalized perturbation (1 , N - 1) -fold DTs are used to find their higher-order rational solitons and rogue wave solutions in terms of determinants. The dynamics behaviors of these rogue waves are discussed in detail for different parameters and time, which display the interesting RW and soliton structures including the triangle, pentagon, heptagon profiles, etc. Moreover, we find that a new phenomenon that the parameter (a) can control the wave structures of the KP equation from the higher-order rogue waves (a ≠ 0) into higher-order rational solitons (a = 0) in (x, t)-space with y = const . These results may predict the corresponding dynamical phenomena in the models of fluid mechanics and other physically relevant systems.
Rogue waves and W-shaped solitons in the multiple self-induced transparency system
NASA Astrophysics Data System (ADS)
Wang, Xin; Liu, Chong; Wang, Lei
2017-09-01
We study localized nonlinear waves on a plane wave background in the multiple self-induced transparency (SIT) system, which describes an important enhancement of the amplification and control of optical waves compared to the single SIT system. A hierarchy of exact multiparametric rational solutions in a compact determinant representation is presented. We demonstrate that this family of solutions contain known rogue wave solutions and unusual W-shaped soliton solutions. State transitions between the fundamental rogue waves and W-shaped solitons as well as higher-order nonlinear superposition modes are revealed in the zero-frequency perturbation region by the suitable choice for the background wavenumber of the electric field component. Particularly, it is found that the multiple SIT system can admit both stationary and nonstationary W-shaped solitons in contrast to the stationary results in the single SIT system. Moreover, the W-shaped soliton complex which is formed by a certain number of fundamental W-shaped solitons with zero phase parameters and its decomposition mechanism in the case of the nonzero phase parameters are shown. Meanwhile, some important characteristics of the nonlinear waves including trajectories and spectrum are discussed through the numerical and analytical methods.
Ion-acoustic solitons, double layers and rogue waves in plasma having superthermal electrons
NASA Astrophysics Data System (ADS)
Singh Saini, Nareshpal
2016-07-01
Most of the space and astrophysical plasmas contain different type of charged particles with non-Maxwellian velocity distributions (e.g., nonthermal, superthermal, Tsallis ). These distributions are commonly found in the auroral region of the Earth's magnetosphere, planetary magnetosphere, solar and stellar coronas, solar wind, etc. The observations from various satellite missions have confirmed the presence of superthermal particles in space and astrophysical environments. Over the last many years, there have been a much interest in studying the different kind of properties of the electrostatic nonlinear excitations (solitons, double layers, rogue waves etc.) in a multi-component plasmas in the presence of superthermal particles. It has been analyzed that superthermal distributions are more appropriate than Maxwellian distribution for the modeling of space data. It is interesting to study the dynamics of various kinds of solitary waves, Double layers, Shocks etc. in varieties of plasma systems containing different kind of species obeying Lorentzian (kappa-type)/Tsallis distribution. In this talk, I have focused on the study of large amplitude IA solitary structures (bipolar solitary structures, double layers etc.), modulational instability and rogue waves in multicomponent plasmas. The Sagdeev potential method has been employed to setup an energy balance equation, from which we have studied the characteristics of large amplitude solitary waves under the influence of superthermality of charged particles and other plasma parameters. The critical Mach number has been determined, above which solitary structures are observed and its variation with superthermality of electrons and other parameters has also been discussed. Double layers have also been discussed. Multiple scale reductive perturbation method has been employed to derive NLS equation. From the different kind of solutions of this equation, amplitude modulation of envelope solitons and rogue waves have been
Capillary wave measurements on helically-supported capillary channels
NASA Astrophysics Data System (ADS)
Chandurwala, Fahim; Thiessen, David
2010-10-01
NASA is considering power generation by the Rankine cycle to save weight on long-duration manned missions to the moon or Mars. Phase separation technology is critical to this process in microgravity. Arrays of capillary channels might be useful for filtering liquid drops from a flowing vapor. The efficiency of droplet capture by a helically-supported capillary channel is being studied. A droplet impinging on the channel launches capillary waves that propagate down the channel helping to dissipate some of the drop's kinetic energy. High-speed video of the channel combined with image processing allows for measurement of the amplitude and speed of the wave packets. Increasing the pitch of the support structure decreases the wave speed. An understanding of the dynamic response of the channel to drop impact is a first step in predicting drop-capture efficiency.
NASA Astrophysics Data System (ADS)
Abdel-Gawad, H. I.; Tantawy, M.; Abo Elkhair, R. E.
2016-07-01
Rogue waves are more precisely defined as waves whose height is more than twice the significant wave height. This remarkable height was measured (by Draupner in 1995). Thus, the need for constructing a mechanism for the rogue waves is of great utility. This motivated us to suggest a mechanism, in this work, that rogue waves may be constructed via nonlinear interactions of solitons and periodic waves. This suggestion is consolidated here, in an example, by studying the behavior of solutions of the complex (KdV). This is done here by the extending the solutions of its real version.
NASA Astrophysics Data System (ADS)
Manikandan, Kannan; Senthilvelan, Murugaian; Kraenkel, Roberto André
2016-10-01
We construct vector rogue wave solutions of the two-dimensional two coupled nonlinear Schrödinger equations with distributed coefficients, namely diffraction, nonlinearity and gain parameters through similarity transformation technique. We transform the two-dimensional two coupled variable coefficients nonlinear Schrödinger equations into Manakov equation with a constraint that connects diffraction and gain parameters with nonlinearity parameter. We investigate the characteristics of the constructed vector rogue wave solutions with four different forms of diffraction parameters. We report some interesting patterns that occur in the rogue wave structures. Further, we construct vector dark rogue wave solutions of the two-dimensional two coupled nonlinear Schrödinger equations with distributed coefficients and report some novel characteristics that we observe in the vector dark rogue wave solutions.
NASA Astrophysics Data System (ADS)
Goyal, Amit; Raju, Thokala Soloman; Kumar, C. N.; Panigrahi, Prasanta K.
2016-04-01
We analytically explore optical rogue waves in a nonlinear graded-index waveguide, with spatially modulated dispersion, nonlinearity, and linear refractive-index. We study the evolution of first-order rogue wave and rogue wave triplet on Airy-Bessel, sech2, and tanh background beams, and reveal that the characteristics of RWs are well maintained while the amplitude of the first-order RW gets enhanced three times the maximum value of the Airy-Bessel and sech2 background beams and five times in the case of RW triplet. These results could be of great interest in realizing the RWs in experimentally realizable situations on small-amplitude background beams in nonlinear optics.
Breathers and rogue waves for an eighth-order nonlinear Schrödinger equation in an optical fiber
NASA Astrophysics Data System (ADS)
Hu, Wen-Qiang; Gao, Yi-Tian; Zhao, Chen; Lan, Zhong-Zhou
2017-02-01
In this paper, an eighth-order nonlinear Schrödinger equation is investigated in an optical fiber, which can be used to describe the propagation of ultrashort nonlinear pulses. Lax pair and infinitely-many conservation laws are derived to verify the integrability of this equation. Via the Darboux transformation and generalized Darboux transformation, the analytic breather and rogue wave solutions are obtained. Influence of the coefficients of operators in this equation, which represent different order nonlinearity, and the spectral parameter on the propagation and interaction of the breathers and rogue waves is also discussed. We find that (i) the periodic of the breathers decreases as the augment of the spectral parameter; (ii) the coefficients of operators change the compressibility and periodic of the breathers, and can affect the interaction range and temporal-spatial distribution of the rogue waves.
Compressional Alfvénic rogue and solitary waves in magnetohydrodynamic plasmas
Panwar, Anuraj; Rizvi, H.; Ryu, C. M.
2013-08-15
Generation of compressional Alfvénic rogue and solitary waves in magnetohydrodynamic plasmas is investigated. Dispersive effect caused by non-ideal electron inertia currents perpendicular to the ambient magnetic field can balance the nonlinear steepening of waves leading to the formation of a soliton. The reductive perturbation method is used to obtain a Korteweg–de Vries (KdV) equation describing the evolution of the solitary wave. The height of a soliton is proportional to the soliton speed “U” and inversely proportional to plasma “β” (ratio of plasma thermal pressure to pressure of the confining magnetic field) and the width of soliton is proportional to the electron inertial length. KdV equation is used to study the nonlinear evolution of modulationally unstable compressional Alfvénic wavepackets via the nonlinear Schrödinger equation. The characteristics of rogue wave influenced by plasma “β” and the electron inertial length are described.
Crossing sea state and rogue wave probability during the Prestige accident
NASA Astrophysics Data System (ADS)
Trulsen, Karsten; Nieto Borge, José Carlos; Gramstad, Odin; Aouf, Lotfi; Lefèvre, Jean-Michel
2015-10-01
We discuss the crossing sea state and the probability of rogue waves during the accident of the tanker Prestige on 13 November 2002. We present newly computed hindcast spectra for every hour during that day at nearby locations, showing the development of a bimodal sea state with two wave systems crossing at nearly right angle. We employ four different nonlinear models capable of computing the phase-resolved sea surface from the hindcast spectra, allowing us to estimate statistics for the occurrence of rogue waves. At the location and moment of the accident, the models give expected values for the kurtosis κ = 3.0119 ± 0.0078. The models coincide that the maximum crest elevation was about 5-6% larger than the expected maximum crest elevation in a Gaussian sea at the moment of the accident. We also conclude that the possible nonlinear interaction between the two crossing wave systems practically did not modify neither the kurtosis nor the largest crest elevation.
Optical rogue-wave-like extreme value fluctuations in fiber Raman amplifiers.
Hammani, Kamal; Finot, Christophe; Dudley, John M; Millot, Guy
2008-10-13
We report experimental observation and characterization of rogue wave-like extreme value statistics arising from pump-signal noise transfer in a fiber Raman amplifier. Specifically, by exploiting Raman amplification with an incoherent pump, the amplified signal is shown to develop a series of temporal intensity spikes whose peak power follows a power-law probability distribution. The results are interpreted using a numerical model of the Raman gain process using coupled nonlinear Schrödinger equations, and the numerical model predicts results in good agreement with experiment.
Rogue waves lead to the instability in GaN semiconductors.
Yahia, M E; Tolba, R E; El-Bedwehy, N A; El-Labany, S K; Moslem, W M
2015-07-24
A new approach to understand the electron/hole interfaced plasma in GaN high electron mobility transistors (HEMTs). A quantum hydrodynamic model is constructed to include electrons/holes degenerate pressure, Bohm potential, and the exchange/correlation effect and then reduced to the nonlinear Schrödinger equation (NLSE). Numerical analysis of the latter predicts the rough (in)stability domains, which allow for the rogue waves to occur. Our results might give physical solution rather than the engineering one to the intrinsic problems in these high frequency/power transistors.
Controllable Discrete Rogue Wave Solutions of the Ablowitz—Ladik Equation in Optics
NASA Astrophysics Data System (ADS)
Wen, Xiao-Yong
2016-07-01
With the aid of symbolic computation Maple, the discrete Ablowitz—Ladik equation is studied via an algebra method, some new rational solutions with four arbitrary parameters are constructed. By analyzing related parameters, the discrete rogue wave solutions with alterable positions and amplitude for the focusing Ablowitz—Ladik equations are derived. Some properties are discussed by graphical analysis, which might be helpful for understanding physical phenomena in optics. Supported by the Beijing Natural Science Foundation under Grant No. 1153004, and China Postdoctoral Science Foundation under Grant No. 2015M570161 and the Natural Science Foundation of China under Grant No. 61471406
Rogue waves lead to the instability in GaN semiconductors
Yahia, M. E.; Tolba, R. E.; El-Bedwehy, N. A.; El-Labany, S. K.; Moslem, W. M.
2015-01-01
A new approach to understand the electron/hole interfaced plasma in GaN high electron mobility transistors (HEMTs). A quantum hydrodynamic model is constructed to include electrons/holes degenerate pressure, Bohm potential, and the exchange/correlation effect and then reduced to the nonlinear Schrödinger equation (NLSE). Numerical analysis of the latter predicts the rough (in)stability domains, which allow for the rogue waves to occur. Our results might give physical solution rather than the engineering one to the intrinsic problems in these high frequency/power transistors. PMID:26206731
Slunyaev, A; Pelinovsky, E; Sergeeva, A; Chabchoub, A; Hoffmann, N; Onorato, M; Akhmediev, N
2013-07-01
The rogue wave solutions (rational multibreathers) of the nonlinear Schrödinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5 are considered. A higher accuracy of wave propagation in space is reached using the modified NLS equation, also known as the Dysthe equation. This numerical modeling allowed us to directly compare simulations with recent results of laboratory measurements in Chabchoub et al. [Phys. Rev. E 86, 056601 (2012)]. In order to achieve even higher physical accuracy, we employed fully nonlinear simulations of potential Euler equations. These simulations provided us with basic characteristics of long time evolution of rational solutions of the NLS equation in the case of near-breaking conditions. The analytic NLS solutions are found to describe the actual wave dynamics of steep waves reasonably well.
Transversally periodic solitary gravity-capillary waves.
Milewski, Paul A; Wang, Zhan
2014-01-08
When both gravity and surface tension effects are present, surface solitary water waves are known to exist in both two- and three-dimensional infinitely deep fluids. We describe here solutions bridging these two cases: travelling waves which are localized in the propagation direction and periodic in the transverse direction. These transversally periodic gravity-capillary solitary waves are found to be of either elevation or depression type, tend to plane waves below a critical transverse period and tend to solitary lumps as the transverse period tends to infinity. The waves are found numerically in a Hamiltonian system for water waves simplified by a cubic truncation of the Dirichlet-to-Neumann operator. This approximation has been proved to be very accurate for both two- and three-dimensional computations of fully localized gravity-capillary solitary waves. The stability properties of these waves are then investigated via the time evolution of perturbed wave profiles.
Transversally periodic solitary gravity–capillary waves
Milewski, Paul A.; Wang, Zhan
2014-01-01
When both gravity and surface tension effects are present, surface solitary water waves are known to exist in both two- and three-dimensional infinitely deep fluids. We describe here solutions bridging these two cases: travelling waves which are localized in the propagation direction and periodic in the transverse direction. These transversally periodic gravity–capillary solitary waves are found to be of either elevation or depression type, tend to plane waves below a critical transverse period and tend to solitary lumps as the transverse period tends to infinity. The waves are found numerically in a Hamiltonian system for water waves simplified by a cubic truncation of the Dirichlet-to-Neumann operator. This approximation has been proved to be very accurate for both two- and three-dimensional computations of fully localized gravity–capillary solitary waves. The stability properties of these waves are then investigated via the time evolution of perturbed wave profiles. PMID:24399922
Dust kinetic Alfvén solitary and rogue waves in a superthermal dusty plasma
Saini, N. S. Singh, Manpreet; Bains, A. S.
2015-11-15
Dust kinetic Alfvén solitary waves (DKASWs) have been examined in a low-β dusty plasma comprising of negatively charged dust grains, superthermal electrons, and ions. A nonlinear Korteweg-de Vries (KdV) equation has been derived using the reductive perturbation method. The combined effects of superthermality of charged particles (via κ), plasma β, obliqueness of propagation (θ), and dust concentration (via f) on the shape and size of the DKASWs have been examined. Only negative potential (rarefactive) structures are observed. Further, characteristics of dust kinetic Alfvén rogue waves (DKARWs), by deriving the non-linear Schrödinger equation (NLSE) from the KdV equation, are studied. Rational solutions of NLSE show that rogue wave envelopes are supported by this plasma model. It is observed that the influence of various plasma parameters (superthermality, plasma β, obliqueness, and dust concentration) on the characteristics of the DKARWs is very significant. This fundamental study may be helpful in understanding the formation of coherent nonlinear structures in space and astrophysical plasma environments where superthermal particles are present.
Dust kinetic Alfvén solitary and rogue waves in a superthermal dusty plasma
NASA Astrophysics Data System (ADS)
Saini, N. S.; Singh, Manpreet; Bains, A. S.
2015-11-01
Dust kinetic Alfvén solitary waves (DKASWs) have been examined in a low-β dusty plasma comprising of negatively charged dust grains, superthermal electrons, and ions. A nonlinear Korteweg-de Vries (KdV) equation has been derived using the reductive perturbation method. The combined effects of superthermality of charged particles (via κ), plasma β, obliqueness of propagation (θ), and dust concentration (via f) on the shape and size of the DKASWs have been examined. Only negative potential (rarefactive) structures are observed. Further, characteristics of dust kinetic Alfvén rogue waves (DKARWs), by deriving the non-linear Schrödinger equation (NLSE) from the KdV equation, are studied. Rational solutions of NLSE show that rogue wave envelopes are supported by this plasma model. It is observed that the influence of various plasma parameters (superthermality, plasma β, obliqueness, and dust concentration) on the characteristics of the DKARWs is very significant. This fundamental study may be helpful in understanding the formation of coherent nonlinear structures in space and astrophysical plasma environments where superthermal particles are present.
Rogue waves in crossing seas: The Louis Majesty accident
NASA Astrophysics Data System (ADS)
Cavaleri, L.; Bertotti, L.; Torrisi, L.; Bitner-Gregersen, E.; Serio, M.; Onorato, M.
2012-11-01
We analyze the sea state conditions during which the accident of the cruise ship Louis Majesty took place. The ship was hit by a large wave that destroyed some windows at deck number five and caused two fatalities. Using the wave model (WAM), driven by the Consortium for Small-Scale Modelling (COSMO-ME) winds, we perform a detailed hindcast of the local wave conditions. The results reveal the presence of two comparable wave systems characterized almost by the same frequency. We discuss such sea state conditions in the framework of a system of two coupled Nonlinear Schrödinger (CNLS) equations, each of which describe the dynamics of a single spectral peak. For some specific parameters, we discuss the breather solutions of the CNLS equations and estimate the maximum wave amplitude. Even though, due to the lack of measurements, it is impossible to establish the nature of the wave that caused the accident, we show that the angle between the two wave systems during the accident was close to the condition for which the maximum amplitude of the breather solution is observed.
Sun, Wen-Rong; Liu, De-Yin; Xie, Xi-Yang
2017-04-01
We report the existence and properties of vector breather and semirational rogue-wave solutions for the coupled higher-order nonlinear Schrödinger equations, which describe the propagation of ultrashort optical pulses in birefringent optical fibers. Analytic vector breather and semirational rogue-wave solutions are obtained with Darboux dressing transformation. We observe that the superposition of the dark and bright contributions in each of the two wave components can give rise to complicated breather and semirational rogue-wave dynamics. We show that the bright-dark type vector solitons (or breather-like vector solitons) with nonconstant speed interplay with Akhmediev breathers, Kuznetsov-Ma solitons, and rogue waves. By adjusting parameters, we note that the rogue wave and bright-dark soliton merge, generating the boomeron-type bright-dark solitons. We prove that the rogue wave can be excited in the baseband modulation instability regime. These results may provide evidence of the collision between the mixed ultrashort soliton and rogue wave.
Wang, Lei Li, Min; Qi, Feng-Hua; Xu, Tao
2015-03-15
Under investigation in this paper is a variable-coefficient derivative nonlinear Schrödinger (vc-DNLS) equation modeling the nonlinear Alfvén waves in the inhomogeneous plasmas. The modulation instability is examined for this inhomogeneous nonlinear model. The nonautonomous breather and rogue wave solutions of the vc-DNLS equation are obtained via the modified Darboux transformation. It is found that the velocity and amplitude of the breather can be controlled by the inhomogeneous magnetic field and nonuniform density. Such novel phenomena as breather amplification and nonlinear Talbot effect-like property are demonstrated with the proper choices of the inhomogeneous parameters. Furthermore, dynamics of the fundamental rogue wave, periodical rogue wave, and composite rogue wave are graphically discussed. The trajectories and amplitudes of the rogue waves can be manipulated by the inhomogeneous magnetic field and nonuniform density. In addition, the nonlinear tunneling of the rogue waves and breathers is studied. As an application, a sample model is treated with our results, and the graphical illustrations exhibit the compressing, expanding, and fluctuating phenomena of the Alfvén rogue waves.
Oscillon dynamics and rogue wave generation in Faraday surface ripples.
Xia, H; Maimbourg, T; Punzmann, H; Shats, M
2012-09-14
We report new experimental results which suggest that the generation of extreme wave events in the Faraday surface ripples is related to the increase in the horizontal mobility of oscillating solitons (oscillons). The analysis of the oscillon trajectories in a horizontal plane shows that at higher vertical acceleration, oscillons move chaotically, merge and form enclosed areas on the water surface. The probability of the formation of such craters, which precede large wave events, increases with the increase in horizontal mobility.
Rogue waves in crossing seas: the Louis Majesty accident
NASA Astrophysics Data System (ADS)
Cavaleri, L.; Bertotti, L.; Torrisi, L.; Bitner-Gregersen, E. M.; Serio, M.; Onorato, M.
2012-04-01
We analyze the sea state conditions during which the accident of the cruise ship Louis Majesty took place. The ship was hit by a large wave that destroyed some windows at deck number five and caused two fatalities. Using the WAM model, driven by the COSMO-ME winds, we perform a detailed hindcast of the local wave conditions. The results reveal the presence of two comparable wave systems characterized almost by the same frequency. We discuss such sea state condition in the framework of a system of two coupled Nonlinear Schr¨odinger, CNLS, equations, each of which describing the dynamics of a single spectral peak. For some specific parameters, we discuss the breather solutions of the CNLS equations and estimate the maximum wave amplitude. Even though,due to the lack of measurements, it is impossible to establish the nature of the wave that caused the accident, we show that the angle between the two wave systems during theaccident is close to the condition for which the maximum amplitude of the breather solution is observed.
Particle trajectories in linear periodic capillary and capillary-gravity water waves.
Henry, David
2007-09-15
Surface tension plays a significant role as a restoration force in the setting of small-amplitude waves, leading to pure capillary and gravity-capillary waves. We show that within the framework of linear theory, the particle paths in a periodic gravity-capillary or pure capillary wave propagating at the surface of water over a flat bed are not closed.
Sun, Wen-Rong; Tian, Bo Jiang, Yan; Zhen, Hui-Ling
2014-04-15
Plasmas are the main constituent of the Universe and the cause of a vast variety of astrophysical, space and terrestrial phenomena. The inhomogeneous nonlinear Schrödinger equation is hereby investigated, which describes the propagation of an electron plasma wave packet with a large wavelength and small amplitude in a medium with a parabolic density and constant interactional damping. By virtue of the double Wronskian identities, the equation is proved to possess the double-Wronskian soliton solutions. Analytic one- and two-soliton solutions are discussed. Amplitude and velocity of the soliton are related to the damping coefficient. Asymptotic analysis is applied for us to investigate the interaction between the two solitons. Overtaking interaction, head-on interaction and bound state of the two solitons are given. From the non-zero potential Lax pair, the first- and second-order rogue-wave solutions are constructed via a generalized Darboux transformation, and influence of the linear and parabolic density profiles on the background density and amplitude of the rogue wave is discussed. -- Highlights: •Double-Wronskian soliton solutions are obtained and proof is finished by virtue of some double Wronskian identities. •Asymptotic analysis is applied for us to investigate the interaction between the two solitons. •First- and second-order rogue-wave solutions are constructed via a generalized Darboux transformation. •Influence of the linear and parabolic density profiles on the background density and amplitude of the rogue wave is discussed.
NASA Astrophysics Data System (ADS)
El-Tantawy, S. A.; Aboelenen, Tarek
2017-05-01
Planar and nonplanar (cylindrical and spherical) ion-acoustic super rogue waves in an unmagnetized electronegative plasma are investigated, both analytically (for planar geometry) and numerically (for planar and nonplanar geometries). Using a reductive perturbation technique, the basic set of fluid equations is reduced to a nonplanar/modified nonlinear Schrödinger equation (NLSE), which describes a slow modulation of the nonlinear wave amplitude. The local modulational instability of the ion-acoustic structures governed by the planar and nonplanar NLSE is reported. Furthermore, the existence region of rogue waves is strictly defined. The parameters used in our calculations are from the lab observation data. The local discontinuous Galerkin (LDG) method is used to find rogue wave solutions of the planar and nonplanar NLSE and to prove L2 stability of this method. Also, it is found that the numerical simulations and the exact (analytical) solutions of the planar NLSE match remarkably well and numerical examples show that the convergence orders of the proposed LDG method are N + 1 when polynomials of degree N are used. Moreover, it is noted that the spherical rogue waves travel faster than their cylindrical counterpart. Also, the numerical solution showed that the spherical and cylindrical amplitudes of the localized pulses decrease with the increase in the time | τ |.
Theoretical and experimental evidence of non-symmetric doubly localized rogue waves.
He, Jingsong; Guo, Lijuan; Zhang, Yongshuai; Chabchoub, Amin
2014-11-08
We present determinant expressions for vector rogue wave (RW) solutions of the Manakov system, a two-component coupled nonlinear Schrödinger (NLS) equation. As a special case, we generate a family of exact and non-symmetric RW solutions of the NLS equation up to third order, localized in both space and time. The derived non-symmetric doubly localized second-order solution is generated experimentally in a water wave flume for deep-water conditions. Experimental results, confirming the characteristic non-symmetric pattern of the solution, are in very good agreement with theory as well as with numerical simulations, based on the modified NLS equation, known to model accurately the dynamics of weakly nonlinear wave packets in deep water.
Theoretical and experimental evidence of non-symmetric doubly localized rogue waves
He, Jingsong; Guo, Lijuan; Zhang, Yongshuai; Chabchoub, Amin
2014-01-01
We present determinant expressions for vector rogue wave (RW) solutions of the Manakov system, a two-component coupled nonlinear Schrödinger (NLS) equation. As a special case, we generate a family of exact and non-symmetric RW solutions of the NLS equation up to third order, localized in both space and time. The derived non-symmetric doubly localized second-order solution is generated experimentally in a water wave flume for deep-water conditions. Experimental results, confirming the characteristic non-symmetric pattern of the solution, are in very good agreement with theory as well as with numerical simulations, based on the modified NLS equation, known to model accurately the dynamics of weakly nonlinear wave packets in deep water. PMID:25383023
Wave amplification in the framework of forced nonlinear Schrödinger equation: The rogue wave context
NASA Astrophysics Data System (ADS)
Slunyaev, Alexey; Sergeeva, Anna; Pelinovsky, Efim
2015-05-01
Irregular waves which experience the time-limited external forcing within the framework of the nonlinear Schrödinger (NLS) equation are studied numerically. It is shown that the adiabatically slow pumping (the time scale of forcing is much longer than the nonlinear time scale) results in selective enhancement of the solitary part of the wave ensemble. The slow forcing provides eventually wider wavenumber spectra, larger values of kurtosis and higher probability of large waves. In the opposite case of rapid forcing the nonlinear waves readjust passing through the stage of fast surges of statistical characteristics. Single forced envelope solitons are considered with the purpose to better identify the role of coherent wave groups. An approximate description on the basis of solutions of the integrable NLS equation is provided. Applicability of the Benjamin-Feir Index to forecasting of conditions favourable for rogue waves is discussed.
Panwar, Anuraj; Ryu, Chang-Mo
2014-06-15
The modulational instability and associated rogue structures of a slow magnetosonic wave are investigated for a Hall magnetohydrodynamic plasma. Nonlinear Schrodinger equation is obtained by using the multiple scale method, which shows a modulationally unstable slow magnetosonic mode evolving into bright wavepackets. The dispersive effects induced by the Hall electron current increase with the increase in plasma β and become weaker as the angle of propagation increases. The growth rate of the modulational instability also increases with the increase in plasma β. The growth rate is greatest for the parallel propagation and drops to zero for perpendicular propagation. The envelope wavepacket of a slow magnetosonic is widened with less oscillations as plasma β increases. But the wavepacket becomes slightly narrower and more oscillatory as the angle of propagation increases. Further a non-stationary envelope solution of the Peregrine soliton is analyzed for rogue waves. The Peregrine soliton contracts temporally and expands spatially with increase in plasma β. However, the width of a slow magnetosonic Peregrine soliton decreases both temporally and spatially with increase of the propagation angle.
Spatiotemporal chaos and two-dimensional dissipative rogue waves in Lugiato-Lefever model
NASA Astrophysics Data System (ADS)
Panajotov, Krassimir; Clerc, Marcel G.; Tlidi, Mustapha
2017-06-01
Driven nonlinear optical cavities can exhibit complex spatiotemporal dynamics. We consider the paradigmatic Lugiato-Lefever model describing driven nonlinear optical resonator. This model is one of the most-studied nonlinear equations in optics. It describes a large spectrum of nonlinear phenomena from bistability, to periodic patterns, localized structures, self-pulsating localized structures and to a complex spatiotemporal behavior. The model is considered also as prototype model to describe several optical nonlinear devices such as Kerr media, liquid crystals, left handed materials, nonlinear fiber cavity, and frequency comb generation. We focus our analysis on a spatiotemporal chaotic dynamics in one-dimension. We identify a route to spatiotemporal chaos through an extended quasiperiodicity. We have estimated the Kaplan-Yorke dimension that provides a measure of the strange attractor complexity. Likewise, we show that the Lugiato-Leferver equation supports rogues waves in two-dimensional settings. We characterize rogue-wave formation by computing the probability distribution of the pulse height. Contribution to the Topical Issue "Theory and Applications of the Lugiato-Lefever Equation", edited by Yanne K. Chembo, Damia Gomila, Mustapha Tlidi, Curtis R. Menyuk.
Observation of gravity-capillary wave turbulence.
Falcon, Eric; Laroche, Claude; Fauve, Stéphan
2007-03-02
We report the observation of the crossover between gravity and capillary wave turbulence on the surface of mercury. The probability density functions of the turbulent wave height are found to be asymmetric and thus non-Gaussian. The surface wave height displays power-law spectra in both regimes. In the capillary region, the exponent is in fair agreement with weak turbulence theory. In the gravity region, it depends on the forcing parameters. This can be related to the finite size of the container. In addition, the scaling of those spectra with the mean energy flux is found in disagreement with weak turbulence theory for both regimes.
NASA Astrophysics Data System (ADS)
Lu, Luyao; Xia, Ling; Ye, Xuesong; Cheng, Heping
2010-06-01
Calcium homeostasis is considered to be one of the most important factors for the contraction and relaxation of the heart muscle. However, under some pathological conditions, such as heart failure (HF), calcium homeostasis is disordered, and spontaneous waves may occur. In this study, we developed a mathematical model of formation and propagation of a calcium wave based upon a governing system of diffusion-reaction equations presented by Izu et al (2001 Biophys. J. 80 103-20) and integrated non-clustered or 'rogue' ryanodine receptors (rogue RyRs) into a two-dimensional (2D) model of ventricular myocytes isolated from failing hearts in which sarcoplasmic reticulum (SR) Ca2+ pools are partially unloaded. The model was then used to simulate the effect of rogue RyRs on initiation and propagation of the calcium wave in ventricular myocytes with HF. Our simulation results show that rogue RyRs can amplify the diastolic SR Ca2+ leak in the form of Ca2+ quarks, increase the probability of occurrence of spontaneous Ca2+ waves even with smaller SR Ca2+ stores, accelerate Ca2+ wave propagation, and hence lead to delayed afterdepolarizations (DADs) and cardiac arrhythmia in the diseased heart. This investigation suggests that incorporating rogue RyRs in the Ca2+ wave model under HF conditions provides a new view of Ca2+ dynamics that could not be mimicked by adjusting traditional parameters involved in Ca2+ release units and other ion channels, and contributes to understanding the underlying mechanism of HF.
Lu, Luyao; Xia, Ling; Ye, Xuesong; Cheng, Heping
2010-05-26
Calcium homeostasis is considered to be one of the most important factors for the contraction and relaxation of the heart muscle. However, under some pathological conditions, such as heart failure (HF), calcium homeostasis is disordered, and spontaneous waves may occur. In this study, we developed a mathematical model of formation and propagation of a calcium wave based upon a governing system of diffusion-reaction equations presented by Izu et al (2001 Biophys. J. 80 103-20) and integrated non-clustered or 'rogue' ryanodine receptors (rogue RyRs) into a two-dimensional (2D) model of ventricular myocytes isolated from failing hearts in which sarcoplasmic reticulum (SR) Ca(2+) pools are partially unloaded. The model was then used to simulate the effect of rogue RyRs on initiation and propagation of the calcium wave in ventricular myocytes with HF. Our simulation results show that rogue RyRs can amplify the diastolic SR Ca(2+) leak in the form of Ca(2+) quarks, increase the probability of occurrence of spontaneous Ca(2+) waves even with smaller SR Ca(2+) stores, accelerate Ca(2+) wave propagation, and hence lead to delayed afterdepolarizations (DADs) and cardiac arrhythmia in the diseased heart. This investigation suggests that incorporating rogue RyRs in the Ca(2+) wave model under HF conditions provides a new view of Ca(2+) dynamics that could not be mimicked by adjusting traditional parameters involved in Ca(2+) release units and other ion channels, and contributes to understanding the underlying mechanism of HF.
Statistics of rogue waves in random sea states and their dependence on inverse scattering data.
NASA Astrophysics Data System (ADS)
Schober, Constance
2014-05-01
Extreme waves are frequently modeled using the nonlinear Schrodinger (NLS) equation and it's higher order extensions (HONLS). In earlier work we introduced δ, the 'splitting distance' between two consecutive simple points in the Floquet spectrum of the associated Zakharov-Shabaat problem of the NLS equation, as a measure of proximity to instabilities in the wavefield. As and alternative to the Benjamin-Feir index, the splitting distance can be seen as a measure of the localization of the energy in the wave field. In [1] we correlated the development of localized rogue waves in random sea states characterized by JONSWAP spectra with the splitting distance δ. In [2] Sura shows that the kurtosis (κ) and skewness (s) of deep ocean field data obey the relationship κ = 3/2s2 + c which is not satisfied by Gaussian or double exponential noise. Here we show that sea states modeled using the HONLS equation and random phase JONSWAP initial data exhibit a significant deviation from Gaussianity and satisfy Sura's relation between the skewness and kurtosis. For the HONLS equation, δ is not invariant in time. We determine both the initial splitting distance δ0 and the time averaged splitting distance δavg. We find that the maximum strength, skewness, and kurtosis of the sea state are strongly dependent on δavg. Using the Mori-Janssen relationship between kurtosis and P, the probability a wave height exceeds a given quantity, we determine P(δavg). References 1 A.L. Islas and C.M. Schober, Predicting rogue waves in random oceanic sea states, Phys. Fluids 17 (2005) 2 P. Sura and S.T. Gille, Stochastic dynamics of sea surface height variability, J. Phys. Oceanogr. 40 (2010).
Optical turbulence and transverse rogue waves in a cavity with triple-quantum-dot molecules
NASA Astrophysics Data System (ADS)
Eslami, M.; Khanmohammadi, M.; Kheradmand, R.; Oppo, G.-L.
2017-09-01
We show that optical turbulence extreme events can exist in the transverse dynamics of a cavity containing molecules of triple quantum dots under conditions close to tunneling-induced transparency. These nanostructures, when coupled via tunneling, form a four-level configuration with tunable energy-level separations. We show that such a system exhibits multistability and bistability of Turing structures in instability domains with different critical wave vectors. By numerical simulation of the mean-field equation that describes the transverse dynamics of the system, we show that the simultaneous presence of two transverse solutions with opposite nonlinearities gives rise to a series of turbulent structures with the capability of generating two-dimensional rogue waves.
Närhi, Mikko; Wetzel, Benjamin; Billet, Cyril; Toenger, Shanti; Sylvestre, Thibaut; Merolla, Jean-Marc; Morandotti, Roberto; Dias, Frederic; Genty, Goëry; Dudley, John M
2016-12-19
Modulation instability is a fundamental process of nonlinear science, leading to the unstable breakup of a constant amplitude solution of a physical system. There has been particular interest in studying modulation instability in the cubic nonlinear Schrödinger equation, a generic model for a host of nonlinear systems including superfluids, fibre optics, plasmas and Bose-Einstein condensates. Modulation instability is also a significant area of study in the context of understanding the emergence of high amplitude events that satisfy rogue wave statistical criteria. Here, exploiting advances in ultrafast optical metrology, we perform real-time measurements in an optical fibre system of the unstable breakup of a continuous wave field, simultaneously characterizing emergent modulation instability breather pulses and their associated statistics. Our results allow quantitative comparison between experiment, modelling and theory, and are expected to open new perspectives on studies of instability dynamics in physics.
NASA Astrophysics Data System (ADS)
Närhi, Mikko; Wetzel, Benjamin; Billet, Cyril; Toenger, Shanti; Sylvestre, Thibaut; Merolla, Jean-Marc; Morandotti, Roberto; Dias, Frederic; Genty, Goëry; Dudley, John M.
2016-12-01
Modulation instability is a fundamental process of nonlinear science, leading to the unstable breakup of a constant amplitude solution of a physical system. There has been particular interest in studying modulation instability in the cubic nonlinear Schrödinger equation, a generic model for a host of nonlinear systems including superfluids, fibre optics, plasmas and Bose-Einstein condensates. Modulation instability is also a significant area of study in the context of understanding the emergence of high amplitude events that satisfy rogue wave statistical criteria. Here, exploiting advances in ultrafast optical metrology, we perform real-time measurements in an optical fibre system of the unstable breakup of a continuous wave field, simultaneously characterizing emergent modulation instability breather pulses and their associated statistics. Our results allow quantitative comparison between experiment, modelling and theory, and are expected to open new perspectives on studies of instability dynamics in physics.
Närhi, Mikko; Wetzel, Benjamin; Billet, Cyril; Toenger, Shanti; Sylvestre, Thibaut; Merolla, Jean-Marc; Morandotti, Roberto; Dias, Frederic; Genty, Goëry; Dudley, John M.
2016-01-01
Modulation instability is a fundamental process of nonlinear science, leading to the unstable breakup of a constant amplitude solution of a physical system. There has been particular interest in studying modulation instability in the cubic nonlinear Schrödinger equation, a generic model for a host of nonlinear systems including superfluids, fibre optics, plasmas and Bose–Einstein condensates. Modulation instability is also a significant area of study in the context of understanding the emergence of high amplitude events that satisfy rogue wave statistical criteria. Here, exploiting advances in ultrafast optical metrology, we perform real-time measurements in an optical fibre system of the unstable breakup of a continuous wave field, simultaneously characterizing emergent modulation instability breather pulses and their associated statistics. Our results allow quantitative comparison between experiment, modelling and theory, and are expected to open new perspectives on studies of instability dynamics in physics. PMID:27991513
Slunyaev, A V; Pelinovsky, E N
2016-11-18
The role of multiple soliton and breather interactions in the formation of very high waves is disclosed within the framework of the integrable modified Korteweg-de Vries (MKdV) equation. Optimal conditions for the focusing of many solitons are formulated explicitly. Namely, trains of ordered solitons with alternate polarities evolve to huge strongly localized transient waves. The focused wave amplitude is exactly the sum of the focusing soliton heights; the maximum wave inherits the polarity of the fastest soliton in the train. The focusing of several solitary waves or/and breathers may naturally occur in a soliton gas and will lead to rogue-wave-type dynamics; hence, it represents a new nonlinear mechanism of rogue wave generation. The discovered scenario depends crucially on the soliton polarities (phases), and is not taken into account by existing kinetic theories. The performance of the soliton mechanism of rogue wave generation is shown for the example of the focusing MKdV equation, when solitons possess "frozen" phases (certain polarities), though the approach is efficient in some other integrable systems which admit soliton and breather solutions.
NASA Astrophysics Data System (ADS)
Slunyaev, A. V.; Pelinovsky, E. N.
2016-11-01
The role of multiple soliton and breather interactions in the formation of very high waves is disclosed within the framework of the integrable modified Korteweg-de Vries (MKdV) equation. Optimal conditions for the focusing of many solitons are formulated explicitly. Namely, trains of ordered solitons with alternate polarities evolve to huge strongly localized transient waves. The focused wave amplitude is exactly the sum of the focusing soliton heights; the maximum wave inherits the polarity of the fastest soliton in the train. The focusing of several solitary waves or/and breathers may naturally occur in a soliton gas and will lead to rogue-wave-type dynamics; hence, it represents a new nonlinear mechanism of rogue wave generation. The discovered scenario depends crucially on the soliton polarities (phases), and is not taken into account by existing kinetic theories. The performance of the soliton mechanism of rogue wave generation is shown for the example of the focusing MKdV equation, when solitons possess "frozen" phases (certain polarities), though the approach is efficient in some other integrable systems which admit soliton and breather solutions.
Two different kinds of rogue waves in weakly crossing sea states.
Ruban, V P
2009-06-01
Formation of giant waves in sea states with two spectral maxima centered at close wave vectors k_{0}+/-Deltak/2 in the Fourier plane is numerically simulated using the fully nonlinear model for long-crested water waves [V. P. Ruban, Phys. Rev. E 71, 055303(R) (2005)]. Depending on an angle theta between the vectors k_{0} and Deltak , which determines a typical orientation of interference stripes in the physical plane, rogue waves arise having different spatial structure. If theta less, < or = arctan(1/sqrt[2]) , then typical giant waves are relatively long fragments of essentially two-dimensional (2D) ridges, separated by wide valleys and consisting of alternating oblique crests and troughs. At nearly perpendicular k_{0} and Deltak , the interference minima develop to coherent structures similar to the dark solitons of the nonlinear Schrodinger equation, and a 2D freak wave looks much as a piece of a one-dimensional freak wave bounded in the transversal direction by two such dark solitons.
Guo, Shimin Mei, Liquan
2014-11-15
The amplitude modulation of ion-acoustic waves is investigated in an unmagnetized plasma containing positive ions, negative ions, and electrons obeying a kappa-type distribution that is penetrated by a positive ion beam. By considering dissipative mechanisms, including ionization, negative-positive ion recombination, and electron attachment, we introduce a comprehensive model for the plasma with the effects of sources and sinks. Via reductive perturbation theory, the modified nonlinear Schrödinger equation with a dissipative term is derived to govern the dynamics of the modulated waves. The effect of the plasma parameters on the modulation instability criterion for the modified nonlinear Schrödinger equation is numerically investigated in detail. Within the unstable region, first- and second-order dissipative ion-acoustic rogue waves are present. The effect of the plasma parameters on the characteristics of the dissipative rogue waves is also discussed.
NASA Astrophysics Data System (ADS)
Xie, Xi-Yang; Tian, Bo; Jiang, Yan; Sun, Wen-Rong; Sun, Ya; Gao, Yi-Tian
2016-07-01
Under investigation in this paper is an inhomogeneous nonlinear system, which describes the marginally-unstable baroclinic wave packets in a geophysical fluid or ultra-short pulses in nonlinear optics with certain inhomogeneous medium existing. By virtue of a kind of the Darboux transformation, under the Painlevé integrable condition, the first- and second-order bright and dark rogue-wave solutions are derived. Properties of the first- and second-order bright and dark rogue waves with α(t), which measures the state of the basic flow, and β(t), representing the interaction of the wave packet and mean flow, are graphically presented and analyzed: α(t) and β(t) have no influence on the wave packet, but affect the correction of the basic flow. When we choose α(t) as a constant and linear function, respectively, the shapes of the first- and second-order dark rogue waves change, and the peak heights and widths of them alter with the value of β(t) changing.
Rogue waves for a system of coupled derivative nonlinear Schrödinger equations.
Chan, H N; Malomed, B A; Chow, K W; Ding, E
2016-01-01
Rogue waves (RWs) are unexpectedly strong excitations emerging from an otherwise tranquil background. The nonlinear Schrödinger equation (NLSE), a ubiquitous model with wide applications to fluid mechanics, optics, plasmas, etc., exhibits RWs only in the regime of modulation instability (MI) of the background. For a system of multiple waveguides, the governing coupled NLSEs can produce regimes of MI and RWs, even if each component has dispersion and cubic nonlinearity of opposite signs. A similar effect is demonstrated here for a system of coupled derivative NLSEs (DNLSEs) where the special feature is the nonlinear self-steepening of narrow pulses. More precisely, these additional regimes of MI and RWs for coupled DNLSEs depend on the mismatch in group velocities between the components, and the parameters for cubic nonlinearity and self-steepening. RWs considered in this paper differ from those of the NLSEs in terms of the amplification ratio and criteria of existence. Applications to optics and plasma physics are discussed.
The role of PR in the formation of psychological readiness for a rogue wave events.
NASA Astrophysics Data System (ADS)
Chaykovskaya, N.; Rodin, A.
2012-04-01
In recent years the study of psychological foundations of human behavior when dealing with rogue waves has received increasing attention. However, this problem is only in the interest of a narrow circle of specialists, while the task is to explain the rules of behavior when dealing with the phenomenon to anyone who can get into this situation. This problem can only be solved by media and PR-specialists working in this field. PR- specialists are required to convey to people the need of correct action stereotype for assault element, because, as it is known, a fact only becomes a fact when it is written about in a newspaper or is made a story about in a summary of radio or TV news. This publication is devoted to the developing of forms and methods of PR-specialists activity in this area.
NASA Astrophysics Data System (ADS)
Wu, Xiao-Yu; Tian, Bo; Chai, Han-Peng; Sun, Yan
2017-08-01
Under investigation in this letter is a (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation, which describes the weakly dispersive waves propagating in a fluid. Employing the Hirota method and symbolic computation, we obtain the lump, breather-wave and rogue-wave solutions under certain constraints. We graphically study the lump waves with the influence of the parameters h1, h3 and h5 which are all the real constants: When h1 increases, amplitude of the lump wave increases, and location of the peak moves; when h3 increases, lump wave’s amplitude decreases, but location of the peak keeps unchanged; when h5 changes, lump wave’s peak location moves, but amplitude keeps unchanged. Breather waves and rogue waves are displayed: Rogue waves emerge when the periods of the breather waves go to the infinity.
A hybrid model for simulating rogue waves in random seas on a large temporal and spatial scale
NASA Astrophysics Data System (ADS)
Wang, Jinghua; Ma, Q. W.; Yan, S.
2016-05-01
A hybrid model for simulating rogue waves in random seas on a large temporal and spatial scale is proposed in this paper. It is formed by combining the derived fifth order Enhanced Nonlinear Schrödinger Equation based on Fourier transform, the Enhanced Spectral Boundary Integral (ESBI) method and its simplified version. The numerical techniques and algorithm for coupling three models on time scale are suggested. Using the algorithm, the switch between the three models during the computation is triggered automatically according to wave nonlinearities. Numerical tests are carried out and the results indicate that this hybrid model could simulate rogue waves both accurately and efficiently. In some cases discussed, the hybrid model is more than 10 times faster than just using the ESBI method, and it is also much faster than other methods reported in the literature.
Essama, Bedel Giscard Onana; Atangana, Jacques; Frederick, Biya Motto; Mokhtari, Bouchra; Eddeqaqi, Noureddine Cherkaoui; Kofane, Timoleon Crepin
2014-09-01
We investigate the behavior of the electromagnetic wave that propagates in a metamaterial for negative index regime. Second-order dispersion and cubic-quintic nonlinearities are taken into account. The behavior obtained for negative index regime is compared to that observed for absorption regime. The collective coordinates technique is used to characterize the light pulse intensity profile at some frequency ranges. Five frequency ranges have been pointed out. The perfect combination of second-order dispersion and cubic nonlinearity leads to a robust soliton at each frequency range for negative index regime. The soliton peak power progressively decreases for absorption regime. Further, this peak power also decreases with frequency. We show that absorption regime can induce rogue wave trains generation at a specific frequency range. However, this rogue wave trains generation is maintained when the quintic nonlinearity comes into play for negative index regime and amplified for absorption regime at a specific frequency range. It clearly appears that rogue wave behavior strongly depends on the frequency and the regime considered. Furthermore, the stability conditions of the electromagnetic wave have also been discussed at frequency ranges considered for both negative index and absorption regimes.
Ion-acoustic rogue waves and breathers in relativistically degenerate electron-positron plasmas
NASA Astrophysics Data System (ADS)
Abdikian, A.; Ismaeel, S.
2017-08-01
In this paper, we employ a weakly relativistic fluid model to study the nonlinear amplitude modulation of electrostatic waves in an unmagnetized electron-positron-ion plasma. It is assumed that the degeneracy pressure law for electrons and positrons follows the Chandrasekhar limit of state whereas ions are warm and classical. The hydrodynamic approach along with the perturbation method have been applied to obtain the corresponding nonlinear Schrödinger equation (NLSE) in which nonlinearity is in balance with the dispersive terms. Using the NLSE, we could evaluate the modulational instability to show that various types of localized ion acoustic excitations exist in the form of either bright-type envelope solitons or dark-type envelope solitons. The regions of the stable and unstable envelope wave have been confined punctually for various regimes. Furthermore, it is proposed that the exact solutions of the NLSE for breather waves are the rogue waves (RWs), Akhmediev breather (AB), and Kuznetsov-Ma breather (KM) soliton. In order to show that the characteristics of breather structures is influenced by the plasma parameters (namely, relativistic parameter, positron concentration, and ionic temperature), the relevant numerical analysis of the NLSE is examined. In particular, it is observed that by increasing the values of the mentioned plasma parameters, the amplitude of the RWs will be decreased. Our results help researchers to explain the formation and dynamics of nonlinear electrostatic excitations in super dense astrophysical regimes.
Inverse scattering transform analysis of rogue waves using local periodization procedure
NASA Astrophysics Data System (ADS)
Randoux, Stéphane; Suret, Pierre; El, Gennady
2016-07-01
The nonlinear Schrödinger equation (NLSE) stands out as the dispersive nonlinear partial differential equation that plays a prominent role in the modeling and understanding of the wave phenomena relevant to many fields of nonlinear physics. The question of random input problems in the one-dimensional and integrable NLSE enters within the framework of integrable turbulence, and the specific question of the formation of rogue waves (RWs) has been recently extensively studied in this context. The determination of exact analytic solutions of the focusing 1D-NLSE prototyping RW events of statistical relevance is now considered as the problem of central importance. Here we address this question from the perspective of the inverse scattering transform (IST) method that relies on the integrable nature of the wave equation. We develop a conceptually new approach to the RW classification in which appropriate, locally coherent structures are specifically isolated from a globally incoherent wave train to be subsequently analyzed by implementing a numerical IST procedure relying on a spatial periodization of the object under consideration. Using this approach we extend the existing classifications of the prototypes of RWs from standard breathers and their collisions to more general nonlinear modes characterized by their nonlinear spectra.
Inverse scattering transform analysis of rogue waves using local periodization procedure
Randoux, Stéphane; Suret, Pierre; El, Gennady
2016-01-01
The nonlinear Schrödinger equation (NLSE) stands out as the dispersive nonlinear partial differential equation that plays a prominent role in the modeling and understanding of the wave phenomena relevant to many fields of nonlinear physics. The question of random input problems in the one-dimensional and integrable NLSE enters within the framework of integrable turbulence, and the specific question of the formation of rogue waves (RWs) has been recently extensively studied in this context. The determination of exact analytic solutions of the focusing 1D-NLSE prototyping RW events of statistical relevance is now considered as the problem of central importance. Here we address this question from the perspective of the inverse scattering transform (IST) method that relies on the integrable nature of the wave equation. We develop a conceptually new approach to the RW classification in which appropriate, locally coherent structures are specifically isolated from a globally incoherent wave train to be subsequently analyzed by implementing a numerical IST procedure relying on a spatial periodization of the object under consideration. Using this approach we extend the existing classifications of the prototypes of RWs from standard breathers and their collisions to more general nonlinear modes characterized by their nonlinear spectra. PMID:27385164
Ginzburg-Landau equation as a heuristic model for generating rogue waves
NASA Astrophysics Data System (ADS)
Lechuga, Antonio
2016-04-01
Envelope equations have many applications in the study of physical systems. Particularly interesting is the case 0f surface water waves. In steady conditions, laboratory experiments are carried out for multiple purposes either for researches or for practical problems. In both cases envelope equations are useful for understanding qualitative and quantitative results. The Ginzburg-Landau equation provides an excellent model for systems of that kind with remarkable patterns. Taking into account the above paragraph the main aim of our work is to generate waves in a water tank with almost a symmetric spectrum according to Akhmediev (2011) and thus, to produce a succession of rogue waves. The envelope of these waves gives us some patterns whose model is a type of Ginzburg-Landau equation, Danilov et al (1988). From a heuristic point of view the link between the experiment and the model is achieved. Further, the next step consists of changing generating parameters on the water tank and also the coefficients of the Ginzburg-Landau equation, Lechuga (2013) in order to reach a sufficient good approach.
Inverse scattering transform analysis of rogue waves using local periodization procedure.
Randoux, Stéphane; Suret, Pierre; El, Gennady
2016-07-07
The nonlinear Schrödinger equation (NLSE) stands out as the dispersive nonlinear partial differential equation that plays a prominent role in the modeling and understanding of the wave phenomena relevant to many fields of nonlinear physics. The question of random input problems in the one-dimensional and integrable NLSE enters within the framework of integrable turbulence, and the specific question of the formation of rogue waves (RWs) has been recently extensively studied in this context. The determination of exact analytic solutions of the focusing 1D-NLSE prototyping RW events of statistical relevance is now considered as the problem of central importance. Here we address this question from the perspective of the inverse scattering transform (IST) method that relies on the integrable nature of the wave equation. We develop a conceptually new approach to the RW classification in which appropriate, locally coherent structures are specifically isolated from a globally incoherent wave train to be subsequently analyzed by implementing a numerical IST procedure relying on a spatial periodization of the object under consideration. Using this approach we extend the existing classifications of the prototypes of RWs from standard breathers and their collisions to more general nonlinear modes characterized by their nonlinear spectra.
Laser absorption waves in metallic capillaries
NASA Astrophysics Data System (ADS)
Anisimov, V. N.; Arutiunian, R. V.; Bol'Shov, L. A.; Kanevskii, M. F.; Kondrashov, V. V.
1987-07-01
The propagation of laser absorption waves in metallic capillaries was studied experimentally and numerically during pulsed exposure to CO2 laser radiation. The dependence of the plasma front propagation rate on the initial air pressure in the capillary is determined. In a broad range of parameters, the formation time of the optically opaque plasma layer is governed by the total laser pulse energy from the beginning of the exposure to the instant screening appears, and is weakly dependent on the pulse shape and gas pressure.
Waves in hyperbolic and double negative metamaterials including rogues and solitons.
Boardman, A D; Alberucci, A; Assanto, G; Grimalsky, V V; Kibler, B; McNiff, J; Nefedov, I S; Rapoport, Yu G; Valagiannopoulos, C A
2017-03-17
considered with a model of the response of hyperbolic metamaterials in terms of the homogenisation ('effective medium') approach. The model has a macroscopic dielectric tensor encompassing at least one negative eigenvalue. It is shown that light propagating in the presence of hyperbolic dispersion undergoes negative (anomalous) diffraction. The theory is ten broadened out to include the influence of the orientation of the optical axis with respect to the propagation wave vector. Optical rogue waves are discussed in terms of how they are influenced, but not suppressed, by a metamaterial background. It is strongly discussed that metamaterials and optical rogue waves have both been making headlines in recent years and that they are, separately, large areas of research to study. A brief background of the inevitable linkage of them is considered and important new possibilities are discussed. After this background is revealed some new rogue wave configurations combining the two areas are presented alongside a discussion of the way forward for the future.
NASA Astrophysics Data System (ADS)
El-Tantawy, S. A.
2016-05-01
We examine the likelihood of the ion-acoustic rogue waves propagation in a non-Maxwellian electronegative plasma in the framework of the family of the Korteweg-de Vries (KdV) equations (KdV/modified KdV/Extended KdV equation). For this purpose, we use the reductive perturbation technique to carry out this study. It is known that the family of the KdV equations have solutions of distinct structures such as solitons, shocks, kinks, cnoidal waves, etc. However, the dynamics of the nonlinear rogue waves is governed by the nonlinear Schrödinger equation (NLSE). Thus, the family of the KdV equations is transformed to their corresponding NLSE developing a weakly nonlinear wave packets. We show the possible region for the existence of the rogue waves and define it precisely for typical parameters of space plasmas. We investigate numerically the effects of relevant physical parameters, namely, the negative ion relative concentration, the nonthermal parameter, and the mass ratio on the propagation of the rogue waves profile. The present study should be helpful in understanding the salient features of the nonlinear structures such as, ion-acoustic solitary waves, shock waves, and rogue waves in space and in laboratory plasma where two distinct groups of ions, i.e. positive and negative ions, and non-Maxwellian (nonthermal) electrons are present.
Wen, Xiao-Yong; Yang, Yunqing; Yan, Zhenya
2015-07-01
In this paper, a simple and constructive method is presented to find the generalized perturbation (n,M)-fold Darboux transformations (DTs) of the modified nonlinear Schrödinger (MNLS) equation in terms of fractional forms of determinants. In particular, we apply the generalized perturbation (1,N-1)-fold DTs to find its explicit multi-rogue-wave solutions. The wave structures of these rogue-wave solutions of the MNLS equation are discussed in detail for different parameters, which display abundant interesting wave structures, including the triangle and pentagon, etc., and may be useful to study the physical mechanism of multirogue waves in optics. The dynamical behaviors of these multi-rogue-wave solutions are illustrated using numerical simulations. The same Darboux matrix can also be used to investigate the Gerjikov-Ivanov equation such that its multi-rogue-wave solutions and their wave structures are also found. The method can also be extended to find multi-rogue-wave solutions of other nonlinear integrable equations.
NASA Astrophysics Data System (ADS)
Liu, Junyang; Hang, Chao; Huang, Guoxiang
2016-06-01
We propose a scheme to demonstrate the existence of optical Peregrine rogue waves and Akhmediev and Kuznetsov-Ma breathers and realize their active control via electromagnetically induced transparency (EIT). The system we suggest is a cold, Λ -type three-level atomic gas interacting with a probe and a control laser fields and working under EIT condition. We show that, based on EIT with an incoherent optical pumping, which can be used to cancel optical absorption, (1+1)-dimensional optical Peregrine rogue waves, Akhmediev breathers, and Kuznetsov-Ma breathers can be generated with very low light power. In addition, we demonstrate that the Akhmediev and Kuznetsov-Ma breathers in (2+1)-dimensions obtained can be actively manipulated by using an external magnetic field. As a result, these breathers can display trajectory deflections and bypass obstacles during propagation.
NASA Astrophysics Data System (ADS)
Yu, Fajun
2017-02-01
Starting from a discrete spectral problem, we derive a hierarchy of nonlinear discrete equations which include the Ablowitz-Ladik (AL) equation. We analytically study the discrete rogue-wave (DRW) solutions of AL equation with three free parameters. The trajectories of peaks and depressions of profiles for the first- and second-order DRWs are produced by means of analytical and numerical methods. In particular, we study the solutions with dispersion in parity-time ( P T ) symmetric potential for Ablowitz-Musslimani equation. And we consider the non-autonomous DRW solutions, parameters controlling and their interactions with variable coefficients, and predict the long-living rogue wave solutions. Our results might provide useful information for potential applications of synthetic P T symmetric systems in nonlinear optics and condensed matter physics.
NASA Astrophysics Data System (ADS)
Wang, Lei; Qi, Feng-Hua; Tang, Bing; Shi, Yu-Ying
2016-12-01
Under investigation in this paper is a variable-coefficient AB (vcAB) system, which describes marginally unstable baroclinic wave packets in geophysical fluids and ultra-short pulses in nonlinear optics. The modulation instability analysis of solutions with variable coefficients in the presence of a small perturbation is studied. The modified Darboux transformation (mDT) of the vcAB system is constructed via a gauge transformation. The first-order non-autonomous rogue wave solutions of the vcAB system are presented based on the mDT. It is found that the wave amplitude of B exhibits two types of structures, i.e. the double-peak structure appears if the plane-wave solution parameter ω is equal to zero, while selecting ω≠0 yields a single-peak one. Effects of the variable coefficients on the rogue waves are graphically discussed in detail. The periodic rogue wave and composite rogue wave are obtained with different inhomogeneous parameters. Additionally, the nonlinear tunneling of the rogue waves through a conventional hyperbolic nonlinear well and barrier are investigated.
Wen, Xiao-Yong; Yan, Zhenya
2015-12-01
We study higher-order rogue wave (RW) solutions of the coupled integrable dispersive AB system (also called Pedlosky system), which describes the evolution of wave-packets in a marginally stable or unstable baroclinic shear flow in geophysical fluids. We propose its continuous-wave (CW) solutions and existent conditions for their modulation instability to form the rogue waves. A new generalized N-fold Darboux transformation (DT) is proposed in terms of the Taylor series expansion for the spectral parameter in the Darboux matrix and its limit procedure and applied to the CW solutions to generate multi-rogue wave solutions of the coupled AB system, which satisfy the general compatibility condition. The dynamical behaviors of these higher-order rogue wave solutions demonstrate both strong and weak interactions by modulating parameters, in which some weak interactions can generate the abundant triangle, pentagon structures, etc. Particularly, the trajectories of motion of peaks and depressions of profiles of the first-order RWs are explicitly analyzed. The generalized DT method used in this paper can be extended to other nonlinear integrable systems. These results may be useful for understanding the corresponding rogue-wave phenomena in fluid mechanics and related fields.
Heavy ion-acoustic rogue waves in electron-positron multi-ion plasmas
NASA Astrophysics Data System (ADS)
Chowdhury, N. A.; Mannan, A.; Hasan, M. M.; Mamun, A. A.
2017-09-01
The nonlinear propagation of heavy-ion-acoustic (HIA) waves (HIAWs) in a four-component multi-ion plasma (containing inertial heavy negative ions and light positive ions, as well as inertialess nonextensive electrons and positrons) has been theoretically investigated. The nonlinear Schrödinger (NLS) equation is derived by employing the reductive perturbation method. It is found that the NLS equation leads to the modulational instability (MI) of HIAWs, and to the formation of HIA rogue waves (HIARWs), which are due to the effects of nonlinearity and dispersion in the propagation of HIAWs. The conditions for the MI of HIAWs and the basic properties of the generated HIARWs are identified. It is observed that the striking features (viz., instability criteria, growth rate of MI, amplitude and width of HIARWs, etc.) of the HIAWs are significantly modified by the effects of nonextensivity of electrons and positrons, the ratio of light positive ion mass to heavy negative ion mass, the ratio of electron number density to light positive ion number density, the ratio of electron temperature to positron temperature, etc. The relevancy of our present investigation to the observations in space (viz., cometary comae and earth's ionosphere) and laboratory (viz., solid-high intense laser plasma interaction experiments) plasmas is pointed out.
Rogue waves in injected semiconductor lasers with current modulation: role of the modulation phase.
Ahuja, Jatin; Nalawade, Dhananjay Bhiku; Zamora-Munt, Jordi; Vilaseca, Ramon; Masoller, Cristina
2014-11-17
Semiconductor lasers with continuous-wave optical injection display a rich variety of behaviors, including stable locking, periodic or chaotic oscillations, excitable pulses, etc. Within the chaotic regime it has been shown that the laser intensity can display extreme pulses, which have been identified as optical rogue waves (RWs), and it has also been shown that such extreme pulses can be completely suppressed via direct modulation of the laser current, with appropriated modulation amplitude and frequency. Here we perform a numerical analysis of the RW statistics and show that, when RWs are not suppressed by current modulation, their probability of occurrence strongly depends on the phase of the modulation. If the modulation is slow (the modulation frequency, fmod, is below the relaxation oscillation frequency, fro), the RWs occur within a well-defined interval of values of the modulation phase, i.e., there is a "safe" window of phases where no RWs occur. The most extreme RWs occur for modulation phases that are at the boundary of the safe window. When the modulation is fast (fmod > fro), there is no safe phase window; however, the RWs are likely to occur at particular values of the modulation phase. Our findings are of interest for the study of RWs in other systems, where a similar response to external forcing could be observed, and we hope that they will motivate experimental investigations to further elucidate the role of the modulation phase in the likelihood of the occurrence of RWs.
Zhong, Wei-Ping; Belić, Milivoj; Zhang, Yiqi
2015-02-09
Nonlinear Schrödinger equation with simple quadratic potential modulated by a spatially-varying diffraction coefficient is investigated theoretically. Second-order rogue wave breather solutions of the model are constructed by using the similarity transformation. A modal quantum number is introduced, useful for classifying and controlling the solutions. From the solutions obtained, the behavior of second order Kuznetsov-Ma breathers (KMBs), Akhmediev breathers (ABs), and Peregrine solitons is analyzed in particular, by selecting different modulation frequencies and quantum modal parameter. We show how to generate interesting second order breathers and related hybrid rogue waves. The emergence of true rogue waves - single giant waves that are generated in the interaction of KMBs, ABs, and Peregrine solitons - is explicitly displayed in our analytical solutions.
NASA Astrophysics Data System (ADS)
Yu, Dang-Jun; Zhang, Jie-Fang
2016-10-01
Based on the modified Darboux transformation method, starting from zero solution and the plane wave solution, the hierarchies of rational solutions and breather solutions with "high frequency" and "low frequency" of the coupled nonlinear Schrödinger equation in parity-time symmetric nonlinear couplers with gain and loss are constructed, respectively. From these results, some basic characteristics of multi-rogue waves and multi-breathers are studied. Based on the property of rogue wave as the "quantum" of pattern structure in rogue wave hierarchy, we further study the novel structures of the superposed Akhmediev breathers, Kuznetsov-Ma solitons and their combined structures. It is expected that these results may give new insight into the context of the optical communications and Bose-Einstein condensations.
NASA Astrophysics Data System (ADS)
Wen, Xiao-Yong; Yan, Zhenya
2016-11-01
The novel generalized perturbation (n, M)-fold Darboux transformations (DTs) are reported for the (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation and its extension by using the Taylor expansion of the Darboux matrix. The generalized perturbation (1, N-1)-fold DTs are used to find their higher-order rational solitons and rogue wave solutions in terms of determinants. The dynamics behaviors of these rogue waves are discussed in detail for different parameters and time, which display the interesting RW and soliton structures including the triangle, pentagon, heptagon profiles, etc. Moreover, we find that a new phenomenon that the parameter (a) can control the wave structures of the KP equation from the higher-order rogue waves (a>0 or a<0) into higher-order rational solitons (a = 0) in (x, t)-space with y=const. These results may predict the corresponding dynamical phenomena in the models of fluid mechanics and other physically relevant systems.
Wen, Xiao-Yong; Yan, Zhenya; Malomed, Boris A
2016-12-01
An integrable system of two-component nonlinear Ablowitz-Ladik equations is used to construct complex rogue-wave (RW) solutions in an explicit form. First, the modulational instability of continuous waves is studied in the system. Then, new higher-order discrete two-component RW solutions of the system are found by means of a newly derived discrete version of a generalized Darboux transformation. Finally, the perturbed evolution of these RW states is explored in terms of systematic simulations, which demonstrates that tightly and loosely bound RWs are, respectively, nearly stable and strongly unstable solutions.
NASA Astrophysics Data System (ADS)
Wen, Xiao-Yong; Yan, Zhenya; Malomed, Boris A.
2016-12-01
An integrable system of two-component nonlinear Ablowitz-Ladik equations is used to construct complex rogue-wave (RW) solutions in an explicit form. First, the modulational instability of continuous waves is studied in the system. Then, new higher-order discrete two-component RW solutions of the system are found by means of a newly derived discrete version of a generalized Darboux transformation. Finally, the perturbed evolution of these RW states is explored in terms of systematic simulations, which demonstrates that tightly and loosely bound RWs are, respectively, nearly stable and strongly unstable solutions.
Guo, Shimin; Mei, Liquan; Sun, Anbang
2013-05-15
The nonlinear propagation of planar and nonplanar (cylindrical and spherical) ion-acoustic waves in an unmagnetized electron–positron–ion–dust plasma with two-electron temperature distributions is investigated in the context of the nonextensive statistics. Using the reductive perturbation method, a modified nonlinear Schrödinger equation is derived for the potential wave amplitude. The effects of plasma parameters on the modulational instability of ion-acoustic waves are discussed in detail for planar as well as for cylindrical and spherical geometries. In addition, for the planar case, we analyze how the plasma parameters influence the nonlinear structures of the first- and second-order ion-acoustic rogue waves within the modulational instability region. The present results may be helpful in providing a good fit between the theoretical analysis and real applications in future spatial observations and laboratory plasma experiments. -- Highlights: ► Modulational instability of ion-acoustic waves in a new plasma model is discussed. ► Tsallis’s statistics is considered in the model. ► The second-order ion-acoustic rogue wave is studied for the first time.
Rogue waves driven by polarization instabilities in a long ring fiber oscillator
NASA Astrophysics Data System (ADS)
Kolpakov, S. A.; Kbashi, Hani; Sergeyev, Sergey
2017-05-01
We present an experimental and theoretical results of a study of a complex nonlinear polarization dynamics in a passively self-mode-locked erbium-doped fiber oscillator implemented in a ring configuration and operating near lasing threshold. The theoretical model consists of seven coupled non-linear equations and takes into account both orthogonal states of polarizations in the fiber. The experiment confirmed the existence of seven eigenfrequencies, predicted by the model due to polarization instability near lasing threshold. By adjusting the state of polarization of the pump and in-cavity birefringence we changed some eigenfrequencies from being different (non-degenerate state) to matching (degenerate state). The non-degenerate states of oscillator lead to the L-shaped probability distribution function and true rogue wave regime with a positive dominant Lyapunov exponent value between 1.4 and 2.6. Small detuning from partially degenerate case also leads to L-shaped probability distribution function with the tail trespassing eight standard deviations threshold, giving periodic patterns of pulses along with positive dominant Lyapunov exponent of a filtered signal between 0.6 and 3.2. The partial degeneration, in turn, guides to quasi-symmetric distribution and the value of dominant Lyapunov exponent of 42 which is a typical value for systems with a source of the strongly nonhomogeneous external noise.
Predictability of rogue events.
Birkholz, Simon; Brée, Carsten; Demircan, Ayhan; Steinmeyer, Günter
2015-05-29
Using experimental data from three different rogue wave supporting systems, determinism, and predictability of the underlying dynamics are evaluated with methods of nonlinear time series analysis. We included original records from the Draupner platform in the North Sea as well as time series from two optical systems in our analysis. One of the latter was measured in the infrared tail of optical fiber supercontinua, the other in the fluence profiles of multifilaments. All three data sets exhibit extreme-value statistics and exceed the significant wave height in the respective system by a factor larger than 2. Nonlinear time series analysis indicates a different degree of determinism in the systems. The optical fiber scenario is found to be driven by quantum noise whereas rogue waves emerge as a consequence of turbulence in the others. With the large number of rogue events observed in the multifilament system, we can systematically explore the predictability of such events in a turbulent system. We observe that rogue events do not necessarily appear without a warning, but are often preceded by a short phase of relative order. This surprising finding sheds some new light on the fascinating phenomenon of rogue waves.
NASA Astrophysics Data System (ADS)
Saini, N. S.; Kaur, Barjinder; Singh, Manpreet; Bains, A. S.
2017-07-01
A theoretical investigation is carried out to study small amplitude dust kinetic Alfvén solitary waves (DKASWs) and rogue waves in a low-β, electron depleted plasma consisting of negatively charged dust grains and two temperature ions which are modelled by q-nonextensive distribution. A nonlinear Korteweg-de Vries equation, which governs the evolution of DKASWs, has been derived using the reductive perturbation method. Combined effects of the nonextensivity of ions, plasma beta, temperature ratio of low and high temperature ions, concentration of ions as well as dust, and angle of propagation (θ) have been studied in detail on the propagation properties of DKASWs. Only negative potential Alfvénic solitary waves are observed in the present study. Further, the study is extended for dust kinetic Alfvén rogue wave (DKARW) solutions. The properties of DKARWs, influenced by plasma parameters in question, are discussed in detail. The findings of this study may be useful to understand the formation of nonlinear coherent structures in Saturn's F-ring.
Driben, Rodislav; Babushkin, Ihar
2012-12-15
Soliton fusion is a fascinating and delicate phenomenon that manifests itself in optical fibers in case of interaction between copropagating solitons with small temporal and wavelength separation. We show that the mechanism of acceleration of a trailing soliton by dispersive waves radiated from the preceding one provides necessary conditions for soliton fusion at the advanced stage of supercontinuum generation in photonic-crystal fibers. As a result of fusion, large-intensity robust light structures arise and propagate over significant distances. In the presence of small random noise the delicate condition for the effective fusion between solitons can easily be broken, making the fusion-induced giant waves a rare statistical event. Thus oblong-shaped giant accelerated waves become excellent candidates for optical rogue waves.
Guo, Shimin Mei, Liquan
2014-08-15
Dust-ion-acoustic (DIA) rogue waves are investigated in a three-dimensional magnetized plasma containing nonthermal electrons featuring Tsallis distribution, both positive and negative ions, and immobile dust grains having both positive and negative charges. Via the reductive perturbation method, a (3 + 1)-dimensional nonlinear Schrödinger (NLS) equation is derived to govern the dynamics of the DIA wave packets. The modulation instability of DIA waves described by the (3 + 1)-dimensional NLS equation is investigated. By means of the similarity transformation and symbolic computation, both the first- and second-order rogue wave solutions of the (3 + 1)-dimensional NLS equation are constructed in terms of rational functions. Moreover, the dynamics properties and the effects of plasma parameters on the nonlinear structures of rogue waves are discussed in detail. The results could be useful for understanding the physical mechanism of rogue waves in laboratory experiments where pair-ion plasmas with electrons and dust grains can be found.
Kedziora, David J; Ankiewicz, Adrian; Akhmediev, Nail
2012-06-01
We present an explicit analytic form for the two-breather solution of the nonlinear Schrödinger equation with imaginary eigenvalues. It describes various nonlinear combinations of Akhmediev breathers and Kuznetsov-Ma solitons. The degenerate case, when the two eigenvalues coincide, is quite involved. The standard inverse scattering technique does not generally provide an answer to this scenario. We show here that the solution can still be found as a special limit of the general second-order expression and appears as a mixture of polynomials with trigonometric and hyperbolic functions. A further restriction of this particular case, where the two eigenvalues are equal to i, produces the second-order rogue wave with two free parameters considered as differential shifts. The illustrations reveal a precarious dependence of wave profile on the degenerate eigenvalues and differential shifts. Thus we establish a hierarchy of second-order solutions, revealing the interrelated nature of the general case, the rogue wave, and the degenerate breathers.
NASA Astrophysics Data System (ADS)
Du, Zhong; Tian, Bo; Wu, Xiao-Yu; Liu, Lei; Sun, Yan
2017-07-01
Subpicosecond or femtosecond optical pulse propagation in the inhomogeneous fiber can be described by a higher-order nonlinear Schrödinger equation with variable coefficients, which is investigated in the paper. Via the Ablowitz-Kaup-Newell-Segur system and symbolic computation, the Lax pair and infinitely-many conservation laws are deduced. Based on the Lax pair and a modified Darboux transformation technique, the first- and second-order rogue wave solutions are constructed. Effects of the groupvelocity dispersion and third-order dispersion on the properties of the first- and second-order rouge waves are graphically presented and analyzed: The groupvelocity dispersion and third-order dispersion both affect the ranges and shapes of the first- and second-order rogue waves: The third-order dispersion can produce a skew angle of the first-order rogue wave and the skew angle rotates counterclockwise with the increase of the groupvelocity dispersion, when the groupvelocity dispersion and third-order dispersion are chosen as the constants; When the groupvelocity dispersion and third-order dispersion are taken as the functions of the propagation distance, the linear, X-shaped and parabolic trajectories of the rogue waves are obtained.
Noninvasive measurement of viscosity from damping of capillary waves.
Behroozi, F; Lambert, B; Buhrow, B
2003-01-01
Capillary waves are surface waves on fluids with wavelengths in the millimeter range. The determination of viscosity from the damping of capillary waves is of great practical importance as it affords the possibility of measuring the viscosity of fluids noninvasively. In this paper a noncontact method for generation and detection of capillary waves on fluid is described. A miniature laser interferometer is employed to measure noninvasively the wave amplitude and its attenuation with a resolution of about 10 nm. As a test case, the attenuation data for capillary waves on pure water are used to obtain the kinematic viscosity of water as a function of temperature. The results compare favorably with the most reliable published data on the subject.
NASA Astrophysics Data System (ADS)
Jia, Shu-Liang; Gao, Yi-Tian; Zhao, Chen; Lan, Zhong-Zhou; Feng, Yu-Jie
2017-01-01
Under investigation in this paper is a sixth-order variable-coefficient nonlinear Schrödinger equation in an ocean or optical fiber. Through the Darboux transformation (DT) and generalized DT, we obtain the multi-soliton solutions, breathers and rogue waves. Choosing different values of α( x), β( x), γ( x) and δ( x), which are the coefficients of the third-, fourth-, fifth- and sixth-order dispersions, respectively, we investigate their effects on those solutions, where x is the scaled propagation variable. When α( x), β( x), γ( x) and δ( x) are chosen as the linear, parabolic and periodic functions, we obtain the parabolic, cubic and quasi-periodic solitons, respectively. Head-on and overtaking interactions between the two solitons are presented, and the interactions are elastic. Besides, with certain values of the spectral parameter λ, a shock region between the two solitons appears, and the interaction is inelastic. Interactions between two kinds of the breathers are also studied, and we find that the interaction regions are similar to those of the second-order rogue waves. Rogue waves are split into some first-order rogue waves when α( x), β( x), γ( x) and δ( x) are the periodic or odd-numbered functions.
NASA Astrophysics Data System (ADS)
Chefranov, Sergey; Chefranov, Alexander
2016-04-01
Linear hydrodynamic stability theory for the Hagen-Poiseuille (HP) flow yields a conclusion of infinitely large threshold Reynolds number, Re, value. This contradiction to the observation data is bypassed using assumption of the HP flow instability having hard type and possible for sufficiently high-amplitude disturbances. HP flow disturbance evolution is considered by nonlinear hydrodynamic stability theory. Similar is the case of the plane Couette (PC) flow. For the plane Poiseuille (PP) flow, linear theory just quantitatively does not agree with experimental data defining the threshold Reynolds number Re= 5772 ( S. A. Orszag, 1971), more than five-fold exceeding however the value observed, Re=1080 (S. J. Davies, C. M. White, 1928). In the present work, we show that the linear stability theory conclusions for the HP and PC on stability for any Reynolds number and evidently too high threshold Reynolds number estimate for the PP flow are related with the traditional use of the disturbance representation assuming the possibility of separation of the longitudinal (along the flow direction) variable from the other spatial variables. We show that if to refuse from this traditional form, conclusions on the linear instability for the HP and PC flows may be obtained for finite Reynolds numbers (for the HP flow, for Re>704, and for the PC flow, for Re>139). Also, we fit the linear stability theory conclusion on the PP flow to the experimental data by getting an estimate of the minimal threshold Reynolds number as Re=1040. We also get agreement of the minimal threshold Reynolds number estimate for PC with the experimental data of S. Bottin, et.al., 1997, where the laminar PC flow stability threshold is Re = 150. Rogue waves excitation mechanism in oppositely directed currents due to the PC flow linear instability is discussed. Results of the new linear hydrodynamic stability theory for the HP, PP, and PC flows are published in the following papers: 1. S.G. Chefranov, A
Yang, Yunqing; Yan, Zhenya; Malomed, Boris A
2015-10-01
We analytically study rogue-wave (RW) solutions and rational solitons of an integrable fifth-order nonlinear Schrödinger (FONLS) equation with three free parameters. It includes, as particular cases, the usual NLS, Hirota, and Lakshmanan-Porsezian-Daniel equations. We present continuous-wave (CW) solutions and conditions for their modulation instability in the framework of this model. Applying the Darboux transformation to the CW input, novel first- and second-order RW solutions of the FONLS equation are analytically found. In particular, trajectories of motion of peaks and depressions of profiles of the first- and second-order RWs are produced by means of analytical and numerical methods. The solutions also include newly found rational and W-shaped one- and two-soliton modes. The results predict the corresponding dynamical phenomena in extended models of nonlinear fiber optics and other physically relevant integrable systems.
Dam break problem for the focusing nonlinear Schrödinger equation and the generation of rogue waves
NASA Astrophysics Data System (ADS)
El, G. A.; Khamis, E. G.; Tovbis, A.
2016-09-01
We propose a novel, analytically tractable, scenario of the rogue wave formation in the framework of the small-dispersion focusing nonlinear Schrödinger (NLS) equation with the initial condition in the form of a rectangular barrier (a ‘box’). We use the Whitham modulation theory combined with the nonlinear steepest descent for the semi-classical inverse scattering transform, to describe the evolution and interaction of two counter-propagating nonlinear wave trains—the dispersive dam break flows—generated in the NLS box problem. We show that the interaction dynamics results in the emergence of modulated large-amplitude quasi-periodic breather lattices whose amplitude profiles are closely approximated by the Akhmediev and Peregrine breathers within certain space-time domain. Our semi-classical analytical results are shown to be in excellent agreement with the results of direct numerical simulations of the small-dispersion focusing NLS equation.
Numerical simulation of the resonantly excited capillary-gravity waves
NASA Astrophysics Data System (ADS)
Hanazaki, Hideshi; Hirata, Motonori; Okino, Shinya
2015-11-01
Capillary gravity waves excited by an obstacle are investigated by a direct numerical simulation. In the flow without capillary effects, it is well known that large-amplitude upstream advancing solitary waves are generated periodically under the resonant condition, i.e., when the phase velocity of the long surface waves and the mean flow velocity agrees. With capillary effects, solutions of the Euler equations show the generation of very short waves further upstream of the solitary waves and also in the depression region downstream of the obstacle. The overall characteristics of these waves agree with the solutions of the forced fifth-order KdV equation, while the weakly nonlinear theory generally overestimates the wavelength of the short waves.
Microscale capillary wave turbulence excited by high frequency vibration.
Blamey, Jeremy; Yeo, Leslie Y; Friend, James R
2013-03-19
Low frequency (O(10 Hz-10 kHz)) vibration excitation of capillary waves has been extensively studied for nearly two centuries. Such waves appear at the excitation frequency or at rational multiples of the excitation frequency through nonlinear coupling as a result of the finite displacement of the wave, most often at one-half the excitation frequency in so-called Faraday waves and twice this frequency in superharmonic waves. Less understood, however, are the dynamics of capillary waves driven by high-frequency vibration (>O(100 kHz)) and small interface length scales, an arrangement ideal for a broad variety of applications, from nebulizers for pulmonary drug delivery to complex nanoparticle synthesis. In the few studies conducted to date, a marked departure from the predictions of classical Faraday wave theory has been shown, with the appearance of broadband capillary wave generation from 100 Hz to the excitation frequency and beyond, without a clear explanation. We show that weak wave turbulence is the dominant mechanism in the behavior of the system, as evident from wave height frequency spectra that closely follow the Rayleigh-Jeans spectral response η ≈ ω(-17/12) as a consequence of a period-halving, weakly turbulent cascade that appears within a 1 mm water drop whether driven by thickness-mode or surface acoustic Rayleigh wave excitation. However, such a cascade is one-way, from low to high frequencies. The mechanism of exciting the cascade with high-frequency acoustic waves is an acoustic streaming-driven turbulent jet in the fluid bulk, driving the fundamental capillary wave resonance through the well-known coupling between bulk flow and surface waves. Unlike capillary waves, turbulent acoustic streaming can exhibit subharmonic cascades from high to low frequencies; here it appears from the excitation frequency all the way to the fundamental modes of the capillary wave at some four orders of magnitude in frequency less than the excitation frequency
A Simple Theory of Capillary-Gravity Wave Turbulence
NASA Technical Reports Server (NTRS)
Glazman, Roman E.
1995-01-01
Employing a recently proposed 'multi-wave interaction' theory, inertial spectra of capillary gravity waves are derived. This case is characterized by a rather high degree of nonlinearity and a complicated dispersion law. The absence of scale invariance makes this and some other problems of wave turbulence (e.g., nonlinear inertia gravity waves) intractable by small-perturbation techniques, even in the weak-turbulence limit. The analytical solution obtained in the present work for an arbitrary degree of nonlinearity is shown to be in reasonable agreement with experimental data. The theory explains the dependence of the wave spectrum on wind input and describes the accelerated roll-off of the spectral density function in the narrow sub-range separating scale-invariant regimes of purely gravity and capillary waves, while the appropriate (long- and short-wave) limits yield power laws corresponding to the Zakharov-Filonenko and Phillips spectra.
Nonlocal resonances in weak turbulence of gravity-capillary waves.
Aubourg, Quentin; Mordant, Nicolas
2015-04-10
We report a laboratory investigation of weak turbulence of water surface waves in the gravity-capillary crossover. By using time-space-resolved profilometry and a bicoherence analysis, we observe that the nonlinear processes involve three-wave resonant interactions. By studying the solutions of the resonance conditions, we show that the nonlinear interaction is dominantly one dimensional and involves collinear wave vectors. Furthermore, taking into account the spectral widening due to weak nonlinearity explains why nonlocal interactions are possible between a gravity wave and high-frequency capillary ones. We observe also that nonlinear three-wave coupling is possible among gravity waves, and we raise the question of the relevance of this mechanism for oceanic waves.
NASA Astrophysics Data System (ADS)
Zhang, Hai-Qiang; Chen, Jian
2016-04-01
In this paper, we study a higher-order variable coefficient nonlinear Schrödinger (NLS) equation, which plays an important role in the control of the ultrashort optical pulse propagation in nonlinear optical systems. Then, we construct a generalized Darboux transformation (GDT) for the higher-order variable coefficient NLS equation. The Nth order rogue wave solution is obtained by the iterative rule and it can be expressed by the determinant form. As application, we calculate rogue waves (RWs) from first- to fourth-order in accordance with different kinds of parameters. In particular, the dynamical properties and spatial-temporal structures of RWs are discussed and compared with Hirota equation through some figures.
Nonlinear dynamics of short traveling capillary-gravity waves.
Borzi, C H; Kraenkel, R A; Manna, M A; Pereira, A
2005-02-01
We establish a Green-Nagdhi model equation for capillary-gravity waves in (2+1) dimensions. Through the derivation of an asymptotic equation governing short-wave dynamics, we show that this system possesses (1+1) traveling-wave solutions for almost all the values of the Bond number theta (the special case theta=1/3 is not studied). These waves become singular when their amplitude is larger than a threshold value, related to the velocity of the wave. The limit angle at the crest is then calculated. The stability of a wave train is also studied via a Benjamin-Feir modulational analysis.
Priya, N Vishnu; Senthilvelan, M; Lakshmanan, M
2014-06-01
We construct dark-dark soliton, general breather (GB), Akhmediev breather (AB), Ma soliton (MS), and rogue wave (RW) solutions of a coupled generalized nonlinear Schrödinger (CGNLS) equation. While dark-dark solitons are captured in the defocusing regime of the CGNLS system, the other solutions, namely, GB, AB, MS, and RW, are identified in the focusing regime. We also analyze the structures of GB, AB, MS, and RW profiles with respect to the four-wave mixing parameter. We show that when we increase the value of the real part of the four-wave mixing parameter, the number of peaks in the breather profile increases and the width of each peak shrinks. Interestingly, the direction of this profile also changes due to this change. As far as the RW profile is concerned the width of the peak becomes very thin when we increase the value of this parameter. Further, we consider the RW solution as the starting point, derive AB, MS, and GB in the reverse direction, and show that the solutions obtained in both directions match each other. In the course of the reverse analysis we also demonstrate how to capture the RW solutions directly from AB and MS.
Dynamics of the higher-order rogue waves for a generalized mixed nonlinear Schrödinger model
NASA Astrophysics Data System (ADS)
Wang, Lei; Jiang, Dong-Yang; Qi, Feng-Hua; Shi, Yu-Ying; Zhao, Yin-Chuan
2017-01-01
Under investigation in this paper is a generalized mixed nonlinear Schrödinger equation (GMNLSE) which arises in several physical areas including the quantum field theory, weakly nonlinear dispersive water waves, and nonlinear optics. The linear stability analysis is performed and the instability zones as well as the modulational instability gain are obtained and discussed. Higher-order rogue waves (RWs) in terms of the determinants for the GMNLSE model are constructed by the N-fold Darboux transformation. Several patterns of the RWs are illustrated, such as the fundamental pattern, triangular pattern, circular pattern, pentagon pattern, circular-triangular pattern, and circular-fundamental pattern. Effects of the nonlinear parameters on the RWs are discussed. It is found that the nonlinear terms affect the widths and velocities of the RWs, although the amplitudes of these waves remain unchanged. The semirational RW solution, which is a combination of rational and exponential functions, is derived to describe the interaction between the RW and multi-breather.
El-Tantawy, S. A.; Moslem, W. M.
2014-05-15
Solitons (small-amplitude long-lived waves) collision and rogue waves (large-amplitude short-lived waves) in non-Maxwellian electron-positron-ion plasma have been investigated. For the solitons collision, the extended Poincaré-Lighthill-Kuo perturbation method is used to derive the coupled Korteweg-de Vries (KdV) equations with the quadratic nonlinearities and their corresponding phase shifts. The calculations reveal that both positive and negative polarity solitons can propagate in the present model. At critical value of plasma parameters, the coefficients of the quadratic nonlinearities disappear. Therefore, the coupled modified KdV (mKdV) equations with cubic nonlinearities and their corresponding phase shifts have been derived. The effects of the electron-to-positron temperature ratio, the ion-to-electron temperature ratio, the positron-to-ion concentration, and the nonextensive parameter on the colliding solitons profiles and their corresponding phase shifts are examined. Moreover, generation of ion-acoustic rogue waves from small-amplitude initial perturbations in plasmas is studied in the framework of the mKdV equation. The properties of the ion-acoustic rogue waves are examined within a nonlinear Schrödinger equation (NLSE) that has been derived from the mKdV equation. The dependence of the rogue wave profile on the relevant physical parameters has been investigated. Furthermore, it is found that the NLSE that has been derived from the KdV equation cannot support the propagation of rogue waves.
A Simple Theory of Capillary-Gravity Wave Turbulence
NASA Technical Reports Server (NTRS)
Glazman, Roman E.
1993-01-01
Employing a recently proposed 'multi-wave interaction' theory [JFM, 243, 623-625], spectra of capillary-gravity waves are derived. This case is characterized by a rather high degree of nonlinearity and a complicated dispersion law. The resultant absence of scale invariance makes this and some other problems of wave turbulence (e.g., nonlinear Rossby waves) intractable by small-perturbation techniques, even in the weak turbulence limit. The analytical solution obtained in the present work is shown to be in good agreement with experimental data. Its low- and high-frequency limits yield power-laws characterizing spectra of purely gravity and capillary waves, respectively. In the limits of weak and strong linearity, these reduce of the Zakharov-Filonenko and Phillips spectra, respectively.
Resonant Interactions of Capillary-Gravity Water Waves
NASA Astrophysics Data System (ADS)
Martin, Calin Iulian
2016-11-01
We show here that capillary-gravity wave trains can propagate at the free surface of a rotational water flow of constant non-zero vorticity over a flat bed only if the flow is two-dimensional. Moreover, we also show that the vorticity must have only one non zero component which points in the horizontal direction orthogonal to the direction of wave propagation. This result is of relevance in the study of nonlinear resonances of wave trains. We perform such a study for three- and four wave interactions.
Observation of Thermal Equilibrium in Capillary Wave Turbulence.
Michel, Guillaume; Pétrélis, François; Fauve, Stéphan
2017-04-07
We investigate capillary wave turbulence at scales larger than the forcing one. At such scales, our measurements show that the surface waves dynamics is the one of a thermal equilibrium state in which the effective temperature is related to the injected power. We characterize this evolution with a scaling law and report the statistical properties of the large-scale surface elevation depending on this effective temperature.
On the evolution of a rogue wave along the orthogonal direction of the (t, x)-plane
NASA Astrophysics Data System (ADS)
Yuan, Feng; Qiu, Deqin; Liu, Wei; Porsezian, K.; He, Jingsong
2017-03-01
The localization characters of the first-order rogue wave (RW) solution u of the Kundu-Eckhaus equation is studied in this paper. We discover a full process of the evolution for the contour line with height c2 + d along the orthogonal direction of the (t, x)-plane for a first-order RW |u|2: A point at height 9c2 generates a convex curve for 3c2 ≤ d < 8c2, whereas it becomes a concave curve for 0 < d < 3c2, next it reduces to a hyperbola on asymptotic plane (i.e. equivalently d = 0), and the two branches of the hyperbola become two separate convex curves when -c2 < d < 0 , and finally they reduce to two separate points at d = -c2 . Using the contour line method, the length, width, and area of the RW at height c2 + d(0 < d < 8c2) , i.e. above the asymptotic plane, are defined. We study the evolutions of three above-mentioned localization characters on d through analytical and visual methods. The phase difference between the Kundu-Eckhaus and the nonlinear Schrodinger equation is also given by an explicit formula.
Steep gravity-capillary waves within the internal resonance regime
NASA Astrophysics Data System (ADS)
Perlin, Marc; Ting, Chao-lung
1992-11-01
Steep gravity-capillary waves are studied experimentally in a channel. The range of cyclic frequencies investigated is 6.94-9.80 Hz; namely, the high-frequency portion of the regime of internal resonances according to the weakly nonlinear theory (Wilton's ripples). These wave trains are stable according to the nonlinear Schrödinger equation. The experimental wave trains are generated by large, sinusoidal oscillations of the wavemaker. A comparison is made between the measured wave fields and the (symmetric) numerical solutions of Schwartz and Vanden-Broeck [J. Fluid Mech. 95, 119 (1979)], Chen and Saffman [Stud. Appl. Math. 60, 183 (1979); 62, 95 (1980)], and Huh (Ph.D. dissertation, University of Michigan, 1991). The waves are shown to be of slightly varying asymmetry as they propagate downstream. Their symmetric parts, isolated by determining the phase which provides the smallest mean-square antisymmetric part, compare favorably with the ``gravity-type'' wave solutions determined by numerical computations. The antisymmetric part of the wave profile is always less than 30% of the peak-to-peak height of the symmetric part. As nonlinearity is increased, the amplitudes of the short-wave undulations in the trough of the primary wave increase; however, there are no significant changes in these short-wave frequencies. The lowest frequency primary-wave experiments, which generate the highest frequency short-wave undulations, exhibit more rapid viscous decay of these high-frequency waves than do the higher-frequency primary wave experiments.
NASA Astrophysics Data System (ADS)
Zhang, Guoqiang; Yan, Zhenya; Wen, Xiao-Yong
2017-07-01
The integrable coupled nonlinear Schrödinger equations with four-wave mixing are investigated. We first explore the conditions for modulational instability of continuous waves of this system. Secondly, based on the generalized N-fold Darboux transformation (DT), beak-shaped higher-order rogue waves (RWs) and beak-shaped higher-order rogue wave pairs are derived for the coupled model with attractive interaction in terms of simple determinants. Moreover, we derive the simple multi-dark-dark and kink-shaped multi-dark-dark solitons for the coupled model with repulsive interaction through the generalizing DT. We explore their dynamics and classifications by different kinds of spatial-temporal distribution structures including triangular, pentagonal, `claw-like' and heptagonal patterns. Finally, we perform the numerical simulations to predict that some dark solitons and RWs are stable enough to develop within a short time. The results would enrich our understanding on nonlinear excitations in many coupled nonlinear wave systems with transition coupling effects.
Zhang, Guoqiang; Yan, Zhenya; Wen, Xiao-Yong
2017-07-01
The integrable coupled nonlinear Schrödinger equations with four-wave mixing are investigated. We first explore the conditions for modulational instability of continuous waves of this system. Secondly, based on the generalized N-fold Darboux transformation (DT), beak-shaped higher-order rogue waves (RWs) and beak-shaped higher-order rogue wave pairs are derived for the coupled model with attractive interaction in terms of simple determinants. Moreover, we derive the simple multi-dark-dark and kink-shaped multi-dark-dark solitons for the coupled model with repulsive interaction through the generalizing DT. We explore their dynamics and classifications by different kinds of spatial-temporal distribution structures including triangular, pentagonal, 'claw-like' and heptagonal patterns. Finally, we perform the numerical simulations to predict that some dark solitons and RWs are stable enough to develop within a short time. The results would enrich our understanding on nonlinear excitations in many coupled nonlinear wave systems with transition coupling effects.
Capillary-gravity waves generated by a slow moving object.
Chepelianskii, A D; Chevy, F; Raphaël, E
2008-02-22
We investigate theoretically and experimentally the capillary-gravity waves created by a small object moving steadily at the water-air interface along a circular trajectory. It is well established that, for straight uniform motion, no steady waves appear at velocities below the minimum phase velocity c(min)=23 cm s(-1). We demonstrate that no such velocity threshold exists for a steady circular motion, for which, even for small velocities, a finite wave drag is experienced by the object. This wave drag originates from the emission of a spiral-like wave pattern. Our results are in good agreement with direct experimental observations of the wave pattern created by a circularly moving needle in contact with water. Our study leads to new insights into the problem of animal locomotion at the water-air interface.
Stability of steep gravity capillary solitary waves in deep water
NASA Astrophysics Data System (ADS)
Calvo, David C.; Akylas, T. R.
2002-02-01
The stability of steep gravity capillary solitary waves in deep water is numerically investigated using the full nonlinear water-wave equations with surface tension. Out of the two solution branches that bifurcate at the minimum gravity capillary phase speed, solitary waves of depression are found to be stable both in the small-amplitude limit when they are in the form of wavepackets and at finite steepness when they consist of a single trough, consistent with observations. The elevation-wave solution branch, on the other hand, is unstable close to the bifurcation point but becomes stable at finite steepness as a limit point is passed and the wave profile features two well-separated troughs. Motivated by the experiments of Longuet-Higgins & Zhang (1997), we also consider the forced problem of a localized pressure distribution applied to the free surface of a stream with speed below the minimum gravity capillary phase speed. We find that the finite-amplitude forced solitary-wave solution branch computed by Vanden-Broeck & Dias (1992) is unstable but the branch corresponding to Rayleigh’s linearized solution is stable, in agreement also with a weakly nonlinear analysis based on a forced nonlinear Schrödinger equation. The significance of viscous effects is assessed using the approach proposed by Longuet-Higgins (1997): while for free elevation waves the instability predicted on the basis of potential-flow theory is relatively weak compared with viscous damping, the opposite turns out to be the case in the forced problem when the forcing is strong. In this régime, which is relevant to the experiments of Longuet-Higgins & Zhang (1997), the effects of instability can easily dominate viscous effects, and the results of the stability analysis are used to propose a theoretical explanation for the persistent unsteadiness of the forced wave profiles observed in the experiments.
NASA Astrophysics Data System (ADS)
Konno, Hidetoshi
2017-06-01
The paper presents the birth-death stochastic process of an optical rogue wave with a long memory described by a fractional master equation. An exact analytic expression for the probability generating function is obtained with an integral representation of the confluent Heun function. This enables a full statistical analysis under any initial condition. It is demonstrated that the present mathematical approach can be utilized for the analysis of birth-death stochastic processes when the generating function can be described by a class of Heun differential equations.
Experimental investigation of three-wave interactions of capillary surface-waves
NASA Astrophysics Data System (ADS)
Berhanu, Michael; Cazaubiel, Annette; Deike, Luc; Jamin, Timothee; Falcon, Eric
2014-11-01
We report experiments studying the non-linear interaction between two crossing wave-trains of gravity-capillary surface waves generated in a closed laboratory tank. Using a capacitive wave gauge and Diffusive Light Photography method, we detect a third wave of smaller amplitude whose frequency and wavenumber are in agreement with the weakly non-linear triadic resonance interaction mechanism. By performing experiments in stationary and transient regimes and taking into account the viscous dissipation, we estimate directly the growth rate of the resonant mode in comparison with theory. These results confirm at least qualitatively and extend earlier experimental results obtained only for unidirectional wave train. Finally we discuss relevance of three-wave interaction mechanisms in recent experiment studying capillary wave turbulence.
Rogue events in the group velocity horizon.
Demircan, Ayhan; Amiranashvili, Shalva; Brée, Carsten; Mahnke, Christoph; Mitschke, Fedor; Steinmeyer, Günter
2012-01-01
The concept of rogue waves arises from a mysterious and potentially calamitous phenomenon of oceanic surfaces. There is mounting evidence that they are actually commonplace in a variety of different physical settings. A set of defining criteria has been advanced; this set is of great generality and therefore applicable to a wide class of systems. The question arises naturally whether there are generic mechanisms responsible for extreme events in different systems. Here we argue that under suitable circumstances nonlinear interaction between weak and strong waves results in intermittent giant waves with all the signatures of rogue waves. To obtain these circumstances only a few basic conditions must be met. Then reflection of waves at the so-called group-velocity horizon occurs. The connection between rogue waves and event horizons, seemingly unrelated physical phenomena, is identified as a feature common in many different physical systems.
Rogue events in the group velocity horizon
Demircan, Ayhan; Amiranashvili, Shalva; Brée, Carsten; Mahnke, Christoph; Mitschke, Fedor; Steinmeyer, Günter
2012-01-01
The concept of rogue waves arises from a mysterious and potentially calamitous phenomenon of oceanic surfaces. There is mounting evidence that they are actually commonplace in a variety of different physical settings. A set of defining criteria has been advanced; this set is of great generality and therefore applicable to a wide class of systems. The question arises naturally whether there are generic mechanisms responsible for extreme events in different systems. Here we argue that under suitable circumstances nonlinear interaction between weak and strong waves results in intermittent giant waves with all the signatures of rogue waves. To obtain these circumstances only a few basic conditions must be met. Then reflection of waves at the so-called group-velocity horizon occurs. The connection between rogue waves and event horizons, seemingly unrelated physical phenomena, is identified as a feature common in many different physical systems. PMID:23152941
NASA Astrophysics Data System (ADS)
Akhmediev, Nail; Ankiewicz, Adrian
2011-04-01
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.
Akhmediev, Nail; Ankiewicz, Adrian
2011-04-01
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.
Periodic optical rogue waves (PORWs) in parity-time (PT) symmetric Bragg-grating structure
NASA Astrophysics Data System (ADS)
Gupta, Samit Kumar; Sarma, Amarendra K.
2014-10-01
In this work, we present an analytical investigation of traveling wave solution in a nonlinear Bragg grating structure with the core of the optical fiber having PT-symmetric refractive index distribution. Under the approximation of weak-nonlinearity and above the PT-threshold region, the existence of highly intense, well-localized periodic train of pulses has been explored for the backward-propagating wave for some suitable choice of the parameter values of the system. The result of the present study might be useful in practical purpose in generating high-power, periodic optical pulses.
NASA Astrophysics Data System (ADS)
Okal, Emile; de Beer, Coenie; Visser, Johan; Kalligeris, Nikos
2013-04-01
In the early hours of Wednesday, 27 August 1969, the village of Dwarskersbos, Western Cape, South Africa, was inundated by a wave which flooded houses and damaged small boats. This small tsunami took place in the absence of any seismic source or extreme weather, and its origin has remained mysterious. In September 2010, we conducted a field survey based on the interview of nine elderly witnesses still living in the village, using techniques developed earlier for the study of the 1946 Aleutian and 1956 Greek tsunamis. We measured 13 locations, with run-up reaching 2.9 m for a maximum inundation of 260 m from the sea shore. The most remarkable aspect of our dataset is the extreme concentration of the flooding along a stretch of coastline of less than 2 km. In particular, the tsunami did not reach the communities located on the opposite side of St. Helena's Bay, nor did it affect Elands Bay and Lamberts Bay, respectively 43 and 68 km to the North. In order to investigate the possible origin of the Dwarskersbos tsunami, we first simulated an underwater landslide taking place in a canyon 20 km Northwest of Shelley Point, using the MOST code. This model predicts comparable amplitudes along most of the regional coastlines, and thus fails to explain the documented concentration at Dwarskersbos. By contrast, we explore a meteorological origin for the event by simulating the coupling between a possible squall (modeled as a steep pressure front) propagating over St. Helena's Bay and the oceanic column, using Proudman's [1953] original model, as applied by Platzman [1958] to the case of the 1954 Chicago rogue wave. We find that a front moving at 15 m/s in the azimuth N100E can resonate exclusively with the shallow bathymetry off Dwarskersbos, and thus explain most of the features revealed by our survey. This interpretation would be in contrast to the case of the tsunami of 21 August 2008, for which a comprehensive seriesof maregraphs along a 900-km stretch of coastline
Single-shot observation of optical rogue waves in integrable turbulence using time microscopy
NASA Astrophysics Data System (ADS)
Suret, Pierre; Koussaifi, Rebecca El; Tikan, Alexey; Evain, Clément; Randoux, Stéphane; Szwaj, Christophe; Bielawski, Serge
2016-10-01
Optical fibres are favourable tabletop laboratories to investigate both coherent and incoherent nonlinear waves. In particular, exact solutions of the one-dimensional nonlinear Schrödinger equation such as fundamental solitons or solitons on finite background can be generated by launching periodic, specifically designed coherent waves in optical fibres. It is an open fundamental question to know whether these coherent structures can emerge from the nonlinear propagation of random waves. However the typical sub-picosecond timescale prevented--up to now--time-resolved observations of the awaited dynamics. Here, we report temporal `snapshots' of random light using a specially designed `time-microscope'. Ultrafast structures having peak powers much larger than the average optical power are generated from the propagation of partially coherent waves in optical fibre and are recorded with 250 femtoseconds resolution. Our experiment demonstrates the central role played by `breather-like' structures such as the Peregrine soliton in the emergence of heavy-tailed statistics in integrable turbulence.
Single-shot observation of optical rogue waves in integrable turbulence using time microscopy
Suret, Pierre; Koussaifi, Rebecca El; Tikan, Alexey; Evain, Clément; Randoux, Stéphane; Szwaj, Christophe; Bielawski, Serge
2016-01-01
Optical fibres are favourable tabletop laboratories to investigate both coherent and incoherent nonlinear waves. In particular, exact solutions of the one-dimensional nonlinear Schrödinger equation such as fundamental solitons or solitons on finite background can be generated by launching periodic, specifically designed coherent waves in optical fibres. It is an open fundamental question to know whether these coherent structures can emerge from the nonlinear propagation of random waves. However the typical sub-picosecond timescale prevented—up to now—time-resolved observations of the awaited dynamics. Here, we report temporal ‘snapshots' of random light using a specially designed ‘time-microscope'. Ultrafast structures having peak powers much larger than the average optical power are generated from the propagation of partially coherent waves in optical fibre and are recorded with 250 femtoseconds resolution. Our experiment demonstrates the central role played by ‘breather-like' structures such as the Peregrine soliton in the emergence of heavy-tailed statistics in integrable turbulence. PMID:27713416
Single-shot observation of optical rogue waves in integrable turbulence using time microscopy.
Suret, Pierre; Koussaifi, Rebecca El; Tikan, Alexey; Evain, Clément; Randoux, Stéphane; Szwaj, Christophe; Bielawski, Serge
2016-10-07
Optical fibres are favourable tabletop laboratories to investigate both coherent and incoherent nonlinear waves. In particular, exact solutions of the one-dimensional nonlinear Schrödinger equation such as fundamental solitons or solitons on finite background can be generated by launching periodic, specifically designed coherent waves in optical fibres. It is an open fundamental question to know whether these coherent structures can emerge from the nonlinear propagation of random waves. However the typical sub-picosecond timescale prevented-up to now-time-resolved observations of the awaited dynamics. Here, we report temporal 'snapshots' of random light using a specially designed 'time-microscope'. Ultrafast structures having peak powers much larger than the average optical power are generated from the propagation of partially coherent waves in optical fibre and are recorded with 250 femtoseconds resolution. Our experiment demonstrates the central role played by 'breather-like' structures such as the Peregrine soliton in the emergence of heavy-tailed statistics in integrable turbulence.
Floquet analysis of Kuznetsov-Ma breathers: A path towards spectral stability of rogue waves
NASA Astrophysics Data System (ADS)
Cuevas-Maraver, J.; Kevrekidis, P. G.; Frantzeskakis, D. J.; Karachalios, N. I.; Haragus, M.; James, G.
2017-07-01
In the present work, we aim at taking a step towards the spectral stability analysis of Peregrine solitons, i.e., wave structures that are used to emulate extreme wave events. Given the space-time localized nature of Peregrine solitons, this is a priori a nontrivial task. Our main tool in this effort will be the study of the spectral stability of the periodic generalization of the Peregrine soliton in the evolution variable, namely the Kuznetsov-Ma breather. Given the periodic structure of the latter, we compute the corresponding Floquet multipliers, and examine them in the limit where the period of the orbit tends to infinity. This way, we extrapolate towards the stability of the limiting structure, namely the Peregrine soliton. We find that multiple unstable modes of the background are enhanced, yet no additional unstable eigenmodes arise as the Peregrine limit is approached. We explore the instability evolution also in direct numerical simulations.
Regularity for steady periodic capillary water waves with vorticity.
Henry, David
2012-04-13
In the following, we prove new regularity results for two-dimensional steady periodic capillary water waves with vorticity, in the absence of stagnation points. Firstly, we prove that if the vorticity function has a Hölder-continuous first derivative, then the free surface is a smooth curve and the streamlines beneath the surface will be real analytic. Furthermore, once we assume that the vorticity function is real analytic, it will follow that the wave surface profile is itself also analytic. A particular case of this result includes irrotational fluid flow where the vorticity is zero. The property of the streamlines being analytic allows us to gain physical insight into small-amplitude waves by justifying a power-series approach.
Liu, Meng; Cai, Ze-Rong; Hu, Song; Luo, Ai-Ping; Zhao, Chu-Jun; Zhang, Han; Xu, Wen-Cheng; Luo, Zhi-Chao
2015-10-15
We reported on the generation of dissipative rogue waves (DRWs) induced by long-range chaotic multi-pulse interactions in a fiber laser based on a topological insulator (TI)-deposited microfiber photonic device. By virtue of the simultaneous saturable absorption effect and high nonlinearity provided by the TI-deposited microfiber, a localized, chaotic multi-pulse wave packet with strong long-range nonlinear interactions could be obtained, which gives rise to the formation of DRWs. The results might enhance the understanding of DRWs in optical systems, and further demonstrated that the TI-deposited microfiber could be considered as an excellent photonic device with both saturable absorption and highly nonlinear effects for the application field of nonlinear optics.
Capillary-wave description of rapid directional solidification.
Korzhenevskii, Alexander L; Bausch, Richard; Schmitz, Rudi
2012-02-01
A recently introduced capillary-wave description of binary-alloy solidification is generalized to include the procedure of directional solidification. For a class of model systems a universal dispersion relation of the unstable eigenmodes of a planar steady-state solidification front is derived, which readjusts previously known stability considerations. We moreover establish a differential equation for oscillatory motions of a planar interface that offers a limit-cycle scenario for the formation of solute bands and, taking into account the Mullins-Sekerka instability, of banded structures.
Entanglement effects in capillary waves on liquid polymer films.
Jiang, Zhang; Mukhopadhyay, Mrinmay K; Song, Sanghoon; Narayanan, Suresh; Lurio, L B; Kim, Hyunjung; Sinha, Sunil K
2008-12-12
Overdamped surface capillary wave relaxations on molten polymer films were measured using x-ray photon correlation spectroscopy. We found a transition from a single through a stretched to another single exponential regime as the temperature is decreased from well above to near the bulk glass transition temperature. A universal scaling of the dynamics was discovered over a wide range of film thicknesses, temperatures, and molecular weights (except in the multiple relaxation regime). These observations are justified by hydrodynamic theory and the time-temperature superposition principle by considering an effective viscosity instead of the bulk zero shear viscosity.
Experimental study of three-wave interactions among capillary-gravity surface waves
NASA Astrophysics Data System (ADS)
Haudin, Florence; Cazaubiel, Annette; Deike, Luc; Jamin, Timothée; Falcon, Eric; Berhanu, Michael
2016-04-01
In propagating wave systems, three- or four-wave resonant interactions constitute a classical nonlinear mechanism exchanging energy between the different scales. Here we investigate three-wave interactions for gravity-capillary surface waves in a closed laboratory tank. We generate two crossing wave trains and we study their interaction. Using two optical methods, a local one (laser doppler vibrometry) and a spatiotemporal one (diffusive light photography), a third wave of smaller amplitude is detected, verifying the three-wave resonance conditions in frequency and in wave number. Furthermore, by focusing on the stationary regime and by taking into account viscous dissipation, we directly estimate the growth rate of the resonant mode. The latter is then compared to the predictions of the weakly nonlinear triadic resonance interaction theory. The obtained results confirm qualitatively and extend previous experimental results obtained only for collinear wave trains. Finally, we discuss the relevance of three-wave interaction mechanisms in recent experiments studying gravity-capillary turbulence.
Experimental study of three-wave interactions among capillary-gravity surface waves.
Haudin, Florence; Cazaubiel, Annette; Deike, Luc; Jamin, Timothée; Falcon, Eric; Berhanu, Michael
2016-04-01
In propagating wave systems, three- or four-wave resonant interactions constitute a classical nonlinear mechanism exchanging energy between the different scales. Here we investigate three-wave interactions for gravity-capillary surface waves in a closed laboratory tank. We generate two crossing wave trains and we study their interaction. Using two optical methods, a local one (laser doppler vibrometry) and a spatiotemporal one (diffusive light photography), a third wave of smaller amplitude is detected, verifying the three-wave resonance conditions in frequency and in wave number. Furthermore, by focusing on the stationary regime and by taking into account viscous dissipation, we directly estimate the growth rate of the resonant mode. The latter is then compared to the predictions of the weakly nonlinear triadic resonance interaction theory. The obtained results confirm qualitatively and extend previous experimental results obtained only for collinear wave trains. Finally, we discuss the relevance of three-wave interaction mechanisms in recent experiments studying gravity-capillary turbulence.
Wave drag due to generation of capillary-gravity surface waves
NASA Astrophysics Data System (ADS)
Burghelea, Teodor; Steinberg, Victor
2002-11-01
The onset of the wave resistance via the generation of capillary-gravity waves by a small object moving with a velocity V is investigated experimentally. Due to the existence of a minimum phase velocity Vc for surface waves, the problem is similar to the generation of rotons in superfluid helium near their minimum. In both cases, waves or rotons are produced at V>Vc due to Cherenkov radiation. We find that the transition to the wave drag state is continuous: in the vicinity of the bifurcation the wave resistance force is proportional to (V-Vc) for various fluids. This observation contradicts the theory of Raphaël and de Gennes. We also find that the reduced wave drag force for different fluids and different ball size may be scaled in such a way that all the data collapse on a single curve. The capillary-gravity wave pattern and the shape of the wave-generating region are investigated both experimentally and theoretically. Good agreement between the theory and the experimental data is found in this case.
Capillary Waves And Energy Coupling In Laser Materials Processing
NASA Astrophysics Data System (ADS)
Gasser, A.; Herziger, G.; Holtgen, B.; Kreutz, E. W.; Treusch, H. G.
1987-09-01
Static and dynamic measurements of the incident laser power, of the diffuse and specular reflected power have been performed in order to determine the absorption behavior of various metals and semiconductors during the interaction with powerful CO2-and Nd:YAG-laser-radiation. The absorptivity of the vapor and laser-induced plasma was probed by high-speed photography and measurements of conductivity transients as a function of intensity, composition, and pressure of the ambient atmosphere. For I
Rogue run-up events at the North Sea coast
NASA Astrophysics Data System (ADS)
Didenkulova, Ira; Blossier, Brice; Daly, Christopher; Herbst, Gabriel; Senichev, Dmitry; Winter, Christian
2015-04-01
On the 1st of January, 1995, the Statoil-operated "Draupner" platform located in the North Sea recorded the so-called "New Year wave". Since then, rogue waves have been the topic of active scientific discussions and investigations. Waves of extreme height appearing randomly at the sea surface have been measured in both deep and shallow waters and have been involved in a number of ship accidents. Nowadays rogue waves are frequently recorded all over the world with several different instruments (range finders installed on offshore platforms, deployed buoys, radars including SAR, etc.). Rogue wave also occur at the coast, where they appear as either sudden flooding of coastal areas or high splashes over steep banks or sea walls. These waves are especially dangerous for beach users and lead regularly to human injuries and fatalities. Despite numerous reports of human accidents, coastal rogue waves have not yet been recorded experimentally. In this paper we discuss the recording of rogue wave events at German North Sea coasts by using high-resolution beach cameras. The recorded rogue waves are observed during different tide levels and different weather conditions. Possible mechanisms of their generation are discussed.
Interaction of the Radar Waves with the Capillary Waves on the Ocean.
1983-05-01
capillary spectrum. 3. To determine empirically the variation of radar scattering coefficient from the sea over a wide range of angles of incidence...wave height. From the signal return and the instantaneous area of the observed spot, the scattering coefficient could be determined . The result of...so one can state pp/7 X o)I. _ 5 (6.15~b) where: A(u) is constant at a given windspeed 68 For determination of instantaneous scattering coefficient
Diffusing light photography of solitons and capillary-wave turbulence
Wright, W.; Budak, R.; Putterman, S. )
1994-11-01
The attenuation of light propagating through a slab of water (containing a dilute concentration of polyballs) is approximately proportional to its thickness. Application of this insight to the local elevation of a fluid surface has enabled us to use photography to determine the instantaneous global topography of the surface of a fluid in motion. Use of diffusing light enables us to obtain images that are free of the caustics which plague shadowgraphs. Applications include breather solitons and wave turbulence which results from the nonlinear interaction of a broadband spectrum of high amplitude surface ripples. Measurements indicate that as the amplitude of excitation of the surface of water is increased the wave number of the capillary motion displays a transition to a broadband spectrum. The temporal response of a single pixel yields the power spectrum of the surface height as a function of frequency [ital f].'' The numerous harmonics which can be seen at low amplitude merge at high amplitude into a broadband spectrum which goes as 1/[ital f][sup 3]. This technique should permit the measurement of turbulent parameters which go beyond the purported range of current theories. [Work supported by US DOE Division of Engineering and Geophysics and NASA Microgravity.
NASA Astrophysics Data System (ADS)
Ball, Philip
2015-07-01
Once thought to be the stuff of exaggeration by seafaring folk, we now know that giant “rogue” waves that soar to heights of up to 30 m really do occur at sea. But scientists can't yet agree on why they happen, as Philip Ball reports.
Energy flux measurement from the dissipated energy in capillary wave turbulence.
Deike, Luc; Berhanu, Michael; Falcon, Eric
2014-02-01
We study experimentally the influence of dissipation on stationary capillary wave turbulence on the surface of a liquid by changing its viscosity. We observe that the frequency power-law scaling of the capillary spectrum departs significantly from its theoretical value when the dissipation is increased. The energy dissipated by capillary waves is also measured and found to increase nonlinearly with the mean power injected within the liquid. Here we propose an experimental estimation of the energy flux at every scale of the capillary cascade. The latter is found to be nonconstant through the scales. For fluids of low enough viscosity, we found that both capillary spectrum scalings with the frequency and the newly defined mean energy flux are in good agreement with wave turbulence theory. The Kolmogorov-Zakharov constant is then experimentally estimated and compared to its theoretical value.
Surface-wave capillary plasmas in helium: modeling and experiment
NASA Astrophysics Data System (ADS)
Santos, M.; Alves, L. L.; Noel, C.; Belmonte, T.
2012-10-01
In this paper we use both simulations and experiments to study helium discharges (99.999% purity) sustained by surface-waves (2.45 GHz frequency), in capillary tubes (3 mm radius) at atmospheric pressure. Simulations use a self-consistent homogeneous and stationary collisional-radiative model that solves the rate balance equations for the different species present in the plasma (electrons, the He^+ and He2^+ ions, the He(n<7) excited states and the He2* excimers) and the gas thermal balance equation, coupled to the two-term electron Boltzmann equation (including direct and stepwise collisions as well as electron-electron collisions). Experiments use optical emission spectroscopy diagnostics to measure the electron density (Hβ Stark broadening), the gas temperature (ro-vibrational transitions of OH, present at trace concentrations), and the populations of different excited states. Model predictions at 1.7x10^13 cm-3 electron density (within the range estimated experimentally) are in good agreement with measurements (deviations < 10%) of (i) the excitation spectrum and the excitation temperatures (2795 ± 115 K, obtained from the Boltzmann-plot of the excited state populations, with energies lying between 22.7 and 24.2 eV), (ii) the power coupled to the plasma (˜ 180 ± 10 W), and (iii) the gas temperature (˜ 1700 ± 100 K). We discuss the extreme dependence of model results (particularly the gas temperature) on the power coupled to the plasma.
NASA Astrophysics Data System (ADS)
Anisimov, V. N.; Kozolupenko, A. P.; Sebrant, A. Yu
1988-12-01
An experimental investigation was made of the plasma transparency to heating radiation in capillaries when absorption waves propagated in these capillaries as a result of interaction with a CO2 laser pulse of 5-μs duration. When the length of the capillary was in excess of 20 mm, total absorption of the radiation by the plasma was observed at air pressures of 1-100 kPa. When the capillary length was 12 mm, a partial recovery of the transparency took place. A comparison was made with the dynamics and recovery of the plasma transparency when breakdown of air took place near the free surface.
On the physical mechanism of front-back asymmetry of nonlinear gravity-capillary waves
NASA Astrophysics Data System (ADS)
Dosaev, Alexander; Troitskaya, Yulia; Shrira, Victor
2016-04-01
In nature wind waves of all scales are asymmetric both with respect to the horizontal and vertical axes. The front-back (or fore-aft asymmetry), i.e. the asymmetry with respect to the vertical axis, manifests itself in steeper front slopes. Although it can be important for remote sensing of sea surface and wave field interaction with wind, especially for the waves of gravity-capillary range, at present the understanding of physical mechanisms causing the gravity-capillary waves asymmetry and its dependence on parameters is very poor; there has been no study dedicated to this problem. Here we address this gap. The decimetre-range water waves in many respects essentially differ from the waves of other ranges: wind forcing is stronger, steep waves develop a characteristic pattern of capillary ripples on their forward slopes. These 'parasitic capillaries', generated by a narrow pressure distribution associated with an underlying longer wave' crest, remain quasi-stationary with regard to the longer wave. The train of capillaries is localised on the front slope and decays towards the trough. We investigate the nature of the asymmetry of such waves by extensive numerical simulations of the Euler equations employing the method of conformal mapping for two-dimensional potential flow and taking into account wave generation by wind and dissipation due to molecular viscosity. We examine the role of various factors contributing to the wave profile asymmetry: wind pumping, viscous stresses, the Reynolds stresses caused by ripples and found the latter to be by far the most important. It is the lop-sided ripple distribution which leads to noticeable fore-aft asymmetry of the mean wave profile. We also found how the asymmetry depends on wavelength, steepness, wind and viscosity, which enables us to parametrize these dependencies for applications in microwave remote sensing and wave generation.
Capillary-gravity waves on a liquid film of arbitrary depth: analysis of the wave resistance.
Wędołowski, Karol; Napiórkowski, Marek
2013-10-01
We discuss the wave resistance in the case of an externally perturbed viscous liquid film of arbitrary thickness. Emphasis is placed on the dependence of the wave resistance on the film thickness H, the length scale b characterizing the external perturbation, and its velocity V. In particular, the effectiveness of the mechanisms of capillary-gravity waves and the viscous dissipation localized in the vicinity of the perturbation are compared and discussed as functions of H and V. We show that, in general, the wave resistance is a nonmonotonous function of H with a maximum whose amplitude and position depend on b and V. In the case of small H the wave resistance depends on a parameter S proportional V/H(3). We find three different regimes of this parameter in which the wave resistance behaves like S(r) with the exponent r equal to 1, 1/3, and -1. These results are also obtained independently within the thin liquid film approximation. This allows us to assess the range of validity of the thin liquid film approximation in various cases, in particular its dependence on the perturbation length scale b.
Numerical simulation of the capillary-gravity waves excited by an obstacle
NASA Astrophysics Data System (ADS)
Hanazaki, Hideshi; Inomata, Ryosuke
2016-11-01
Capillary gravity waves excited by an obstacle are investigated by the unsteady numerical solution of the Euler equations. It is well known that the large-amplitude upstream advancing solitary waves are generated periodically under the resonant condition of Fr =1 (Fr: Froude number), i.e., when the phase velocity of the long surface waves agrees with the mean flow speed. With capillary effects (Bo>0), short waves are newly generated by the upstream solitary waves of large amplitude. In this study it is investigated how the characteristics of the solitary waves and the short waves, especially their amplitudes, change due to the variation of the obstacle height and the Froude number. The results will be compared also with the solutions of the forced KdV-type equations.
Isotropic-nematic interface in suspensions of hard rods: mean-field properties and capillary waves.
Wolfsheimer, S; Tanase, C; Shundyak, K; van Roij, R; Schilling, T
2006-06-01
We present a study of the isotropic-nematic interface in a system of hard spherocylinders. First we compare results from Monte Carlo simulations and Onsager density functional theory for the interfacial profiles of the orientational order parameter and the density. Those interfacial properties that are not affected by capillary waves are in good agreement, despite the fact that Onsager theory overestimates the coexistence densities. Then we show results of a Monte Carlo study of the capillary waves of the interface. In agreement with recent theoretical investigations [Elgeti and Schmid, Eur. Phys. J. E 18, 407 (2005)] we find a strongly anisotropic capillary wave spectrum. For the wave numbers accessed in our simulations, the spectrum is quadratic, i.e., elasticity does not play a role. We conjecture that this effect is due to the strong bending rigidity of the director field in suspensions of spherocylinders.
Confining capillary waves to control aerosol droplet size from surface acoustic wave nebulisation
NASA Astrophysics Data System (ADS)
Nazarzadeh, Elijah; Reboud, Julien; Wilson, Rab; Cooper, Jonathan M.
Aerosols play a significant role in targeted delivery of medication through inhalation of drugs in a droplet form to the lungs. Delivery and targeting efficiencies are mainly linked to the droplet size, leading to a high demand for devices that can produce aerosols with controlled sizes in the range of 1 to 5 μm. Here we focus on enabling the control of the droplet size of a liquid sample nebulised using surface acoustic wave (SAW) generated by interdigitated transducers on a piezoelectric substrate (lithium niobate). The formation of droplets was monitored through a high-speed camera (600,000 fps) and the sizes measured using laser diffraction (Spraytec, Malvern Ltd). Results show a wide droplet size distribution (between 0.8 and 400 μm), while visual observation (at fast frame rates) revealed that the large droplets (>100 μm) are ejected due to large capillary waves (80 to 300 μm) formed at the free surface of liquid due to leakage of acoustic radiation of the SAWs, as discussed in previous literature (Qi et al. Phys Fluids, 2008). To negate this effect, we show that a modulated structure, specifically with feature sizes, typically 200 μm, prevents formation of large capillary waves by reducing the degrees of freedom of the system, enabling us to obtain a mean droplet size within the optimum range for drug delivery (<10 μm). This work was supported by an EPSRC grant (EP/K027611/1) and an ERC Advanced Investigator Award (340117-Biophononics).
Extreme events in Faraday waves
NASA Astrophysics Data System (ADS)
Punzmann, Horst; Shats, Michael; Xia, Hua
2014-05-01
Observations of extreme wave events in the ocean are rare due to their low statistical probability. In the laboratory however, the evolution of extreme wave events can be studied in great detail with high spatial and temporal resolution. The reported surface wave experiments in the short wavelength gravity-capillary range aim to contribute to the understanding of some of the underlying mechanisms for rogue wave generation. In this talk, we report on extreme wave events in parametrically excited Faraday waves. Faraday waves appear if a fluid is accelerated (normal to the fluid surface) above a critical threshold. A variety of novel tools have been deployed to characterize the 2D surface elevation. The results presented show spatio-temporal and statistical data on the surface wave conditions leading up to extreme wave events. The peak in wave amplitude during such an event is shown to exceed six times the standard deviation of the average wave field with significantly increased statistical probability compared to the background wave field [1]. The experiments also show that parametrically excited waves can be viewed as assembles of oscillons [2] (or oscillating solitons) where modulation instability seems to play a crucial role in their formation. More detailed studies on the oscillon dynamics reveal that the onset of an increased probability of extreme wave events correlates with the increase in the oscillons mobility and merger [3]. Reference: 1. Xia H., Maimbourg T., Punzmann H., and Shats M., Oscillon dynamics and rogue wave generation in Faraday surface ripples, Physical Review Letters 109, 114502 (2012) 2. Shats M., Xia H., and Punzmann H., Parametrically excited water surface ripples as ensembles of oscillons, Physical Review Letters 108, 034502 (2012) 3. Shats M., Punzmann H., Xia H., Capillary rogue waves, Physical Review Letters, 104, 104503 (2010)
Self-consistent theory of capillary-gravity-wave generation by small moving objects.
Chepelianskii, A D; Schindler, M; Chevy, F; Raphaël, E
2010-01-01
We investigate theoretically the onset of capillary-gravity waves created by a small object moving at the water-air interface. It is well established that, for straight uniform motion, no steady waves appear at velocities below the minimum phase velocity c(min)=23 cm/s. At higher velocities, the emission of capillary-gravity waves creates an additional drag force. The behavior of this force near the critical velocity is still poorly understood. A linear-response theory where the object is replaced by an effective pressure source predicts a singular behavior for the wave drag. However, experimental data tend to indicate a more continuous transition. In this paper, we show that a proper treatment of the flow equations around the obstacle can regularize wave emission, even in the linear wave approximation, thereby ensuring a continuous behavior of the drag force.
Space-time chaos of capillary waves parametrically excited by noise
Ezerskii, A.B.; Matusov, P.A.
1995-04-01
In experiments with parametrically excited capillary waves on the surface of a liquid with random pumping it was found that the transition to an irregular wave field starts to occur at a low supercriticality. Pulsations in the intensity of the ripples with almost complete preservation of the wave-field structure were noticed. The characteristic frequency of the pulsations calculated from experimental samples turned out to depend on the supercriticality. The results of numerical modeling were in good agreement with experiment.
Experimental observation of gravity-capillary solitary waves generated by a moving air-suction
NASA Astrophysics Data System (ADS)
Park, Beomchan; Cho, Yeunwoo
2016-11-01
Gravity-capillary solitary waves are generated by a moving "air-suction" forcing instead of a moving "air-blowing" forcing. The air-suction forcing moves horizontally over the surface of deep water with speeds close to the minimum linear phase speed cmin = 23 cm/s. Three different states are observed according to forcing speed below cmin. At relatively low speeds below cmin, small-amplitude linear circular depressions are observed, and they move steadily ahead of and along with the moving forcing. As the forcing speed increases close to cmin, however, nonlinear 3-D gravity-capillary solitary waves are observed, and they move steadily ahead of and along with the moving forcing. Finally, when the forcing speed is very close to cmin, oblique shedding phenomena of 3-D gravity-capillary solitary waves are observed ahead of the moving forcing. We found that all the linear and nonlinear wave patterns generated by the air-suction forcing correspond to those generated by the air-blowing forcing. The main difference is that 3-D gravity-capillary solitary waves are observed "ahead of" the air-suction forcing, whereas the same waves are observed "behind" the air-blowing forcing. This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2014R1A1A1002441).
Highly nonlinear standing water waves with small capillary effect
NASA Astrophysics Data System (ADS)
Schultz, William W.; vanden-Broeck, Jean-Marc; Jiang, Lei; Perlin, Marc
1998-08-01
We calculate spatially and temporally periodic standing waves using a spectral boundary integral method combined with Newton iteration. When surface tension is neglected, the non-monotonic behaviour of global wave properties agrees with previous computations by Mercer & Roberts (1992). New accurate results near the limiting form of gravity waves are obtained by using a non-uniform node distribution. It is shown that the crest angle is smaller than 90° at the largest calculated crest curvature. When a small amount of surface tension is included, the crest form is changed significantly. It is necessary to include surface tension to numerically reproduce the steep standing waves in Taylor's (1953) experiments. Faraday-wave experiments in a large-aspect-ratio rectangular container agree with our computations. This is the first time such high-amplitude, periodic waves appear to have been observed in laboratory conditions. Ripple formation and temporal symmetry breaking in the experiments are discussed.
Capillary Gravity Waves over an Obstruction - Forced Generalized KdV equation
NASA Astrophysics Data System (ADS)
Choi, Jeongwhan; Whang, S. I.; Sun, Shu-Ming
2013-11-01
Capillary gravity surface waves of an ideal fluid flow over an obstruction is considered. When the Bond number is near the critical value 1/3, a forced generalized KdV equation of fifth order is derived. We study the equation analytically and numerically. Existence and stability of solutions are studied and new types of numerical solutions are found.
Stability of Steep Gravity--Capillary Solitary Waves in Deep Water
NASA Astrophysics Data System (ADS)
Akylas, T. R.; Calvo, D. C.
2000-11-01
The stability of steep gravity--capillary solitary waves in deep water is numerically investigated using the full nonlinear water-wave equations with surface tension. As was found in prior work based on model equations for small-amplitude solitary waves in shallow water, out of the two solution branches that bifurcate at the minimum gravity--capillary phase speed, solitary waves of depression again turn out to be stable while those of elevation are unstable to small disturbances. Motivated by the experiments of Longuet-Higgins & Zhang (Phys. Fluids 9:1963--1968, 1997), we also consider the forced problem of a localised pressure distribution applied to the free surface of a stream with speed below the minimum gravity--capillary phase speed. We find that the finite-amplitude forced solitary-wave solution branch computed by Vanden-Broeck & Dias (J. Fluid Mech. 240:549--557, 1992) is unstable but the branch corresponding to Rayleigh's linearised solution is stable. The significance of viscous effects is assessed; the effects of instability in steep waves generally are comparable to, and in some cases greater than, those of dissipation. These findings are discussed in connection with the experimental observations of Longuet-Higgins & Zhang.
Instability of water jet: Aerodynamically induced acoustic and capillary waves
NASA Astrophysics Data System (ADS)
Broman, Göran I.; Rudenko, Oleg V.
2012-09-01
High-speed water jet cutting has important industrial applications. To further improve the cutting performance it is critical to understand the theory behind the onset of instability of the jet. In this paper, instability of a water jet flowing out from a nozzle into ambient air is studied. Capillary forces and compressibility of the liquid caused by gas bubbles are taken into account, since these factors have shown to be important in previous experimental studies. A new dispersion equation, generalizing the analogous Rayleigh equation, is derived. It is shown how instability develops because of aerodynamic forces that appear at the streamlining of an initial irregularity of the equilibrium shape of the cross-section of the jet and how instability increases with increased concentration of gas bubbles. It is also shown how resonance phenomena are responsible for strong instability. On the basis of the theoretical explanations given, conditions for stable operation are indicated.
A numerical study on parasitic capillary waves using unsteady conformal mapping
NASA Astrophysics Data System (ADS)
Murashige, Sunao; Choi, Wooyoung
2017-01-01
This paper describes fully nonlinear computation of unsteady motion of parasitic capillary waves that appear on the front face of steep gravity waves progressing on water of infinite depth, within the framework of irrotational plane flow. As an alternative to the widely-used boundary integral method with mixed-Eulerian-Lagrangian (MEL) time updating, we focus on a numerical method based on unsteady conformal mapping, which will be hereafter referred to as the unsteady hodograph transformation (UHT) method. In this method, we solve the nonlinear evolution equations to find an unsteady conformal map in a complex plane with which the flow domain is mapped onto the unit disk while the free surface is fixed on the unit circle. The aim of this work is to compare the UHT method with the MEL method and find a more efficient method to compute parasitic capillary waves. From linear stability analysis, it is found that a critical difference between these two methods arises from the kernel of cotangent function in singular integrals, and the UHT method can avoid some numerical instability due to it. Numerical examples demonstrate that the UHT method is more suitable than the MEL method for not only parasitic capillary waves, but also capillary dominated waves. In particular, the UHT method requires no artificial techniques, such as filtering, to control numerical errors, in these examples. In addition, another major difference between the two methods is observed in terms of the clustering property of sample points on the free surface, depending on the restoring force of waves (gravity or surface tension).
NASA Astrophysics Data System (ADS)
Duncan, J. H.; Diorio, J. D.; Lisiewski, A.; Harris, R.
2009-11-01
The wave pattern generated by a small pressure source moving across a water surface at speeds less than the minimum phase speed for linear gravity-capillary waves (cmin = 23 cm/s) was investigated experimentally. The resulting wave pattern was measured using cinematic shadowgraph and laser-induced fluorescence (LIF) techniques. The results show the existence of several distinct behavioral states. At low speeds, no wave behavior is observed and the pattern resembles the symmetric stationary condition. However, at a critical speed, but still below cmin, the pattern undergoes a sudden transition to an asymmetric state with a stationary, 2D solitary wave that forms behind the pressure source. This solitary wave is elongated in the cross-stream relative to the stream-wise direction and resembles gravity-capillary ``lumps'' observed in previous numerical calculations. As the translation speed approaches cmin, another time-dependent behavior is observed characterized by periodic ``shedding'' from a V-shaped solitary wave pattern. This work will be discussed in conjunction with the recent numerical calculations of T. Akylas and his research group.
NASA Astrophysics Data System (ADS)
Mitsotakis, Dimitrios; Dutykh, Denys; Assylbekuly, Aydar; Zhakebayev, Dauren
2017-05-01
In this Letter we consider long capillary-gravity waves described by a fully nonlinear weakly dispersive model. First, using the phase space analysis methods we describe all possible types of localized travelling waves. Then, we especially focus on the critical regime, where the surface tension is exactly balanced by the gravity force. We show that our long wave model with a critical Bond number admits stable travelling wave solutions with a singular crest. These solutions are usually referred to in the literature as peakons or peaked solitary waves. They satisfy the usual speed-amplitude relation, which coincides with Scott-Russel's empirical formula for solitary waves, while their decay rate is the same regardless their amplitude. Moreover, they can be of depression or elevation type independent of their speed. The dynamics of these solutions are studied as well.
Gravity capillary waves in fluid layers under normal electric fields.
Papageorgiou, Demetrios T; Petropoulos, Peter G; Vanden-Broeck, Jean-Marc
2005-11-01
We study the formation and dynamics of interfacial waves on a perfect dielectric ideal fluid layer of finite depth, wetting a solid wall, when the region above the fluid is hydrodynamically passive but has constant permittivity, for example, air. The wall is held at a constant electric potential and a second electrode having a different potential is placed parallel to the wall and infinitely far from it. In the unperturbed state the interface is flat and the normal horizontally uniform electric field is piecewise constant in the liquid and air. We derive a system of long wave nonlinear evolution equations valid for interfacial amplitudes as large as the unperturbed layer depth and which retain gravity, surface tension and electric field effects. It is shown that for given physical parameters there exists a critical value of the voltage potential difference between electrodes, below which the system is dispersive and above which a band of unstable waves is possible centered around a finite wavenumber. In the former case nonlinear traveling waves are calculated and their stability is studied, while in the latter case the instability leads to thinning of the layer with the interface touching down in finite time. A similarity solution of the second kind is found to be dominant near the singularity, and the scaling exponents are determined using analysis and computations.
Gravity-capillary waves in finite depth on flows of constant vorticity.
Hsu, Hung-Chu; Francius, Marc; Montalvo, Pablo; Kharif, Christian
2016-11-01
This paper considers two-dimensional periodic gravity-capillary waves propagating steadily in finite depth on a linear shear current (constant vorticity). A perturbation series solution for steady periodic waves, accurate up to the third order, is derived using a classical Stokes expansion procedure, which allows us to include surface tension effects in the analysis of wave-current interactions in the presence of constant vorticity. The analytical results are then compared with numerical computations with the full equations. The main results are (i) the phase velocity is strongly dependent on the value of the vorticity; (ii) the singularities (Wilton singularities) in the Stokes expansion in powers of wave amplitude that correspond to a Bond number of 1/2 and 1/3, which are the consequences of the non-uniformity in the ordering of the Fourier coefficients, are found to be influenced by vorticity; (iii) different surface profiles of capillary-gravity waves are computed and the effect of vorticity on those profiles is shown to be important, in particular that the solutions exhibit type-2-like wave features, characterized by a secondary maximum on the surface profile with a trough between the two maxima.
Gravity-capillary waves in finite depth on flows of constant vorticity
NASA Astrophysics Data System (ADS)
Hsu, Hung-Chu; Francius, Marc; Montalvo, Pablo; Kharif, Christian
2016-11-01
This paper considers two-dimensional periodic gravity-capillary waves propagating steadily in finite depth on a linear shear current (constant vorticity). A perturbation series solution for steady periodic waves, accurate up to the third order, is derived using a classical Stokes expansion procedure, which allows us to include surface tension effects in the analysis of wave-current interactions in the presence of constant vorticity. The analytical results are then compared with numerical computations with the full equations. The main results are (i) the phase velocity is strongly dependent on the value of the vorticity; (ii) the singularities (Wilton singularities) in the Stokes expansion in powers of wave amplitude that correspond to a Bond number of 1/2 and 1/3, which are the consequences of the non-uniformity in the ordering of the Fourier coefficients, are found to be influenced by vorticity; (iii) different surface profiles of capillary-gravity waves are computed and the effect of vorticity on those profiles is shown to be important, in particular that the solutions exhibit type-2-like wave features, characterized by a secondary maximum on the surface profile with a trough between the two maxima.
An air/sea flux model including the effects of capillary waves
NASA Technical Reports Server (NTRS)
Bourassa, Mark A.
1993-01-01
An improved model of the air/sea interface is developed. The improvements consist in including the effect of capillary (surface tension) waves on the tropical surface fluxes and the consideration of the sea state, both of which increase the magnitude of tropical surface fluxes. Changes in surface stress are most significant in the low wind-speed regions, which include the areas where westerly bursts occur. It is shown that the changes, from the regular wind conditions to those of a westerly burst or El-Nino, can double when the effects of capillary waves are considered. This implies a much stronger coupling between the ocean and the atmosphere than is predicted by other boundary layer models.
Nonlinear Gravity-Capillary Waves on a Compressible Viscous Fluid with Edge Constraints.
1983-05-01
ly x We now cross- differentiate (54) and (55) and subtract one equation from another to obtain -1 2 -1V2(Vlz - w17) = -2y cos 8 By substituting (68...compressible viscous fluid with edge constraints in an inclined, straight channel. The Navier-Stokes equations subject to free surface and rigid bottom...and to construct the Burgers equation for the evolution of the gravity-capillary waves. The Burgers equation may become ill-posed when the Reynolds
Maxwell, Eric J; Tong, William G
2016-05-01
An ultrasensitive label-free antibody-free detection method for malachite green and crystal violet is presented using nonlinear laser wave-mixing spectroscopy and capillary zone electrophoresis. Wave-mixing spectroscopy provides a sensitive absorption-based detection method for trace analytes. This is accomplished by forming dynamic gratings within a sample cell, which diffracts light to create a coherent laser-like signal beam with high optical efficiency and high signal-to-noise ratio. A cubic dependence on laser power and square dependence on analyte concentration make wave mixing sensitive enough to detect molecules in their native form without the use of fluorescent labels for signal enhancement. A 532 nm laser and a 635 nm laser were used for malachite green and crystal violet sample excitation. The use of two lasers of different wavelengths allows the method to simultaneously detect both analytes. Selectivity is obtained through the capillary zone electrophoresis separation, which results in characteristic migration times. Measurement in capillary zone electrophoresis resulted in a limit of detection of 6.9 × 10(-10)M (2.5 × 10(-19) mol) for crystal violet and 8.3 × 10(-11)M (3.0 × 10(-20) mol) for malachite green at S/N of 2.
Capillary wave theory of adsorbed liquid films and the structure of the liquid-vapor interface.
MacDowell, Luis G
2017-08-01
In this paper we try to work out in detail the implications of a microscopic theory for capillary waves under the assumption that the density is given along lines normal to the interface. Within this approximation, which may be justified in terms of symmetry arguments, the Fisk-Widom scaling of the density profile holds for frozen realizations of the interface profile. Upon thermal averaging of capillary wave fluctuations, the resulting density profile yields results consistent with renormalization group calculations in the one-loop approximation. The thermal average over capillary waves may be expressed in terms of a modified convolution approximation where normals to the interface are Gaussian distributed. In the absence of an external field we show that the phenomenological density profile applied to the square-gradient free energy functional recovers the capillary wave Hamiltonian exactly. We extend the theory to the case of liquid films adsorbed on a substrate. For systems with short-range forces, we recover an effective interface Hamiltonian with a film height dependent surface tension that stems from the distortion of the liquid-vapor interface by the substrate, in agreement with the Fisher-Jin theory of short-range wetting. In the presence of long-range interactions, the surface tension picks up an explicit dependence on the external field and recovers the wave vector dependent logarithmic contribution observed by Napiorkowski and Dietrich. Using an error function for the intrinsic density profile, we obtain closed expressions for the surface tension and the interface width. We show the external field contribution to the surface tension may be given in terms of the film's disjoining pressure. From literature values of the Hamaker constant, it is found that the fluid-substrate forces may be able to double the surface tension for films in the nanometer range. The film height dependence of the surface tension described here is in full agreement with results of
Capillary wave theory of adsorbed liquid films and the structure of the liquid-vapor interface
NASA Astrophysics Data System (ADS)
MacDowell, Luis G.
2017-08-01
In this paper we try to work out in detail the implications of a microscopic theory for capillary waves under the assumption that the density is given along lines normal to the interface. Within this approximation, which may be justified in terms of symmetry arguments, the Fisk-Widom scaling of the density profile holds for frozen realizations of the interface profile. Upon thermal averaging of capillary wave fluctuations, the resulting density profile yields results consistent with renormalization group calculations in the one-loop approximation. The thermal average over capillary waves may be expressed in terms of a modified convolution approximation where normals to the interface are Gaussian distributed. In the absence of an external field we show that the phenomenological density profile applied to the square-gradient free energy functional recovers the capillary wave Hamiltonian exactly. We extend the theory to the case of liquid films adsorbed on a substrate. For systems with short-range forces, we recover an effective interface Hamiltonian with a film height dependent surface tension that stems from the distortion of the liquid-vapor interface by the substrate, in agreement with the Fisher-Jin theory of short-range wetting. In the presence of long-range interactions, the surface tension picks up an explicit dependence on the external field and recovers the wave vector dependent logarithmic contribution observed by Napiorkowski and Dietrich. Using an error function for the intrinsic density profile, we obtain closed expressions for the surface tension and the interface width. We show the external field contribution to the surface tension may be given in terms of the film's disjoining pressure. From literature values of the Hamaker constant, it is found that the fluid-substrate forces may be able to double the surface tension for films in the nanometer range. The film height dependence of the surface tension described here is in full agreement with results of
Water Surface Currents, Short Gravity-Capillary Waves and Radar Backscatter
NASA Technical Reports Server (NTRS)
Atakturk, Serhad S.; Katsaros, Kristina B.
1993-01-01
Despite their importance for air-sea interaction and microwave remote sensing of the ocean surface, intrinsic properties of short gravity-capillary waves are not well established. This is largely due to water surface currents and their effects on the direct measurements of wave parameters conducted at a fixed point. Frequencies of small scale waves propagating on a surface which itself is in motion, are subject to Doppler shifts. Hence, the high frequency tail of the wave spectra obtained from such temporal observations is smeared. Conversion of this smeared measured-frequency spectra to intrinsic-frequency (or wavenumber) spectra requires corrections for the Doppler shifts. Such attempts in the past have not been very successful in particular when field data were used. This becomes evident if the amplitude modulation of short waves by underlying long waves is considered. Microwave radar studies show that the amplitude of a short wave component attains its maximum value near the crests and its minimum in the troughs of the long waves. Doppler-shifted wave data yield similar results but much larger in modulation magnitude, as expected. In general, Doppler shift corrections reduce the modulation magnitude. Overcorrection may result in a negligible modulation or even in a strong modulation with the maximum amplitude in the wave troughs. The latter situation is clearly contradictory to our visual observations as well as the radar results and imply that the advection by currents is overestimated. In this study, a differential-advection approach is used in which small scale waves are advected by the currents evaluated not at the free surface, but at a depth proportional to their wavelengths. Applicability of this approach is verified by the excellent agreement in phase and magnitude of short-wave modulation between results based on radar and on wave-gauge measurements conducted on a lake.
Spatiotemporal rogue events in femtosecond filamentation
Majus, D.; Jukna, V.; Valiulis, G.; Dubietis, A.; Faccio, D.
2011-02-15
We present experimental and numerical investigations of optical extreme (rogue) event statistics recorded in the regime of femtosecond pulse filamentation in water. In the spectral domain, the extreme events manifest themselves as either large or small extremes of the spectral intensity, justified by right- or left-tailed statistical distributions, respectively. In the time domain, the observed extreme events are associated with pulse splitting and energy redistribution in space and therefore are exquisitely linked to three-dimensional, spatiotemporal dynamics and formation of the X waves.
Capillary waves at the liquid-vapor interface and the surface tension of water.
Ismail, Ahmed E; Grest, Gary S; Stevens, Mark J
2006-07-07
Capillary waves occurring at the liquid-vapor interface of water are studied using molecular dynamics simulations. In addition, the surface tension, determined thermodynamically from the difference in the normal and tangential pressure at the liquid-vapor interface, is compared for a number of standard three- and four-point water models. We study four three-point models (SPC/E, TIP3P, TIP3P-CHARMM, and TIP3P-Ew) and two four-point models (TIP4P and TIP4P-Ew). All of the models examined underestimate the surface tension; the TIP4P-Ew model comes closest to reproducing the experimental data. The surface tension can also be determined from the amplitude of capillary waves at the liquid-vapor interface by varying the surface area of the interface. The surface tensions determined from the amplitude of the logarithmic divergence of the capillary interfacial width and from the traditional thermodynamic method agree only if the density profile is fitted to an error function instead of a hyperbolic tangent function.
Damping of short gravity-capillary waves due to oil derivatives film on the water surface
NASA Astrophysics Data System (ADS)
Sergievskaya, Irina; Ermakov, Stanislav; Lazareva, Tatyana
2016-10-01
In this paper new results of laboratory studies of damping of gravity-capillary waves on the water surface covered by kerosene are presented and compared with our previous analysis of characteristics of crude oil and diesel fuel films. Investigations of kerosene films were carried out in a wide range values of film thicknesses (from some hundreds millimetres to a few millimetres) and in a wide range of surface wave frequencies (from 10 to 27 Hz). The selected frequency range corresponds to the operating wavelengths of microwave, X- to Ka-band radars typically used for the ocean remote sensing. The studied range of film thickness covers typical thicknesses of routine spills in the ocean. It is obtained that characteristics of waves, measured in the presence of oil derivatives films differ from those for crude oil films, in particular, because the volume viscosity of oil derivatives and crude oil is strongly different. To retrieve parameters of kerosene films from the experimental data the surface wave damping was analyzed theoretically in the frame of a model of two-layer fluid. The films are assumed to be soluble, so the elasticity on the upper and lower boundaries is considered as a function of wave frequency. Physical parameters of oil derivative films were estimated when tuning the film parameters to fit theory and experiment. Comparison between wave damping due to crude oil, kerosene and diesel fuel films have shown some capabilities of distinguishing of oil films from remote sensing of short surface waves.
Interfacial free energy of the NaCl crystal-melt interface from capillary wave fluctuations.
Benet, Jorge; MacDowell, Luis G; Sanz, Eduardo
2015-04-07
In this work we study, by means of molecular dynamics simulations, the solid-liquid interface of NaCl under coexistence conditions. By analysing capillary waves, we obtain the stiffness for different orientations of the solid and calculate the interfacial free energy by expanding the dependency of the interfacial free energy with the solid orientation in terms of cubic harmonics. We obtain an average value for the solid-fluid interfacial free energy of 89 ± 6 mN m(-1) that is consistent with previous results based on the measure of nucleation free energy barriers [Valeriani et al., J. Chem. Phys. 122, 194501 (2005)]. We analyse the influence of the simulation setup on interfacial properties and find that facets prepared as an elongated rectangular stripe give the same results as those prepared as squares for all cases but the 111 face. For some crystal orientations, we observe at small wave-vectors a behaviour not consistent with capillary wave theory and show that this behavior does not depend on the simulation setup.
Evanescent-wave optical Cr VI sensor with a flexible fused-silica capillary as a transducer.
Tao, Shiquan; Sarma, T V S
2006-05-15
A light-guiding, flexible fused-silica (FFS) capillary has been used in designing an optical fiber Cr VI sensor for monitoring Cr VI ions in water samples. The FFS capillary is similar to a conventional silica optical fiber in that it can guide light in the wavelength region from the UV to the near IR but different from a conventional optical fiber in that it is a tubular waveguide. The inner surface of the FFS capillary is fused silica, which one can modify to design an optical fiber chemical sensor. The FFS capillary has a cladding layer plus a protective polymer coating on its outside surface. The cladding layer ensures the ability of the FFS capillary to guide light. The protective coating increases the FFS capillary's mechanical strength and makes it robust for practical applications. Compared with conventional silica optical fibers, it is much easier and more feasible to use this FFS capillary to fabricate long-path (tens of meters to thousands of meters) evanescent-wave based chemical sensors. We describe a Cr VI sensor based on the intrinsic evanescent-wave absorption by Cr VI ions in a water sample filled inside the capillary as an example of use of a FFS capillary in chemical sensor design. This simple sensor, using a 30 m light-guiding FFS capillary as a transducer, has the capability of detecting as little as 31 parts in 10(9) of Cr VI in a water sample, which is close to the detection limit of some sophisticated, expensive analytical instruments.
Breakup of Bubbles or Drops by Capillary Waves Induced by Coalescence or Other Excitations
NASA Astrophysics Data System (ADS)
Zhang, Feng Hua; Taborek, Peter; Burton, Justin; Cheong Khoo, Boo; Thoroddsen, Siggi
2012-02-01
Capillary breakup of a bubble or drop by various excitations is ubiquitous in both nature and technology. Examples include coalescence with another bubble or drop, wetting on a solid surface, impact on a solid surface, detachment from a nozzle, or vibrations driven by acoustic, electrical, or magnetic fields. When the excitation ceases, capillary forces on the surface naturally drive the deformed bubble or drop to recover its spherical shape. However, when the viscosity is small, this recovery can lead to nonlinear oscillations of the interface and a singularity in the flow. Here we use high-speed imaging to investigate the coalescence of bubbles and drops of various sizes. In many cases, coalescence leads to pinch-off events and the formation of the satellite and sub-satellite. Our experiments use pressured xenon gas in glycerol/water mixtures so that the density ratio and viscosity ratio can be varied over many orders of magnitude. We characterize the generation, propagation, and convergence of capillary waves, the formation time and sizes of satellites, and the dynamics of two-fluid pinch-off as a function of the density ratio and viscosity ratio. The work shall benefit the wide-spread applications and fulfill the scientific and public curiosities.
Zhu, Xueyan; Yuan, Quanzi; Zhao, Ya-Pu
2012-01-01
Molecular dynamics simulations were carried out to explore the capillary wave propagation induced by the competition between one upper precursor film (PF) on the graphene and one lower PF on the substrate in electro-elasto-capillarity (EEC). During the wave propagation, the graphene was gradually delaminated from the substrate by the lower PF. The physics of the capillary wave was explored by the molecular kinetic theory. Besides, the dispersion relation of the wave was obtained theoretically. The theory showed that the wave was controlled by the driving work difference of the two PFs. Simulating the EEC process under different electric field intensities (E), the wave velocity was found insensitive to E. We hope this research could expand our knowledge on the wetting, electrowetting and EEC. As a potential application, the electrowetting of the PF between the graphene and the substrate is a promising candidate for delaminating graphene from substrate. PMID:23226593
Capillary waves and the decay of density correlations at liquid surfaces.
Hernández-Muñoz, Jose; Chacón, Enrique; Tarazona, Pedro
2016-12-01
Wertheim predicted strong density-density correlations at free liquid surfaces, produced by capillary wave fluctuations of the interface [M. S. Wertheim, J. Chem. Phys. 65, 2377 (1976)JCPSA60021-960610.1063/1.433352]. That prediction has been used to search for a link between capillary wave (CW) theory and density functional (DF) formalism for classical fluids. In particular, Parry et al. have recently analyzed the decaying tails of these CW effects moving away from the interface as a clue for the extended CW theory [A. O. Parry et al., J. Phys.: Condens. Matter 28, 244013 (2016)JCOMEL0953-898410.1088/0953-8984/28/24/244013], beyond the strict long-wavelength limit studied by Wertheim. Some apparently fundamental inconsistencies between the CW and the DF theoretical views of the fluid interfaces arose from the asymptotic analysis of the CW signal. In this paper we revisit the problem of the CW asymptotic decay with a separation of local non-CW surface correlation effects from those that are a truly nonlocal propagation of the CW fluctuations from the surface towards the liquid bulk.
Capillary waves and the decay of density correlations at liquid surfaces
NASA Astrophysics Data System (ADS)
Hernández-Muñoz, Jose; Chacón, Enrique; Tarazona, Pedro
2016-12-01
Wertheim predicted strong density-density correlations at free liquid surfaces, produced by capillary wave fluctuations of the interface [M. S. Wertheim, J. Chem. Phys. 65, 2377 (1976), 10.1063/1.433352]. That prediction has been used to search for a link between capillary wave (CW) theory and density functional (DF) formalism for classical fluids. In particular, Parry et al. have recently analyzed the decaying tails of these CW effects moving away from the interface as a clue for the extended CW theory [A. O. Parry et al., J. Phys.: Condens. Matter 28, 244013 (2016), 10.1088/0953-8984/28/24/244013], beyond the strict long-wavelength limit studied by Wertheim. Some apparently fundamental inconsistencies between the CW and the DF theoretical views of the fluid interfaces arose from the asymptotic analysis of the CW signal. In this paper we revisit the problem of the CW asymptotic decay with a separation of local non-CW surface correlation effects from those that are a truly nonlocal propagation of the CW fluctuations from the surface towards the liquid bulk.
Spatiotemporal rogue events in optical multiple filamentation.
Birkholz, Simon; Nibbering, Erik T J; Brée, Carsten; Skupin, Stefan; Demircan, Ayhan; Genty, Goëry; Steinmeyer, Günter
2013-12-13
The transient appearance of bright spots in the beam profile of optical filaments formed in xenon is experimentally investigated. Fluence profiles are recorded with high-speed optical cameras at the kilohertz repetition rate of the laser source. A statistical analysis reveals a thresholdlike appearance of heavy-tailed fluence distributions together with the transition from single to multiple filamentation. The multifilament scenario exhibits near-exponential probability density functions, with extreme events exceeding the significant wave height by more than a factor of 10. The extreme events are isolated in space and in time. The macroscopic origin of these experimentally observed heavy-tail statistics is shown to be local refractive index variations inside the nonlinear medium, induced by multiphoton absorption and subsequent plasma thermalization. Microscopically, mergers between filament strings appear to play a decisive role in the observed rogue wave statistics.
Asymmetric Directional Multicast for Capillary Machine-to-Machine Using mmWave Communications.
Kwon, Jung-Hyok; Kim, Eui-Jik
2016-04-11
The huge demand for high data rate machine-to-machine (M2M) services has led to the use of millimeter Wave (mmWave) band communications with support for a multi-Gbps data rate through the use of directional antennas. However, unnecessary sector switching in multicast transmissions with directional antennas results in a long delay, and consequently a low throughput. We propose asymmetric directional multicast (ADM) for capillary M2M to address this problem in mmWave communications. ADM provides asymmetric sectorization that is optimized for the irregular deployment pattern of mulicast group members. In ADM, an M2M gateway builds up asymmetric sectors with a beamwidth of a different size to cover all multicast group members with the minimum number of directional transmissions. The performance of ADM under various simulation environments is evaluated through a comparison with legacy mmWave multicast. The results of the simulation indicate that ADM achieves a better performance in terms of the transmission sectors, the transmission time, and the aggregate throughput when compared with the legacy multicast method.
Asymmetric Directional Multicast for Capillary Machine-to-Machine Using mmWave Communications
Kwon, Jung-Hyok; Kim, Eui-Jik
2016-01-01
The huge demand for high data rate machine-to-machine (M2M) services has led to the use of millimeter Wave (mmWave) band communications with support for a multi-Gbps data rate through the use of directional antennas. However, unnecessary sector switching in multicast transmissions with directional antennas results in a long delay, and consequently a low throughput. We propose asymmetric directional multicast (ADM) for capillary M2M to address this problem in mmWave communications. ADM provides asymmetric sectorization that is optimized for the irregular deployment pattern of mulicast group members. In ADM, an M2M gateway builds up asymmetric sectors with a beamwidth of a different size to cover all multicast group members with the minimum number of directional transmissions. The performance of ADM under various simulation environments is evaluated through a comparison with legacy mmWave multicast. The results of the simulation indicate that ADM achieves a better performance in terms of the transmission sectors, the transmission time, and the aggregate throughput when compared with the legacy multicast method. PMID:27077859
Gravity-capillary waves in countercurrent air/water turbulent flow
NASA Astrophysics Data System (ADS)
Zonta, Francesco; Onorato, Miguel; Soldati, Alfredo
2016-11-01
Using the Direct Numerical Simulation (DNS) of the Navier-Stokes equations, we analyze the dynamics of the interface between air and water when both phases are driven by opposite pressure gradients (countercurrent configuration). The Reynolds number (Re), the Weber number (We) and the Froude number (Fr) fully describe the physical problem. We examine the problem of the transient growth of interface waves for different combinations of physical parameters. Keeping Re constant and varying We and Fr , we show that, in the initial stages of the wave generation process, the amplitude of the interface elevation grows in time as t2 / 5 . Wavenumber spectra, E (kx) , of the surface elevation in the capillary range are in good agreement with the prediction of the Wave Turbulence Theory. Finally, the wave-induced modification of the average wind and current velocity profiles is addressed. CINECA supercomputing centre (Bologna, Italy) and ISCRA Computing Initiative are gratefully acknowledged for generous allowance of computer resources. Support from PRIN (under Grant 2006098584 004) is gratefully acknowledged. Support from Regione Autonoma.
Monroy, Francisco
2017-07-18
From the recent advent of the new soft-micro technologies, the hydrodynamic theory of surface modes propagating on viscoelastic bodies has reinvigorated this field of technology with interesting predictions and new possible applications, so recovering its scientific interest very limited at birth to the academic scope. Today, a myriad of soft small objects, deformable meso- and micro-structures, and macroscopically viscoelastic bodies fabricated from colloids and polymers are already available in the materials catalogue. Thus, one can envisage a constellation of new soft objects fabricated by-design with a functional dynamics based on the mechanical interplay of the viscoelastic material with the medium through their interfaces. In this review, we recapitulate the field from its birth and theoretical foundation in the latest 1980s up today, through its flourishing in the 90s from the prediction of extraordinary Rayleigh modes in coexistence with ordinary capillary waves on the surface of viscoelastic fluids, a fact first confirmed in experiments by Dominique Langevin and me with soft gels [Monroy and Langevin, Phys. Rev. Lett. 81, 3167 (1998)]. With this observational discovery at sight, we not only settled the theory previously formulated a few years before, but mainly opened a new field of applications with soft materials where the mechanical interplay between surface and bulk motions matters. Also, new unpublished results from surface wave experiments performed with soft colloids are reported in this contribution, in which the analytic methods of wave surfing synthetized together with the concept of coexisting capillary-shear modes are claimed as an integrated tool to insightfully scrutinize the bulk rheology of soft solids and viscoelastic fluids. This dedicatory to the figure of Dominique Langevin includes an appraisal of the relevant theoretical aspects of the surface hydrodynamics of viscoelastic fluids, and the coverage of the most important experimental
Energy spectra of 2D gravity and capillary waves with narrow frequency band excitation
NASA Astrophysics Data System (ADS)
Kartashova, E.
2012-02-01
In this letter we present a new method, called increment chain equation method (ICEM), for computing a cascade of distinct modes in a two-dimensional weakly nonlinear wave system generated by narrow frequency band excitation. The ICEM is a means for computing the quantized energy spectrum as an explicit function of frequency ω0 and stationary amplitude A0 of excitation. The physical mechanism behind the generation of the quantized cascade is modulation instability. The ICEM can be used in numerous 2D weakly nonlinear wave systems with narrow frequency band excitation appearing in hydrodynamics, nonlinear optics, electrodynamics, convection theory etc. In this letter the ICEM is demonstrated with examples of gravity and capillary waves with dispersion functions ω(k)~k1/2 and ω(k)~k3/2, respectively, and for two different levels of nonlinearity ɛ=A0k0: small (ɛ~0.1 to 0.25) and moderate (ɛ~0.25 to 0.4).
Dramatic enhancement of capillary wave fluctuations of a decorated water surface
Datta, A.; Kundu, S.; Sanyal, M.K.; Daillant, J.; Luzet, D.; Blot, C.; Struth, B.
2005-04-01
We have demonstrated by x-ray diffuse scattering that a bimolecular layer of a preformed three-tailed amphiphile, ferric stearate, drastically enhances capillary wave fluctuations on water surface due to a reduction in surface tension to 1 mN/m. The bimolecular layer is composed of molecules in symmetric configuration, on top of molecules in asymmetric configuration with ferric ions in contact with water. Unlike the usual Langmuir monolayers, this layer of molecules does not rupture under compression, but becomes thicker. This behavior mimics folding of a membrane on a liquid surface and is closely related to the cohesive interaction brought by the ferric ions. The low effective tension of this artificial membrane depends on the available area and reduces as the microscopic excess area increases.
Capillary waves at liquid-vapor interfaces: a molecular dynamics simulation.
Sides, S W; Grest, G S; Lacasse, M D
1999-12-01
Evidence for capillary waves at a liquid-vapor interface are presented from extensive molecular dynamics simulations of a system containing up to 1.24 million Lennard-Jones particles. Careful measurements show that the total interfacial width depends logarithmically on L(axially), the length of the simulation cell parallel to the interface, as predicted theoretically. The strength of the divergence of the interfacial width on L(axially) depends inversely on the surface tension gamma. This allows us to measure gamma two ways since gamma can also be obtained from the difference in the pressure parallel and perpendicular to the interface. These two independent measures of gamma agree provided that the interfacial order parameter profile is fit to an error function and not a hyperbolic tangent, as often assumed. We explore why these two common fitting functions give different results for gamma.
NASA Astrophysics Data System (ADS)
Kobyakov, D.; Bychkov, V.; Lundh, E.; Bezett, A.; Marklund, M.
2012-08-01
We study the parametric resonance of capillary waves on the interface between two immiscible Bose-Einstein condensates pushed towards each other by an oscillating force. Guided by analytical models, we solve numerically the coupled Gross-Pitaevskii equations for a two-component Bose-Einstein condensate at zero temperature. We show that, at moderate amplitudes of the driving force, the instability is stabilized due to nonlinear modifications of the oscillation frequency. When the amplitude of the driving force is large enough, we observe a detachment of droplets from the Bose-Einstein condensates, resulting in the generation of quantum vortices (skyrmions). We analytically investigate the vortex dynamics, and conditions of quantized vortex generation.
Capillary wave analysis of rough solid-liquid interfaces in nickel
NASA Astrophysics Data System (ADS)
Rozas, R. E.; Horbach, J.
2011-01-01
Crystal-liquid interfaces in nickel are investigated by molecular-dynamics computer simulations. Inhomogeneous systems of size Lx×Ly×Lz with Lz=5Ly are prepared where the crystal fcc phase at different orientations coexists with the liquid phase, separated by planar interfaces in the xy-plane. The lateral dimensions are varied, using two different geometries with Lx=Ly and with LyGtLx. In the framework of capillary wave theory (CWT), anisotropic interfacial stiffnesses and tensions are determined using different predictions of CWT with respect to the spectrum, finite-size broadening and different geometries. From a parameterization in terms of cubic harmonics up to 8th order, the anisotropic interfacial free energy is obtained.
The local structure factor near an interface; beyond extended capillary-wave models
NASA Astrophysics Data System (ADS)
Parry, A. O.; Rascón, C.; Evans, R.
2016-06-01
We investigate the local structure factor S (zq) at a free liquid-gas interface in systems with short-ranged intermolecular forces and determine the corrections to the leading-order, capillary-wave-like, Goldstone mode divergence of S (zq) known to occur for parallel (i.e. measured along the interface) wavevectors q\\to 0 . We show from explicit solution of the inhomogeneous Ornstein-Zernike equation that for distances z far from the interface, where the profile decays exponentially, S (zq) splits unambiguously into bulk and interfacial contributions. On each side of the interface, the interfacial contributions can be characterised by distinct liquid and gas wavevector dependent surface tensions, {σ l}(q) and {σg}(q) , which are determined solely by the bulk two-body and three-body direct correlation functions. At high temperatures, the wavevector dependence simplifies and is determined almost entirely by the appropriate bulk structure factor, leading to positive rigidity coefficients. Our predictions are confirmed by explicit calculation of S (zq) within square-gradient theory and the Sullivan model. The results for the latter predict a striking temperature dependence for {σ l}(q) and {σg}(q) , and have implications for fluctuation effects. Our results account quantitatively for the findings of a recent very extensive simulation study by Höfling and Dietrich of the total structure factor in the interfacial region, in a system with a cut-off Lennard-Jones potential, in sharp contrast to extended capillary-wave models which failed completely to describe the simulation results.
NASA Astrophysics Data System (ADS)
MacKenzie Laxague, Nathan Jean
Short ocean waves play a crucial role in the physical coupling between the ocean and the atmosphere. This is particularly true for gravity-capillary waves, waves of a scale (O(0.01-0.1) m) such that they are similarly restored to equilibrium by gravitational and interfacial tension (capillary) effects. These waves are inextricably linked to the turbulent boundary layer processes which characterize near-interfacial flows, acting as mediators of the momentum, gas, and heat fluxes which bear greatly on surface material transport, tropical storms, and climatic processes. The observation of these waves and the fluid mechanical phenomena which govern their behavior has long posed challenges to the would-be observer. This is due in no small part to the delicacy of centimeter-scale waves and the sensitivity of their properties to disruption via tactile measurement. With the ever-growing interest in satellite remote sensing, direct observations of short wave characteristics are needed along coastal margins. These zones are characterized by a diversity of physical processes which can affect the short-scale sea surface topography that is directly sensed via radar backscatter. In a related vein, these observations are needed to more fully understand the specific hydrodynamic relationship between young, wind-generated gravity-capillary waves and longer gravity waves. Furthermore, understanding of the full oceanic current profile is hampered by a lack of observations in the near-surface domain (z = O(0.01-0.1) m), where flows can differ greatly from those at depth. Here I present the development of analytical techniques for describing gravity-capillary ocean surface waves in order to better understand their role in the mechanical coupling between the atmosphere and ocean. This is divided amongst a number of research topics, each connecting short ocean surface waves to a physical forcing process via the transfer of momentum. One involves the examination of the sensitivity of
Bleibel, J; Dietrich, S; Domínguez, A; Oettel, M
2011-09-16
Using Brownian dynamics simulations, density functional theory, and analytical perturbation theory we study the collapse of a patch of interfacially trapped, micrometer-sized colloidal particles, driven by long-ranged capillary attraction. This attraction is formally analogous to two-dimensional (2D) screened Newtonian gravity with the capillary length λ as the screening length. Whereas the limit λ→∞ corresponds to the global collapse of a self-gravitating fluid, for finite λ[over ^] we predict theoretically and observe in simulations a ringlike density peak at the outer rim of a disclike patch, moving as an inbound shock wave. Possible experimental realizations are discussed.
NASA Astrophysics Data System (ADS)
Bleibel, J.; Dietrich, S.; Domínguez, A.; Oettel, M.
2011-09-01
Using Brownian dynamics simulations, density functional theory, and analytical perturbation theory we study the collapse of a patch of interfacially trapped, micrometer-sized colloidal particles, driven by long-ranged capillary attraction. This attraction is formally analogous to two-dimensional (2D) screened Newtonian gravity with the capillary length λ^ as the screening length. Whereas the limit λ^→∞ corresponds to the global collapse of a self-gravitating fluid, for finite λ^ we predict theoretically and observe in simulations a ringlike density peak at the outer rim of a disclike patch, moving as an inbound shock wave. Possible experimental realizations are discussed.
Capillary wave Hamiltonian for the Landau-Ginzburg-Wilson density functional.
Chacón, Enrique; Tarazona, Pedro
2016-06-22
We study the link between the density functional (DF) formalism and the capillary wave theory (CWT) for liquid surfaces, focused on the Landau-Ginzburg-Wilson (LGW) model, or square gradient DF expansion, with a symmetric double parabola free energy, which has been extensively used in theoretical studies of this problem. We show the equivalence between the non-local DF results of Parry and coworkers and the direct evaluation of the mean square fluctuations of the intrinsic surface, as is done in the intrinsic sampling method for computer simulations. The definition of effective wave-vector dependent surface tensions is reviewed and we obtain new proposals for the LGW model. The surface weight proposed by Blokhuis and the surface mode analysis proposed by Stecki provide consistent and optimal effective definitions for the extended CWT Hamiltonian associated to the DF model. A non-local, or coarse-grained, definition of the intrinsic surface provides the missing element to get the mesoscopic surface Hamiltonian from the molecular DF description, as had been proposed a long time ago by Dietrich and coworkers.
Capillary wave Hamiltonian for the Landau-Ginzburg-Wilson density functional
NASA Astrophysics Data System (ADS)
Chacón, Enrique; Tarazona, Pedro
2016-06-01
We study the link between the density functional (DF) formalism and the capillary wave theory (CWT) for liquid surfaces, focused on the Landau-Ginzburg-Wilson (LGW) model, or square gradient DF expansion, with a symmetric double parabola free energy, which has been extensively used in theoretical studies of this problem. We show the equivalence between the non-local DF results of Parry and coworkers and the direct evaluation of the mean square fluctuations of the intrinsic surface, as is done in the intrinsic sampling method for computer simulations. The definition of effective wave-vector dependent surface tensions is reviewed and we obtain new proposals for the LGW model. The surface weight proposed by Blokhuis and the surface mode analysis proposed by Stecki provide consistent and optimal effective definitions for the extended CWT Hamiltonian associated to the DF model. A non-local, or coarse-grained, definition of the intrinsic surface provides the missing element to get the mesoscopic surface Hamiltonian from the molecular DF description, as had been proposed a long time ago by Dietrich and coworkers.
NASA Astrophysics Data System (ADS)
Hsu, Hung-Chu; Kharif, Christian; Francius, Marc; Chen, Yang-Yih
2015-04-01
In this study a nonlinear Schrödinger equation governing the complex envelope of a capillary-gravity water wave train propagating on uniform vertical shear current is derived. When the vorticity and surface tension vanishes, the classical NLS equation is found. The influence of constant vorticity and surface tension on the well-known stability properties of weakly nonlinear wave packets is studied. It is demonstrated that vorticity and surface tension modifies significantly the modulational instability properties of weakly nonlinear plane waves, namely the growth rate and bandwidth. Comparison with a fully nonlinear approach is conducted, too.
Capillary-Physics Mechanism of Elastic-Wave Mobilization of Residual Oil
NASA Astrophysics Data System (ADS)
Beresnev, I. A.; Pennington, W. D.; Turpening, R. M.
2003-12-01
Much attention has been given to the possibility of vibratory mobilization of residual oil as a method of enhanced recovery. The common features of the relevant applications have nonetheless been inconsistency in the results of field tests and the lack of understanding of a physical mechanism that would explain variable experiences. Such a mechanism can be found in the physics of capillary trapping of oil ganglia, driven through the pore channels by an external pressure gradient. Entrapping of ganglia occurs due to the capillary pressure building on the downstream meniscus entering a narrow pore throat. The resulting internal-pressure imbalance acts against the external gradient, which needs to exceed a certain threshold to carry the ganglion through. The ganglion flow thus exhibits the properties of the Bingham (yield-stress) flow, not the Darcy flow. The application of vibrations is equivalent to the addition of an oscillatory forcing to the constant gradient. When this extra forcing acts along the gradient, an instant "unplugging" occurs, while, when the vibration reverses direction, the flow is plugged. This asymmetry results in an average non-zero flow over one period of vibration, which explains the mobilization effect. The minimum-amplitude and maximum-frequency thresholds apply for the mobilization to occur. When the vibration amplitude exceeds a certain "saturation" level, the flow returns to the Darcy regime. The criterion of the mobilization of a particular ganglion involves the parameters of both the medium (pore geometry, interfacial and wetting properties, fluid viscosity) and the oscillatory field (amplitude and frequency). The medium parameters vary widely under natural conditions. It follows that an elastic wave with a given amplitude and frequency will always produce a certain mobilization effect, mobilizing some ganglia and leaving others intact. The exact macroscopic effect is hard to predict, as it will represent a response of the populations
Rogue States and Deterrence Strategy
2009-04-02
would need to dealt with swiftly, harshly and stand as an example to any other state contemplating such activities.33 Deterrence Theory : United States...Response to Rogue State Proliferation There is a difference between nuclear deterrence theory and nuclear deterrence strategy. Patrick Morgan who serves...deter, while the theory concerns the underlying principles on which any strategy is to rest.”34 For the purposes of this paper, the 1994 Department of
Damage Caused by the Rogue Trustee
ERIC Educational Resources Information Center
O'Banion, Terry
2009-01-01
Fifty-nine community college presidents and chancellors in 16 states report on the damage caused by rogue trustees. While the damage to presidents, other trustees, and faculty and staff is alarming, the damage these trustees cause the college suggests that the rogue trustee may be the single most destructive force ever to plague an educational…
Damage Caused by the Rogue Trustee
ERIC Educational Resources Information Center
O'Banion, Terry
2009-01-01
Fifty-nine community college presidents and chancellors in 16 states report on the damage caused by rogue trustees. While the damage to presidents, other trustees, and faculty and staff is alarming, the damage these trustees cause the college suggests that the rogue trustee may be the single most destructive force ever to plague an educational…
NASA Astrophysics Data System (ADS)
de Poyferré, Thibault; Nguyen, Quang-Huy
2016-07-01
We consider the gravity-capillary waves in any dimension and in fluid domains with general bottoms. Using the paradifferential reduction established in [19], we prove Strichartz estimates for solutions to this problem, at a low regularity level such that initially, the velocity field can be non-Lipschitz up to the free surface. We then use those estimates to solve the Cauchy problem at this level of regularity.
Contours of slope as a measure of gravity-capillary wind waves
NASA Astrophysics Data System (ADS)
Cox, C. S.; Zhang, X.
2012-12-01
Contours of both x and y components of water surface slopes can be generated optically. Two horizontal arrays of thin, linear lamps placed a few meters below the water surface are photographed from above. One array, consisting of a group of colored y-parallel lamps produces contours of x-slope. The value of each contour is recognized by its color. The other array, of x -parallel lamps produces contours of y-slope. When the two arrays are pulsed alternately and photographed by a fast camera, the full structure and evolution of the water surface shape can be monitored. In order to register capillaries down to one or two millimeter wavelengths the light pulses must be as short as 200 micro seconds to avoid smearing Adequate light intensity in such short pulses is generated by a row of high intensity light emitting diodes in each linear lamp. LEDs are advantageous because several different colored types are available. permitting many different contours to be generated. When each emitter has a narrow wavelength range, problems from light dispersion and differential color absorption in the water are avoided. In analyzing the photographs, correct identification of the color in the image of each contour is essential. Color sensing cameras have only the three color coordinates, red, green and blue. It is useful to identify each colored contour image by a unit vector in the 3-space of RGB for comparison with the array of expected values. This enables recognition of the most probable color and an estimate of probable error of the choice. If the probable error is large, the contour can then be discarded because of uncertainty of its value.. The conversion from a small number of contours to a continuous representation of the water surface shape is in theory perfect for a band limited spectrum of waves, but in practice inaccuracies, even at the pixel level, in the location of contours produce errors. The spacing of contours of slope is determined by the physical spacing between
NASA Astrophysics Data System (ADS)
Cho, Yeunwoo
2014-11-01
The shedding phenomena of 3-D viscous gravity-capillary solitary waves generated by a moving air-forcing on the surface of deep water are investigated. Near the resonance where the forcing speed is close to 23 cm/s, two kinds of shedding modes are possible; Anti-symmetric and symmetric modes. A relevant theoretical model equation is numerically solved for the identification of shedding of solitary waves, and is analytically studied in terms of their linear stability to transverse perturbations. Furthermore, by tracing trajectories of shed solitary waves, the decay rate of a 3-D solitary wave due to viscous dissipation is estimated. This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2014R1A1A1002441).
NASA Astrophysics Data System (ADS)
Bhattacharjee, P. K.; McDonnell, A. G.; Prabhakar, R.; Yeo, L. Y.; Friend, J.
2011-02-01
Forming capillary bridges of low-viscosity (lsim10 mPa s) fluids is difficult, making the study of their capillary-thinning behavior and the measurement of the fluid's extensional viscosity difficult as well. Current techniques require some time to form a liquid bridge from the stretching of a droplet. Rapidly stretching a liquid bridge using these methods can cause its breakup if the viscosity is too low. Stretching more slowly allows the bridge to thin and break up before a suitable bridge geometry can be established to provide reliable and accurate rheological data. Using a pulsed surface acoustic wave to eject a jet from a sessile droplet, a capillary bridge may be formed in about 7.5 ms, about seven times quicker than current methods. With this approach, capillary bridges may be formed from Newtonian and non-Newtonian fluids having much lower viscosities—water, 0.04% by weight solution of high-molecular-weight (7 MDa) polystyrene in dioctyl phthalate and 0.25% fibrinogen solution in demineralized water, for example. Details of the relatively simple system used to achieve these results are provided, as are experimental results indicating deviations from a Newtonian response by the low-viscosity non-Newtonian fluids used in our study.
Simulation of Rogue Planet Encounters with the Solar System: Is Planet 9 a Captured Rogue?
NASA Astrophysics Data System (ADS)
Vesper, James; Mason, Paul A.
2017-01-01
Rogue, or free-floating, planets may be abundant in the Galaxy. Several have been observed in the solar neighborhood. They have been predicted to even outnumber stars by a large fraction, and may partially account for dark matter in the disk of the galaxy, as the result of circumbinary planet formation. We performed N-body simulations of rogue encounters with the solar system with a variety of impact parameters. We find that Jupiter mass and higher rogues leave a significant imprint on planetary system architecture. Rogue formation models are therefore constrained by observed planetary system structure. We speculate that if rogue planets are abundant as predicted, then, Planet 9 may be a captured rogue.
Understanding the influence of capillary waves on solvation at the liquid-vapor interface.
Rane, Kaustubh; van der Vegt, Nico F A
2016-03-21
This work investigates the question if surface capillary waves (CWs) affect interfacial solvation thermodynamic properties that determine the propensity of small molecules toward the liquid-vapor interface. We focus on (1) the evaluation of these properties from molecular simulations in a practical manner and (2) understanding them from the perspective of theories in solvation thermodynamics, especially solvent reorganization effects. Concerning the former objective, we propose a computational method that exploits the relationship between an external field acting on the liquid-vapor interface and the magnitude of CWs. The system considered contains the solvent, an externally applied field (f) and the solute molecule fixed at a particular location. The magnitude of f is selected to induce changes in CWs. The difference between the solvation free energies computed in the presence and in the absence of f is then shown to quantify the contribution of CWs to interfacial solvation. We describe the implementation of this method in the canonical ensemble by using a Lennard-Jones solvent and a non-ionic solute. Results are shown for three types of solutes that differ in the nature of short-ranged repulsive (hard-core) interactions. Overall, we observe that CWs have a negligible or very small effect on the interfacial solvation free energy of a solute molecule fixed near the liquid-vapor interface for the above systems. We also explain how the effects of pinning or dampening of CWs caused by a fixed solute are effectively compensated and do not contribute to the solvation free energy.
NASA Astrophysics Data System (ADS)
Diorio, J. D.; Watkins, N.; Zuech, J.; Duncan, J. H.
2008-11-01
There have been several recent numerical investigations that have shown the existence of three-dimensional nonlinear solitary surface wave patterns that propagate with speeds less than the minimum wave phase speed prescribed by linear theory (23 cm/s for clean water). In the present study, wave patterns were generated by translating a small-diameter region of high pressure across a water surface. The high-pressure region was created by forcing air through a small-diameter vertically oriented tube attached to a carriage that propelled it horizontally at speeds near 23 cm/s. The wave pattern was measured with a cinematic LIF technique. It was found that a steady solitary wave pattern can exist at speeds below the linear-theory minimum phase speed, while for speeds above the minimum, a pattern of gravity-capillary waves was produced. The solitary wave pattern, which only appeared when the pressure forcing was large, dissipated rapidly when the forcing was turned off. The streamwise dimension of the solitary wave was much smaller than the transverse dimension.
NASA Astrophysics Data System (ADS)
Masnadi, N.; Duncan, J. H.
2012-11-01
The non-linear response of a water free surface to a localized pressure distribution moving at constant speed just below the minimum phase speed (Cmin ~ 23 cm/s) of gravity-capillary waves is studied experimentally in a long tank. The pressure distribution is generated by blowing air onto the water surface via a vertically oriented 2-mm-ID tube that is mounted on an instrument carriage that is in turn set to move along the tank at constant speeds between 20 and 23 cm/s. A cinematic light refraction method is used to obtain quantitative measurements of the surface deformation pattern behind the air jet. At towing speeds just below Cmin, an unsteady V-shaped wave pattern appears behind the pressure source. From observations of the wave pattern evolution, it is found that localized depressions are generated near the pressure source and propagate in pairs along the two arms of the V-shaped pattern. These are eventually shed from the tips of the pattern and rapidly decay. Measurements of the evolution of the speed of these localized depression patterns are compared to existing measurements of the speeds of steady three-dimensional solitary gravity-capillary waves (lumps) that appear behind the pressure source at even lower towing speeds. Supported by the National Science Foundation Division of Ocean Sciences.
NASA Astrophysics Data System (ADS)
Sato, Masanori; Matsuura, Kazuo; Fujii, Toshitaka
2001-02-01
We show the experimental data of selective ethanol separation from ethanol-water solution, using ultrasonic atomization. Pure ethanol could be obtained directly from a solution with several mol% ethanol-water solution at 10 °C. This result can be explained in terms of parametric decay instability of capillary wave, in which high localization and accumulation of acoustic energy occur, leading to ultrasonic atomization. That is, parametric decay instability condenses the energy of longitudinal waves in a highly localized surface area of the capillary wave, and causes ultrasonic atomization.
NASA Astrophysics Data System (ADS)
Majumder, D. P.; Dhar, A. K.
2015-12-01
A nonlinear spectral transport equation for the narrow band Gaussian random surface wave trains is derived from a fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves. The effect of randomness on the stability of deep water capillary gravity waves in the presence of air flowing over water is investigated. The stability is then considered for an initial homogenous wave spectrum having a simple normal form to small oblique long wave length perturbations for a range of spectral widths. An expression for the growth rate of instability is obtained; in which a higher order contribution comes from the fourth order term in the evolution equation, which is responsible for wave induced mean flow. This higher order contribution produces a decrease in the growth rate. The growth rate of instability is found to decrease with the increase of spectral width and the instability disappears if the spectral width increases beyond a certain critical value, which is not influenced by the fourth order term in the evolution equation.
Anderson localisation and optical-event horizons in rogue-soliton generation
NASA Astrophysics Data System (ADS)
Saleh, Mohammed F.; Conti, Claudio; Biancalana, Fabio
2017-03-01
We unveil the relation between the linear Anderson localisation process and nonlinear modulation instability. Anderson localised modes are formed in certain temporal intervals due to the random background noise. Such localised modes seed the formation of solitary waves that will appear during the modulation instability process at those preferred intervals. Afterwards, optical-event horizon effects between dispersive waves and solitons produce an artificial collective acceleration that favours the collision of solitons, which could eventually lead to a rogue-soliton generation.
NASA Astrophysics Data System (ADS)
Cheung, David L.
2011-08-01
While the interaction of colloidal particles (sizes in excess of 100 nm) with liquid interfaces may be understood in terms of continuum models, which are grounded in macroscopic properties such as surface and line tensions, the behaviour of nanoparticles at liquid interfaces may be more complex. Recent simulations [D. L. Cheung and S. A. F. Bon, Phys. Rev. Lett. 102, 066103 (2009)], 10.1103/PhysRevLett.102.066103 of nanoparticles at an idealised liquid-liquid interface showed that the nanoparticle-interface interaction range was larger than expected due, in part, to the action of thermal capillary waves. In this paper, molecular dynamics simulations of a Lennard-Jones nanoparticle in a binary Lennard-Jones mixture are used to confirm that these previous results hold for more realistic models. Furthermore by including attractive interactions between the nanoparticle and the solvent, it is found that the detachment energy decreases as the nanoparticle-solvent attraction increases. Comparison between the simulation results and recent theoretical predictions [H. Lehle and M. Oettel, J. Phys. Condens. Matter 20, 404224 (2008)], 10.1088/0953-8984/20/40/404224 shows that for small particles the incorporation of capillary waves into the predicted effective nanoparticle-interface interaction improves agreement between simulation and theory.
On asymmetric generalized solitary gravity-capillary waves in finite depth.
Gao, T; Wang, Z; Vanden-Broeck, J-M
2016-10-01
Generalized solitary waves propagating at the surface of a fluid of finite depth are considered. The fluid is assumed to be inviscid and incompressible and the flow to be irrotational. Both the effects of gravity and surface tension are included. It is shown that in addition to the classical symmetric waves, there are new asymmetric solutions. These new branches of solutions bifurcate from the branches of symmetric waves. The detailed bifurcation diagrams as well as typical wave profiles are presented.
Henry-Feugeas, Marie Cecile; Koskas, Pierre
2012-07-01
The recent concept of pulse wave encephalopathy helps understanding the cerebral venous remodeling in aging. This so-called periventricular venous collagenosis is an expected mechanical consequence of the age-related changes in arterial pulsations and the mechanical fatigue of vascular smooth muscles. Unlike arteriolar mechanical stress, venular mechanical stress depends on both the blood pulse wave amplitude and the mechanical properties of the environment tissue. Thereby, there is a preferential periventricular location of venous collagenosis and a mechanistic link between venous collagenosis and foci of white matter rarefaction or leukoaraiosis. The recent concept of pulse wave encephalopathy also helps understanding the widening of retinal venules, the "mirror" of cerebral venules, in various manifestations of pulse wave encephalopathy, including progressive leukoara�osis, lacunar and hemorrhagic "pulse wave" strokes, and dementia. Indeed, the age-related chronic increase in arterial pulsations explains subsequent arteriolar myogenic "fatigue", marked attenuation in the arteriolar myogenic tone and abnormal penetration of the insufficiently dampened arterial pulse wave into the venules. Thus, retinal venular widening, a biomarker of advanced pulse wave encephalopathy, is also increasingly recognized as a biomarker for high cardiovascular risk. All these data support a shift in the concept of chronic cerebrovascular disease, from the classical model which is restricted to steno-occlusive cerebrovascular diseases to an enlarged model which would include the pulse wave encephalopathy concept. Thereby, preventing damage to the cerebral microvasculature by an undampened arterial pulse wave will become a logical target for the prevention and treatment of late-onset cognitive decline.
1993-01-01
doVA22202-4302 adto fte Office of Manaoement and BOW, PaperworkcReduction PrOlec (07040188). Wasbfinton, DC 2=63.1. Agency Use Only (Leave Blank). 2...by R . Lerner and G Trigg, VCH Publishers, Inc., New York. References 1. Watson, K. M., 1990. The coupling of surface and internal gravity waves...Creamer, D., F. Henyey, R . Schult, and J. Wright, 1989. Improved linear representation of ocean surface waves. J. Fluid Mech. 205, 135-161. •2:•2•:i
NASA Astrophysics Data System (ADS)
Cho, Seung Il; Lee, Jong Kyu; Yoon, Woon Ha; Lee, Jong O.; Jung, Sung Soo; Seo, Won Chan
The 1-3 piezoelectric composite transducer with the 60% volume fraction of the PZT-5A was fabricated by the dicing-filling method. The electrical and acoustical characteristics of the 1-3 piezoelectric composite transducer were compared and analyzed by the electrical impedance measurements and the pulse-echo method. The mechanical quality coefficient (Q) and the resonant frequency were 18.5 and 1.6 MHz, respectively. The elastic waves generated during glass capillary breakage were observed by 1-3 piezoelectric composite transducer. The observed AE signals are well matched with the perpendicular component of the particle velocity calculated by computer. The observed AE signal and its frequency spectrum show that the pulse-type signals of AE observed by 1-3 piezoelectric composite transducer may be depend on the the vibration mode of thickness with the plate response of the wide band.
A dimension-breaking phenomenon in the theory of steady gravity-capillary water waves.
Groves, M D; Haragus, M; Sun, S M
2002-10-15
The existence of a line solitary-wave solution to the water-wave problem with strong surface-tension effects was predicted on the basis of a model equation in the celebrated 1895 paper by D. J. Korteweg and G. de Vries and rigorously confirmed a century later by C. J. Amick and K. Kirchgässner in 1989. A model equation derived by B. B. Kadomtsev and V. I. Petviashvili in 1970 suggests that the Korteweg-de Vries line solitary wave belongs to a family of periodically modulated solitary waves which have a solitary-wave profile in the direction of motion and are periodic in the transverse direction. This prediction is rigorously confirmed for the full water-wave problem in the present paper. It is shown that the Korteweg-de Vries solitary wave undergoes a dimension-breaking bifurcation that generates a family of periodically modulated solitary waves. The term dimension-breaking phenomenon describes the spontaneous emergence of a spatially inhomogeneous solution of a partial differential equation from a solution which is homogeneous in one or more spatial dimensions.
Foam on troubled water: Capillary induced finite-time arrest of sloshing waves
NASA Astrophysics Data System (ADS)
Viola, Francesco; Brun, P.-T.; Dollet, Benjamin; Gallaire, François
2016-09-01
Interfacial forces exceed gravitational forces on a scale small relative to the capillary length—two millimeters in the case of an air-water interface—and therefore dominate the physics of sub-millimetric systems. They are of paramount importance for various biological taxa and engineering processes where the motion of a liquid meniscus induces a viscous frictional force that exhibits a sublinear dependence in the meniscus velocity, i.e., a power law with an exponent smaller than one. Interested in the fundamental implications of this dependence, we use a liquid-foam sloshing system as a prototype to exacerbate the effect of sublinear friction on the macroscopic mechanics of multi-phase flows. In contrast to classical theory, we uncover the existence of a finite-time singularity in our system yielding the arrest of the fluid's oscillations. We propose a minimal theoretical framework to capture this effect, thereby amending the paradigmatic damped harmonic oscillator model. Our results suggest that, although often not considered at the macroscale, sublinear capillary forces govern the friction at liquid-solid and liquid-liquid interfaces.
78 FR 60375 - Rogue Valley Terminal Railroad Corporation-Corporate Family Transaction Exemption
Federal Register 2010, 2011, 2012, 2013, 2014
2013-10-01
... TRANSPORTATION Surface Transportation Board Rogue Valley Terminal Railroad Corporation--Corporate Family Transaction Exemption Rogue Valley Terminal Railroad Corporation (Rogue Valley),\\1\\ a Class III rail carrier... White City Terminal & Utility Co. (WCTU) and was indirectly controlled by Berkshire Hathaway...
... Why do capillary hemangiomas on the eyelids cause vision problems? Capillary Hemangiomas of the eyelid can cause ... a capillary hemangioma in the eye socket cause vision problems? A capillary hemangioma in the eye socket ( ...
Capillary-wave models and the effective-average-action scheme of functional renormalization group.
Jakubczyk, P
2011-08-01
We reexamine the functional renormalization-group theory of wetting transitions. As a starting point of the analysis we apply an exact equation describing renormalization group flow of the generating functional for irreducible vertex functions. We show how the standard nonlinear renormalization group theory of wetting transitions can be recovered by a very simple truncation of the exact flow equation. The derivation makes all the involved approximations transparent and demonstrates the applicability of the approach in any spatial dimension d≥2. Exploiting the nonuniqueness of the renormalization-group cutoff scheme, we find, however, that the capillary parameter ω is a scheme-dependent quantity below d=3. For d=3 the parameter ω is perfectly robust against scheme variation.
NASA Astrophysics Data System (ADS)
Zhang, Anliang; Zha, Yan; Zhang, Jiansheng
2014-12-01
A new method for converting a microdroplet on a piezoelectric substrate into continuous fluid flow in microchannels is presented. An interdigital transducer with 27.5 MHz center frequency is fabricated on a 1280 yx-LiNbO3 piezoelectric substrate for exciting surface acoustic wave. A PDMS (Polydimethylsiloxane) microchannel is mounted on the piezoelectric substrate. One end of the microchannel is connected with water absorbing paper, while the other end of the microchannel is in touch with a droplet to be converted. The surface acoustic wave is used for controlling the evaporation velocity of the fluid in the microchannel. Part of fluid in the droplet can be entered into the microchannel and transported there due to the evaporation and capillary effects. Red dye solution is used to demonstrate the conversion of the droplet and the transportation of the fluid in the microchannel. Results show that the droplet on the piezoelectric substrate can successfully be converted into continuous fluid. The flow velocity is increased with the power of the electric signal applied to the interdigital transducer. Average flow velocity is 0.0235μl/s when the power of the electric signal is 30.0dBm. The work is helpful for piezoelectric microfluidic devices for biochemical analysis.
Wind driven capillary-gravity waves on Titan's lakes: Hard to detect or non-existent?
NASA Astrophysics Data System (ADS)
Hayes, A. G.; Lorenz, R. D.; Donelan, M. A.; Manga, M.; Lunine, J. I.; Schneider, T.; Lamb, M. P.; Mitchell, J. M.; Fischer, W. W.; Graves, S. D.; Tolman, H. L.; Aharonson, O.; Encrenaz, P. J.; Ventura, B.; Casarano, D.; Notarnicola, C.
2013-07-01
Saturn's moon Titan has lakes and seas of liquid hydrocarbon and a dense atmosphere, an environment conducive to generating wind waves. Cassini observations thus far, however, show no indication of waves. We apply models for wind wave generation and detection to the Titan environment. Results suggest wind speed thresholds at a reference altitude of 10 m of 0.4-0.7 m/s for liquid compositions varying between pure methane and equilibrium mixtures with the atmosphere (ethane has a threshold of 0.6 m/s), varying primarily with liquid viscosity. This reduced threshold, as compared to Earth, results from Titan's increased atmosphere-to-liquid density ratio, reduced gravity and lower surface tension. General Circulation Models (GCMs) predict wind speeds below derived thresholds near equinox, when available observations of lake surfaces have been acquired. Predicted increases in winds as Titan approaches summer solstice, however, will exceed expected thresholds and may provide constraints on lake composition and/or GCM accuracy through the presence or absence of waves during the Cassini Solstice Mission. A two-scale microwave backscatter model suggests that returns from wave-modified liquid hydrocarbon surfaces may be below the pixel-scale noise floor of Cassini radar images, but can be detectable using real-aperture scatterometry, pixel binning and/or observations obtained in a specular geometry.
Collisional radiative model of an argon atmospheric capillary surface-wave discharge
Yanguas-Gil, A.; Cotrino, J.; Gonzalez-Elipe, A.R.
2004-12-01
The characteristics of a microwave surface-wave sustained plasma operated at atmospheric pressure in an open-ended dielectric tube are investigated theoretically as a first step in the development of a self-consistent model for these discharges. The plasma column is sustained in flowing argon. A surface-wave discharge that fills the whole radial cross section of the discharge tube is considered. With experimental electron temperature profiles [Garcia et al., Spectrochim. Acta, Part B 55, 1733 (2000)] the numerical model is used to test the validity of the different approximations and to study the influence of the different kinetic processes and power loss mechanisms on the discharge.
NASA Astrophysics Data System (ADS)
Masnadi, Naeem; Duncan, James H.
2017-01-01
The unsteady response of a water free surface to a localized pressure source moving at constant speed $U$ in the range $0.95c_\\mathrm{min} \\lesssim U \\leq 1.02 c_\\mathrm{min}$, where $c_\\mathrm{min}$ is the minimum phase speed of linear gravity-capillary waves in deep water, is investigated through experiments and numerical simulations. This unsteady response state, which consists of a V-shaped pattern behind the source and features periodic shedding of pairs of depressions from the tips of the V, was first observed qualitatively by Diorio et al. (Phys. Rev. Let., 103, 214502, 2009) and called state III. In the present investigation, cinematic shadowgraph and refraction-based techniques are utilized to measure the temporal evolution of the free surface deformation pattern downstream of the source as it moves along a towing tank, while numerical simulations of the model equation described by Cho et al. (J. Fluid Mech., 672, 288-306, 2011) are used to extend the experimental results over longer times than are possible in the experiments. From the experiments, it is found that the speed-amplitude characteristics and the shape of the depressions are nearly the same as those of the freely propagating gravity-capillary lumps of inviscid potential theory. The decay rate of the depressions is measured from their height-time characteristics, which are well fitted by an exponential decay law with an order 1 decay constant. It is found that the shedding period of the depression pairs decreases with increasing source strength and speed. As the source speed approaches $c_\\mathrm{min}$, this period tends to about 1~s for all source magnitudes. At the low-speed boundary of state III, a new response with unsteady asymmetric shedding of depressions is found. This response is also predicted by the model equation.
The Lifespan of Small Data Solutions in Two Dimensional Capillary Water Waves
NASA Astrophysics Data System (ADS)
Ifrim, Mihaela; Tataru, Daniel
2017-09-01
This article is concerned with the incompressible, irrotational infinite depth water wave equation in two space dimensions, without gravity but with surface tension. We consider this problem expressed in position-velocity potential holomorphic coordinates, and prove that small data solutions have at least cubic lifespan while small localized data leads to global solutions.
NASA Astrophysics Data System (ADS)
Masnadi, Naeem; Cho, Yeunwoo; Duncan, James H.; Akylas, Triantaphyllos
2015-11-01
The non-linear response of a water free surface to a pressure source moving at speeds near the minimum speed of linear gravity-capillary waves (Cmin ~ 23 cm/s) is investigated with experiments and theory. In the experiments, waves are generated by a vertically oriented air-jet that moves at a constant speed over the water surface in a long tank. The 3-D surface shape behind the air-jet is measured using a cinematic refraction-based technique combined with an LIF technique. At towing speeds just below Cmin, an unsteady pattern is formed where localized depressions periodically appear in pairs and move away from the source along the arms of a downstream V-shaped pattern. This behavior is analogous to the periodic shedding of solitary waves upstream of a source moving at the maximum wave speed in shallow water. The gravity-capillary depressions are rapidly damped by viscosity and their speed-amplitude characteristics closely match those from inviscid calculations of gravity-capillary lumps. The shedding frequency of the lumps in the present experiments increases with both increasing towing speed and air-flow rate. Predictions of this behavior using a model equation that incorporates damping and a quadratic nonlinearity are in good agreement with the experiments. The partial support of the National Science Foundation under grant OCE0751853 is gratefully acknowledged.
Wang, Lei; Zhu, Yu-Jie; Qi, Feng-Hua; Li, Min; Guo, Rui
2015-06-01
In this paper, the nonautonomous Lenells-Fokas (LF) model is investigated. The modulational instability analysis of the solutions with variable coefficients in the presence of a small perturbation is studied. Higher-order soliton, breather, earthwormon, and rogue wave solutions of the nonautonomous LF model are derived via the n-fold variable-coefficient Darboux transformation. The solitons and earthwormons display the elastic collisions. It is found that the nonautonomous LF model admits the higher-order periodic rogue waves, composite rogue waves (rogue wave pair), and oscillating rogue waves, whose dynamics can be controlled by the inhomogeneous nonlinear parameters. Based on the second-order rogue wave, a diamond structure consisting of four first-order rogue waves is observed. In addition, the semirational solutions (the mixed rational-exponential solutions) of the nonautonomous LF model are obtained, which can be used to describe the interactions between the rogue waves and breathers. Our results could be helpful for the design of experiments in the optical fiber communications.
Shang, Barry Z; Voulgarakis, Nikolaos K; Chu, Jhih-Wei
2011-07-28
We introduce a multiscale framework to simulate inhomogeneous fluids by coarse-graining an all-atom molecular dynamics (MD) trajectory onto sequential snapshots of hydrodynamic fields. We show that the field representation of an atomistic trajectory is quantitatively described by a dynamic field-theoretic model that couples hydrodynamic fluctuations with a Ginzburg-Landau free energy. For liquid-vapor interfaces of argon and water, the parameters of the field model can be adjusted to reproduce the bulk compressibility and surface tension calculated from the positions and forces of atoms in an MD simulation. These optimized parameters also enable the field model to reproduce the static and dynamic capillary wave spectra calculated from atomistic coordinates at the liquid-vapor interface. In addition, we show that a density-dependent gradient coefficient in the Ginzburg-Landau free energy enables bulk and interfacial fluctuations to be controlled separately. For water, this additional degree of freedom is necessary to capture both the bulk compressibility and surface tension emergent from the atomistic trajectory. The proposed multiscale framework illustrates that bottom-up coarse-graining and top-down phenomenology can be integrated with quantitative consistency to simulate the interfacial fluctuations in nanoscale transport processes.
... using capillary blood sampling. Disadvantages to capillary blood sampling include: Only a limited amount of blood can be drawn using this method. The procedure has some risks (see below). Capillary ...
Tandiono; Ohl, Siew-Wan; Ow, Dave Siak-Wei; Klaseboer, Evert; Wong, Victor V T; Camattari, Andrea; Ohl, Claus-Dieter
2010-07-21
We present a study on achieving intense acoustic cavitation generated by ultrasonic vibrations in polydimethylsiloxane (PDMS) based microfluidic devices. The substrate to which the PDMS is bonded was forced into oscillation with a simple piezoelectric transducer attached at 5 mm from the device to a microscopic glass slide. The transducer was operated at 100 kHz with driving voltages ranging between 20 V and 230 V. Close to the glass surface, pressure and vibration amplitudes of up to 20 bar and 400 nm were measured respectively. It is found that this strong forcing leads to the excitation of nonlinear surface waves when gas-liquid interfaces are present in the microfluidic channels. Also, it is observed that nuclei leading to intense inertial cavitation are generated by the entrapment of gas pockets at those interfaces. Subsequently, cavitation bubble clusters with void fractions of more than 50% are recorded with high-speed photography at up to 250,000 frames/s. The cavitation clusters can be sustained through the continuous injection of gas using a T-junction in the microfluidic device.
Axisymmetric capillary waves on thin annular liquid sheets. II. Spatial development
NASA Astrophysics Data System (ADS)
Mehring, C.; Sirignano, W. A.
2000-06-01
The forced motion of semi-infinite axisymmetric thin inviscid annular liquid sheets, exiting from a nozzle or atomizer into a surrounding void under zero gravity but with constant gas-core pressure is analyzed by means of the reduced-dimension approach described in C. Mehring and W. A. Sirignano [Phys. Fluids 12, 1417 (2000)]. Linear analytical time-dependent ("limit-cycle") solutions to the pure boundary-value problem are presented as well as linear and nonlinear numerical (transient) solutions to the mixed boundary- and initial-value problem of initially undisturbed sheets harmonically forced at the orifice or nozzle exit. Group velocities for the six independent solutions to the linear boundary-value problem are used to determine the location of boundary conditions. Numerical simulations of the linear transient problem are employed to validate these predictions. Parameter studies on sheet breakup and collapse lengths as well as on breakup and collapse times are reported. The dependence on modulation frequency, modulated disturbance amplitude, Weber number, and annular radius is presented for various cases of the mixed problem, i.e., for linearly or nonlinearly stable and unstable, dilationally or sinusoidally forced sheets. Nonlinear effects often have significant effects on breakup times and lengths or on collapse times and lengths. Nonlinear wave forms can deviate substantially from linear predictions resulting in major impacts on the size of the rings and shells that will remain after breakup.
Federal Register 2010, 2011, 2012, 2013, 2014
2010-08-02
... From the Federal Register Online via the Government Publishing Office ] DEPARTMENT OF AGRICULTURE Forest Service Rogue River-Siskiyou National Forest, Oregon; Motorized Vehicle Use on the Rogue River-Siskiyou National Forest; Intent to Prepare a Supplemental Environmental Impact Statement (SEIS) To...
Enhancing optical extreme events through input wave disorder
NASA Astrophysics Data System (ADS)
Pierangeli, D.; Musarra, G.; Di Mei, F.; Di Domenico, G.; Agranat, A. J.; Conti, C.; DelRe, E.
2016-12-01
We demonstrate how the emergence of extreme events strongly depends on the correlation length of the input field distribution. Observing the behavior of optical waves in turbulent photorefractive propagation with partially incoherent excitations, we find that rogue waves are strongly enhanced for a characteristic input correlation scale. Waveform analysis identifies this scale with a characteristic peak-intensity-independent wave size, suggesting a general role played by saturation in the nonlinear response in rogue phenomena.
39. CAVEMAN BRIDGE, ROGUE RIVER, OREGON STATE HIGHWAY 199. GRANTS ...
39. CAVEMAN BRIDGE, ROGUE RIVER, OREGON STATE HIGHWAY 199. GRANTS PASS, JOSEPHINE COUNTY, OREGON. LOOKING SW. - Redwood National & State Parks Roads, California coast from Crescent City to Trinidad, Crescent City, Del Norte County, CA
40. CAVEMAN BRIDGE, ROGUE RIVER, OREGON STATE HIGHWAY 199. GRANTS ...
40. CAVEMAN BRIDGE, ROGUE RIVER, OREGON STATE HIGHWAY 199. GRANTS PASS, JOSEPHINE COUNTY, OREGON. LOOKING S. - Redwood National & State Parks Roads, California coast from Crescent City to Trinidad, Crescent City, Del Norte County, CA
NASA Astrophysics Data System (ADS)
Shiryaeva, S. O.; Grigor'ev, A. I.; Mikheev, G. E.
2017-08-01
We have derived and analyzed the dispersion equation for capillary waves with an arbitrary symmetry (with arbitrary azimuthal numbers) on the surface of a space-charged cylindrical jet of an ideal incompressible dielectric liquid moving relative to an ideal incompressible dielectric medium. It has been proved that the existence of a tangential jump of the velocity field on the jet surface leads to a periodic Kelvin-Helmholtz- type instability at the interface between the media and plays a destabilizing role. The wavenumber ranges of unstable waves and the instability increments depend on the squared velocity of the relative motion and increase with the velocity. With increasing volume charge density, the critical value of the velocity for the emergence of instability decreases. The reduction of the permittivity of the liquid in the jet or an increase in the permittivity of the medium narrows the regions of instability and leads to an increase in the increments. The wavenumber of the most unstable wave increases in accordance with a power law upon an increase in the volume charge density and velocity of the jet. The variations in the permittivities of the jet and the medium produce opposite effects on the wavenumber of the most unstable wave.
Manipulating localized matter waves in multicomponent Bose-Einstein condensates.
Manikandan, K; Muruganandam, P; Senthilvelan, M; Lakshmanan, M
2016-03-01
We analyze vector localized solutions of two-component Bose-Einstein condensates (BECs) with variable nonlinearity parameters and external trap potentials through a similarity transformation technique which transforms the two coupled Gross-Pitaevskii equations into a pair of coupled nonlinear Schrödinger equations with constant coefficients under a specific integrability condition. In this analysis we consider three different types of external trap potentials: a time-independent trap, a time-dependent monotonic trap, and a time-dependent periodic trap. We point out the existence of different interesting localized structures; namely, rogue waves, dark- and bright-soliton rogue waves, and rogue-wave breatherlike structures for the above three cases of trap potentials. We show how the vector localized density profiles in a constant background get deformed when we tune the strength of the trap parameter. Furthermore, we investigate the nature of the trajectories of the nonautonomous rogue waves. We also construct the dark-dark rogue wave solution for the repulsive-repulsive interaction of two-component BECs and analyze the associated characteristics for the three different kinds of traps. We then deduce single-, two-, and three-composite rogue waves for three-component BECs and discuss the correlated characteristics when we tune the strength of the trap parameter for different trap potentials.
Manipulating localized matter waves in multicomponent Bose-Einstein condensates
NASA Astrophysics Data System (ADS)
Manikandan, K.; Muruganandam, P.; Senthilvelan, M.; Lakshmanan, M.
2016-03-01
We analyze vector localized solutions of two-component Bose-Einstein condensates (BECs) with variable nonlinearity parameters and external trap potentials through a similarity transformation technique which transforms the two coupled Gross-Pitaevskii equations into a pair of coupled nonlinear Schrödinger equations with constant coefficients under a specific integrability condition. In this analysis we consider three different types of external trap potentials: a time-independent trap, a time-dependent monotonic trap, and a time-dependent periodic trap. We point out the existence of different interesting localized structures; namely, rogue waves, dark- and bright-soliton rogue waves, and rogue-wave breatherlike structures for the above three cases of trap potentials. We show how the vector localized density profiles in a constant background get deformed when we tune the strength of the trap parameter. Furthermore, we investigate the nature of the trajectories of the nonautonomous rogue waves. We also construct the dark-dark rogue wave solution for the repulsive-repulsive interaction of two-component BECs and analyze the associated characteristics for the three different kinds of traps. We then deduce single-, two-, and three-composite rogue waves for three-component BECs and discuss the correlated characteristics when we tune the strength of the trap parameter for different trap potentials.
Capillary oscillations on liquid jets
NASA Astrophysics Data System (ADS)
Wetsel, Grover C.
1980-07-01
Capillary oscillations on modulated liquid jets have been investigated using laser illumination and electronic detection of the magnified jet shadow. The amplitudes of several wave harmonics of a growing spatial instability were measured as a function of distance from the orifice for a range of jet velocities and initial-disturbance amplitudes. The experimentally determined growth rates at the fundamental frequency are compared with theories of capillary-wave propagation. An empirically derived explanation of the suppression of satellite formation is given. Experimental evidence for infinite-wavelength capillary oscillations is reported; a description of these oscillations in terms of the Rayleigh theory is presented.
Simulation of Arrhythmogenic Effect of Rogue RyRs in Failing Heart by Using a Coupled Model
Lu, Luyao; Xia, Ling; Zhu, Xiuwei
2012-01-01
Cardiac cells with heart failure are usually characterized by impairment of Ca2+ handling with smaller SR Ca2+ store and high risk of triggered activities. In this study, we developed a coupled model by integrating the spatiotemporal Ca2+ reaction-diffusion system into the cellular electrophysiological model. With the coupled model, the subcellular Ca2+ dynamics and global cellular electrophysiology could be simultaneously traced. The proposed coupled model was then applied to study the effects of rogue RyRs on Ca2+ cycling and membrane potential in failing heart. The simulation results suggested that, in the presence of rogue RyRs, Ca2+ dynamics is unstable and Ca2+ waves are prone to be initiated spontaneously. These release events would elevate the membrane potential substantially which might induce delayed afterdepolarizations or triggered action potentials. Moreover, the variation of membrane potential depolarization is indicated to be dependent on the distribution density of rogue RyR channels. This study provides a new possible arrhythmogenic mechanism for heart failure from subcellular to cellular level. PMID:23056145
Sherer, Brett M.
2003-03-24
Vegetation Management for the Bandon-Rogue-Gold Beach transmission line corridor. This corridor includes the Bandon-Rogue #1 115 kilovolt transmission line from Bandon Substation to Rogue Substation and the Rogue-Gold Beach #1 and #2 115 kilovolt transmission lines, starting at Rogue Substation and ending at Gold Beach Substation.
Functional description of signal processing in the Rogue GPS receiver
NASA Technical Reports Server (NTRS)
Thomas, J. B.
1988-01-01
Over the past year, two Rogue GPS prototype receivers have been assembled and successfully subjected to a variety of laboratory and field tests. A functional description is presented of signal processing in the Rogue receiver, tracing the signal from RF input to the output values of group delay, phase, and data bits. The receiver can track up to eight satellites, without time multiplexing among satellites or channels, simultaneously measuring both group delay and phase for each of three channels (L1-C/A, L1-P, L2-P). The Rogue signal processing described requires generation of the code for all three channels. Receiver functional design, which emphasized accuracy, reliability, flexibility, and dynamic capability, is summarized. A detailed functional description of signal processing is presented, including C/A-channel and P-channel processing, carrier-aided averaging of group delays, checks for cycle slips, acquistion, and distinctive features.
Identification of rogue datasets in serial crystallography.
Assmann, Greta; Brehm, Wolfgang; Diederichs, Kay
2016-06-01
Advances in beamline optics, detectors and X-ray sources allow new techniques of crystallographic data collection. In serial crystallography, a large number of partial datasets from crystals of small volume are measured. Merging of datasets from different crystals in order to enhance data completeness and accuracy is only valid if the crystals are isomorphous, i.e. sufficiently similar in cell parameters, unit-cell contents and molecular structure. Identification and exclusion of non-isomorphous datasets is therefore indispensable and must be done by means of suitable indicators. To identify rogue datasets, the influence of each dataset on CC1/2 [Karplus & Diederichs (2012 ▸). Science, 336, 1030-1033], the correlation coefficient between pairs of intensities averaged in two randomly assigned subsets of observations, is evaluated. The presented method employs a precise calculation of CC1/2 that avoids the random assignment, and instead of using an overall CC1/2, an average over resolution shells is employed to obtain sensible results. The selection procedure was verified by measuring the correlation of observed (merged) intensities and intensities calculated from a model. It is found that inclusion and merging of non-isomorphous datasets may bias the refined model towards those datasets, and measures to reduce this effect are suggested.
NASA Astrophysics Data System (ADS)
Miller, Douglas L.; Dou, Chunyan; Raghavendran, Krishnan
Pulsed ultrasound was found to induce pulmonary capillary hemorrhage (PCH) in mice about 25 years ago but remains a poorly understood risk factor for pulmonary diagnostic ultrasound. In early research using laboratory fixed beam ultrasound, thresholds for PCH had frequency variation from 1-4 MHz similar to the Mechanical Index. In recent research, thresholds for B mode diagnostic ultrasound from 1.5-12 MHz had little dependence on frequency. To compare the diagnostic ultrasound method to laboratory pulsed exposure, thresholds for fixed beam ultrasound were determined using comparable methods at 1.5 and 7.5 MHz. PCH thresholds were lower for simple fixed-beam pulse modes than for B mode and in approximate agreement with early research. However, for comparable timing parameters, PCH thresholds had little dependence on ultrasonic frequency. These findings suggest that the MI may not be directly useful as a dosimetric parameter for safety guidance in pulmonary ultrasound.
Short duration microlensing events: Searching for rogue planets
NASA Astrophysics Data System (ADS)
St. Laurent, Kathryn E.; Di Stefano, Rosanne; Primini, Francis A.; Lew, Wei Peng; Gau, Lai Su; Benson, Sophie
2015-01-01
Einstein described gravitational microlensing in 1936, at the same time suggesting it to be an unobservable phenomenon. He did not foresee technological advancements that would lead to microlensing becoming a productive tool for astronomy. Of particular interest may be the role it has begun to play in the discovery of rogue planets - exoplanets that are not bound to a star or stars. Rogue planets may be formed independently, or they may be formed in the confines of a stellar system and then ejected by gravitational interactions. Currently fewer than a dozen rogue planets are known but estimates of their abundance conservatively start at double the number of stars in our galaxy.The Optical Gravitational Lensing Experiment (OGLE) and Microlensing Observations in Astrophysics (MOA) teams have collectively detected approximately 2500 events this year alone. A significant portion of these events are of short duration, with an Einstein crossing time of less than 10 days. Microlensing events generally occur on a timescale of weeks to months, so short duration events are an interesting class for study, particularly with regard to searches for rogue planets. We have undertaken a systematic study and categorization of the short duration microlensing events from recent OGLE and MOA alerts, with a special eye to identifying exoplanet candidates.
Hamida, Tarek; Babadagli, Tayfun
2007-09-01
Numerous studies done in the last four decades have demonstrated that acoustic stimulation may enhance recovery in oil reservoirs. This technology is not only technically feasible, but also serves as an economical, environmentally friendly alternative to currently accepted enhanced oil recovery (EOR) method. It requires low capital expenditure, and yields almost immediate improvement without any additional EOR agents. Despite a vast body of empirical and theoretical support, this method lacks sufficient understanding to make meaningful and consistent engineering predictions. This is in part due to the complex nature of the physical processes involved, as well as due to a shortage of fundamental/experimental research. Much of what the authors believe is happening within acoustically stimulated porous media is speculative and theoretical. This paper focuses on the effects of ultrasound on the interfacial forces between immiscible fluids. Capillary (spontaneous) imbibition of an aqueous phase into oil (or air)-saturated Berea sandstone and Indiana limestone samples experiments were conducted. Solutions of water, brine (15,000 and 150,000 ppm NaCl), anionic surfactant (sodium dodecyl diphenyloxide disulfonate), nonionic surfactant (alcohol ethoxylate) and polymer (xanthan gum) were prepared as the aqueous phase. Both counter-current and co-current geometries were tested. Due to the intrinsically unforced, gentle nature of the process, and their strong dependence on wettability, interfacial tension, viscosity and density, such experiments provide valuable insight into some of the governing mechanisms behind ultrasonic stimulation.
NASA Astrophysics Data System (ADS)
Ambler, Michael; Vorselaars, Bart; Allen, Michael P.; Quigley, David
2017-02-01
We apply the capillary wave method, based on measurements of fluctuations in a ribbon-like interfacial geometry, to determine the solid-liquid interfacial free energy for both polytypes of ice I and the recently proposed ice 0 within a mono-atomic model of water. We discuss various choices for the molecular order parameter, which distinguishes solid from liquid, and demonstrate the influence of this choice on the interfacial stiffness. We quantify the influence of discretisation error when sampling the interfacial profile and the limits on accuracy imposed by the assumption of quasi one-dimensional geometry. The interfacial free energies of the two ice I polytypes are indistinguishable to within achievable statistical error and the small ambiguity which arises from the choice of order parameter. In the case of ice 0, we find that the large surface unit cell for low index interfaces constrains the width of the interfacial ribbon such that the accuracy of results is reduced. Nevertheless, we establish that the interfacial free energy of ice 0 at its melting temperature is similar to that of ice I under the same conditions. The rationality of a core-shell model for the nucleation of ice I within ice 0 is questioned within the context of our results.
Ambler, Michael; Vorselaars, Bart; Allen, Michael P; Quigley, David
2017-02-21
We apply the capillary wave method, based on measurements of fluctuations in a ribbon-like interfacial geometry, to determine the solid-liquid interfacial free energy for both polytypes of ice I and the recently proposed ice 0 within a mono-atomic model of water. We discuss various choices for the molecular order parameter, which distinguishes solid from liquid, and demonstrate the influence of this choice on the interfacial stiffness. We quantify the influence of discretisation error when sampling the interfacial profile and the limits on accuracy imposed by the assumption of quasi one-dimensional geometry. The interfacial free energies of the two ice I polytypes are indistinguishable to within achievable statistical error and the small ambiguity which arises from the choice of order parameter. In the case of ice 0, we find that the large surface unit cell for low index interfaces constrains the width of the interfacial ribbon such that the accuracy of results is reduced. Nevertheless, we establish that the interfacial free energy of ice 0 at its melting temperature is similar to that of ice I under the same conditions. The rationality of a core-shell model for the nucleation of ice I within ice 0 is questioned within the context of our results.
Compton, S W; Brownlee, R G
1988-05-01
While capillary electrophoresis, or historically related techniques, have been used for over a century, and recognition of the value of this separation methodology has certainly grown rapidly in the past few years, the technique has generally been used by analytical chemists, particularly in Europe and Japan, and small groups of researchers in the United States. Many of the basic instrumentation problems have been solved only relatively recently, and researchers using capillary electrophoresis are now turning their attention to studying specific applications which demonstrate the potential versatility of this electrophoretic technique. The appearance of standardized commercial instrumentation is imminent. With the availability of such technology, capillary electrophoresis will no longer be an academic curiosity, but rather a tool with the potential for routine separations of diverse samples of interest to analyst, researcher, and clinician.
Rational solutions to the KPI equation and multi rogue waves
NASA Astrophysics Data System (ADS)
Gaillard, Pierre
2016-04-01
We construct here rational solutions to the Kadomtsev-Petviashvili equation (KPI) as a quotient of two polynomials in x, y and t depending on several real parameters. This method provides an infinite hierarchy of rational solutions written in terms of polynomials of degrees 2 N(N + 1) in x, y and t depending on 2 N - 2 real parameters for each positive integer N. We give explicit expressions of the solutions in the simplest cases N = 1 and N = 2 and we study the patterns of their modulus in the (x , y) plane for different values of time t and parameters.
Breatherlike solitons extracted from the Peregrine rogue wave.
Yang, Guangye; Wang, Yan; Qin, Zhenyun; Malomed, Boris A; Mihalache, Dumitru; Li, Lu
2014-12-01
Based on the Peregrine solution (PS) of the nonlinear Schrödinger (NLS) equation, the evolution of rational fraction pulses surrounded by zero background is investigated. These pulses display the behavior of a breatherlike solitons. We study the generation and evolution of such solitons extracted, by means of the spectral-filtering method, from the PS in the model of the optical fiber with realistic values of coefficients accounting for the anomalous dispersion, Kerr nonlinearity, and higher-order effects. The results demonstrate that the breathing solitons stably propagate in the fibers. Their robustness against small random perturbations applied to the initial background is demonstrated too.
Localized waves in three-component coupled nonlinear Schrödinger equation
NASA Astrophysics Data System (ADS)
Xu, Tao; Chen, Yong
2016-09-01
We study the generalized Darboux transformation to the three-component coupled nonlinear Schrödinger equation. First- and second-order localized waves are obtained by this technique. In first-order localized wave, we get the interactional solutions between first-order rogue wave and one-dark, one-bright soliton respectively. Meanwhile, the interactional solutions between one-breather and first-order rogue wave are also given. In second-order localized wave, one-dark-one-bright soliton together with second-order rogue wave is presented in the first component, and two-bright soliton together with second-order rogue wave are gained respectively in the other two components. Besides, we observe second-order rogue wave together with one-breather in three components. Moreover, by increasing the absolute values of two free parameters, the nonlinear waves merge with each other distinctly. These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system. Project supported by the Global Change Research Program of China (Grant No. 2015CB953904), the National Natural Science Foundation of China (Grant Nos. 11275072 and 11435005), the Doctoral Program of Higher Education of China (Grant No. 20120076110024), the Network Information Physics Calculation of Basic Research Innovation Research Group of China (Grant No. 61321064), and Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things, China (Grant No. ZF1213).
The rogue nature of hiatuses in a global warming climate
NASA Astrophysics Data System (ADS)
Sévellec, F.; Sinha, B.; Skliris, N.
2016-08-01
The nature of rogue events is their unlikelihood and the recent unpredicted decade-long slowdown in surface warming, the so-called hiatus, may be such an event. However, given decadal variability in climate, global surface temperatures were never expected to increase monotonically with increasing radiative forcing. Here surface air temperature from 20 climate models is analyzed to estimate the historical and future likelihood of hiatuses and "surges" (faster than expected warming), showing that the global hiatus of the early 21st century was extremely unlikely. A novel analysis of future climate scenarios suggests that hiatuses will almost vanish and surges will strongly intensify by 2100 under a "business as usual" scenario. For "CO2 stabilisation" scenarios, hiatus, and surge characteristics revert to typical 1940s values. These results suggest to study the hiatus of the early 21st century and future reoccurrences as rogue events, at the limit of the variability of current climate modelling capability.
NSLS-II BPM System Protection from Rogue Mode Coupling
Blednykh, A.; Bach, B.; Borrelli, A.; Ferreira, M.; Hseuh, H.-C.; Hetzel, C.; Kosciuk, B.; Krinsky, S.; Singh, O.; Vetter, K.
2011-03-28
Rogue mode RF shielding has been successfully designed and implemented into the production multipole vacuum chambers. In order to avoid systematic errors in the NSLS-II BPM system we introduced frequency shift of HOM's by using RF metal shielding located in the antechamber slot of each multipole vacuum chamber. To satisfy the pumping requirement the face of the shielding has been perforated with roughly 50 percent transparency. It stays clear of synchrotron radiation in each chamber.
Two-color walking Peregrine solitary waves.
Baronio, Fabio; Chen, Shihua; Mihalache, Dumitru
2017-09-15
We study the extreme localization of light, evolving upon a non-zero background, in two-color parametric wave interaction in nonlinear quadratic media. We report the existence of quadratic Peregrine solitary waves, in the presence of significant group-velocity mismatch between the waves (or Poynting vector beam walk-off), in the regime of cascading second-harmonic generation. This finding opens a novel path for the experimental demonstration of extreme rogue waves in ultrafast quadratic nonlinear optics.
Clementi, Francesco; Palade, George E.
1969-01-01
Perfusion of the fenestrated capillaries of the intestinal mucosa of the rat with 0.05–0.1 M EDTA removes the diaphragms of the endothelial cells and detaches these cells from one another and from the basement membrane. The latter, even when completely denuded, retains effectively particles of 340 A (average) diameter. Perfusion with histamine (1 µg/ml) results in partial removal of fenestral diaphragms, occasional detachment of the endothelium from the basement membrane, and focal separation of endothelial intercellular junctions. PMID:4979362
Signal-processing theory for the TurboRogue receiver
NASA Technical Reports Server (NTRS)
Thomas, J. B.
1995-01-01
Signal-processing theory for the TurboRogue receiver is presented. The signal form is traced from its formation at the GPS satellite, to the receiver antenna, and then through the various stages of the receiver, including extraction of phase and delay. The analysis treats the effects of ionosphere, troposphere, signal quantization, receiver components, and system noise, covering processing in both the 'code mode' when the P code is not encrypted and in the 'P-codeless mode' when the P code is encrypted. As a possible future improvement to the current analog front end, an example of a highly digital front end is analyzed.
Cohen, Caroline; Mouterde, Timothée; Quéré, David; Clanet, Christophe
2015-01-01
The contraction of a muscle generates a force that decreases when increasing the contraction velocity. This “hyperbolic” force–velocity relationship has been known since the seminal work of A. V. Hill in 1938 [Hill AV (1938) Proc R Soc Lond B Biol Sci 126(843):136–195]. Hill’s heuristic equation is still used, and the sliding-filament theory for the sarcomere [Huxley H, Hanson J (1954) Nature 173(4412):973–976; Huxley AF, Niedergerke R (1954) Nature 173(4412):971–973] suggested how its different parameters can be related to the molecular origin of the force generator [Huxley AF (1957) Prog Biophys Biophys Chem 7:255–318; Deshcherevskiĭ VI (1968) Biofizika 13(5):928–935]. Here, we develop a capillary analog of the sarcomere obeying Hill’s equation and discuss its analogy with muscles. PMID:25944938
Deep-Water Waves: on the Nonlinear Schrödinger Equation and its Solutions
NASA Astrophysics Data System (ADS)
Vitanov, Nikolay K.; Chabchoub, Amin; Hoffmann, Norbert
2013-06-01
We present a brief discussion on the nonlinear Schrödinger equation for modelling the propagation of the deep-water wavetrains and a discussion on its doubly-localized breather solutions, that can be connected to the sudden formation of extreme waves, also known as rogue waves or freak waves.
Paramecium swimming in capillary tube
NASA Astrophysics Data System (ADS)
Jana, Saikat; Um, Soong Ho; Jung, Sunghwan
2012-04-01
Swimming organisms in their natural habitat need to navigate through a wide range of geometries and chemical environments. Interaction with boundaries in such situations is ubiquitous and can significantly modify the swimming characteristics of the organism when compared to ideal laboratory conditions. We study the different patterns of ciliary locomotion in glass capillaries of varying diameter and characterize the effect of the solid boundaries on the velocities of the organism. Experimental observations show that Paramecium executes helical trajectories that slowly transition to straight lines as the diameter of the capillary tubes decreases. We predict the swimming velocity in capillaries by modeling the system as a confined cylinder propagating longitudinal metachronal waves that create a finite pressure gradient. Comparing with experiments, we find that such pressure gradient considerations are necessary for modeling finite sized ciliary organisms in restrictive geometries.
NASA Astrophysics Data System (ADS)
Ali Shan, S.; El-Tantawy, S. A.
2016-07-01
In this work, we examine the nonlinear propagation of planar ion-acoustic freak waves in an unmagnetized plasma consisting of cold positive ions and superthermal electrons subjected to cold positrons beam. For this purpose, the reductive perturbation method is used to derive a nonlinear Schrödinger equation (NLSE) for the evolution of electrostatic potential wave. We determine the domain of the plasma parameters where the rogue waves exist. The effect of the positron beam on the modulational instability of the ion-acoustic rogue waves is discussed. It is found that the region of the modulational stability is enhanced with the increase of positron beam speed and positron population. Second as positrons beam increases the nonlinearities of the plasma system, large amplitude ion acoustic rogue waves are pointed out. The present results will be helpful in providing a good fit between the theoretical analysis and real applications in future laboratory plasma experiments.
Ali Shan, S.; El-Tantawy, S. A.
2016-07-15
In this work, we examine the nonlinear propagation of planar ion-acoustic freak waves in an unmagnetized plasma consisting of cold positive ions and superthermal electrons subjected to cold positrons beam. For this purpose, the reductive perturbation method is used to derive a nonlinear Schrödinger equation (NLSE) for the evolution of electrostatic potential wave. We determine the domain of the plasma parameters where the rogue waves exist. The effect of the positron beam on the modulational instability of the ion-acoustic rogue waves is discussed. It is found that the region of the modulational stability is enhanced with the increase of positron beam speed and positron population. Second as positrons beam increases the nonlinearities of the plasma system, large amplitude ion acoustic rogue waves are pointed out. The present results will be helpful in providing a good fit between the theoretical analysis and real applications in future laboratory plasma experiments.
Rogue Worlds and the Power of the Dark Side
NASA Astrophysics Data System (ADS)
Steffen, Jason H.
2011-09-01
Many models for WIMP dark matter (Weakly Interacting Massive Particles) have both weak-scale couplings to nucleons and the capacity to annihilate into standard-model particles. A consequence of these properties is that dark matter particles near the cores of galaxies can, through nuclear scattering in a planet interior, lose energy and become gravitationally bound to the planet. These dark matter particles can then annihilate into energetic standard model particles providing a significant source of internal heat. In some situations, dark matter annihilations and a modest greenhouse effect can raise the surface temperature of a super-Earth planet above the melting point of water. These temperatures can be sustained for many trillions of years. Thus, it may be possible for even rogue super-Earths, with no stellar host, to sustain habitable conditions almost indefinitely.
The local properties of ocean surface waves by the phase-time method
NASA Technical Reports Server (NTRS)
Huang, Norden E.; Long, Steven R.; Tung, Chi-Chao; Donelan, Mark A.; Yuan, Yeli; Lai, Ronald J.
1992-01-01
A new approach using phase information to view and study the properties of frequency modulation, wave group structures, and wave breaking is presented. The method is applied to ocean wave time series data and a new type of wave group (containing the large 'rogue' waves) is identified. The method also has the capability of broad applications in the analysis of time series data in general.
Nonlinearity Role in Long-Term Interaction of the Ocean Gravity Waves
2012-09-30
the Nonlinear Schrodinger equation and its exact solutions. Numerical simulations of the fully nonlinear Euler equation have also been performed in... Schrodinger breathers, Proceedings of ECMWF Workshop on "Ocean Waves" - 25 to 27 June 2012 [published] • Onorato, M. and Proment, D.; Approximate rogue wave
Turbulent Transitions in Optical Wave Propagation
NASA Astrophysics Data System (ADS)
Pierangeli, D.; Di Mei, F.; Di Domenico, G.; Agranat, A. J.; Conti, C.; DelRe, E.
2016-10-01
We report the direct observation of the onset of turbulence in propagating one-dimensional optical waves. The transition occurs as the disordered hosting material passes from being linear to one with extreme nonlinearity. As the response grows, increased wave interaction causes a modulational unstable quasihomogeneous flow to be superseded by a chaotic and spatially incoherent one. Statistical analysis of high-resolution wave behavior in the turbulent regime unveils the emergence of concomitant rogue waves. The transition, observed in a photorefractive ferroelectric crystal, introduces a new and rich experimental setting for the study of optical wave turbulence and information transport in conditions dominated by large fluctuations and extreme nonlinearity.
Turbulent Transitions in Optical Wave Propagation.
Pierangeli, D; Di Mei, F; Di Domenico, G; Agranat, A J; Conti, C; DelRe, E
2016-10-28
We report the direct observation of the onset of turbulence in propagating one-dimensional optical waves. The transition occurs as the disordered hosting material passes from being linear to one with extreme nonlinearity. As the response grows, increased wave interaction causes a modulational unstable quasihomogeneous flow to be superseded by a chaotic and spatially incoherent one. Statistical analysis of high-resolution wave behavior in the turbulent regime unveils the emergence of concomitant rogue waves. The transition, observed in a photorefractive ferroelectric crystal, introduces a new and rich experimental setting for the study of optical wave turbulence and information transport in conditions dominated by large fluctuations and extreme nonlinearity.
Laboratory study of peculiarities of the freak-wave generation
NASA Astrophysics Data System (ADS)
Rodin, Artem; Tyugin, Dmitry; Kurkin, Andrey; Kurkina, Oxana; Didenkulova, Ira
2017-04-01
A new wave tank for wave measurements in experimental conditions is installed in the year of 2015 in the Nizhny Novgorod State Technical University n.a. R.E. Alekseev, which is now beginning to run. In recent study series of experiments were conducted in order to reproduce analytic solutions of approximate theories in the case of strong nonlinearity. In particular experimental work is aiming to test methods of extreme wave forecasting on the background of the irregular wave field. The statistics of rogue wave heights is studied together with the statistics of rogue wave crests and rogue wave troughs. The full length of the wave tank is 7 meters, which includes the size of the working area of 6.5 m and the rest occupies the hinged-type wavemaker. Width of the wave tank is 0.5 m and height is 1 m. The wavemaker has the amplitude in the range of 0-15 degrees and frequency in the range of 0.1 - 10 Hz. The wave tank set up contains also the basic instrumentation and video fixation system including a high-speed camera. The height of waves generated during strongly nonlinear regimes is comparable to the unperturbed depth of the water in the wave tank. In order to prevent the wave reflection from the walls laboratory facility is equipped with an effective removable louvered wave absorber, mounted on opposite end of the wave tank. Construction of wave absorber has adjustable height and tilt in order to select the most effective way of wave absorption. With this equipment conditions for different wave modes can be arranged: breaking waves, full absorbtion, as well as partial reflection that corresponds to different modes of wave field in the coastal zone. The research was supported within the framework of the Russian Science Foundation grant Nr 16-17-00041.
Altimeter Observations of Baroclinic Oceanic Inertia-Gravity Wave Turbulence
NASA Technical Reports Server (NTRS)
Glazman, R. E.; Cheng, B.
1996-01-01
For a wide range of nonlinear wave processes - from capillary to planetary waves - theory predicts the existence of Kolmogorov-type spectral cascades of energy and other conserved quantities occuring via nonlinear resonant wave-wave interactions. So far, observations of wave turbulence (WT) have been limited to small-scale processes such as surface gravity and capillary-gravity waves.
Reconstruction of arbitrary surface wave fields by refraction global method in a wave tank
NASA Astrophysics Data System (ADS)
Garcia, Heynert; Ludu, Andrei
2015-11-01
We use a new photographic procedure and design to construct reliable system for measurement and analysis of various surface water waves in a wave tank, including rogue and tsunami-like waves. The image of a grid placed at the bottom of the tank (3 feet maximum depth) is deformed by the surface waves and recorded on one or two cameras placed above the water. The measurement of the height and slope of the surface waves is determined by inverse refraction calculations plus the calibration information at four grouped points from capacitive level gauges. This research was supported by ERAU INTERNAL STUDENT RESEARCH AWARD.
Mach-like capillary-gravity wakes.
Moisy, Frédéric; Rabaud, Marc
2014-08-01
We determine experimentally the angle α of maximum wave amplitude in the far-field wake behind a vertical surface-piercing cylinder translated at constant velocity U for Bond numbers Bo(D)=D/λ(c) ranging between 0.1 and 4.2, where D is the cylinder diameter and λ(c) the capillary length. In all cases the wake angle is found to follow a Mach-like law at large velocity, α∼U(-1), but with different prefactors depending on the value of Bo(D). For small Bo(D) (large capillary effects), the wake angle approximately follows the law α≃c(g,min)/U, where c(g,min) is the minimum group velocity of capillary-gravity waves. For larger Bo(D) (weak capillary effects), we recover a law α∼√[gD]/U similar to that found for ship wakes at large velocity [Rabaud and Moisy, Phys. Rev. Lett. 110, 214503 (2013)]. Using the general property of dispersive waves that the characteristic wavelength of the wave packet emitted by a disturbance is of order of the disturbance size, we propose a simple model that describes the transition between these two Mach-like regimes as the Bond number is varied. We show that the new capillary law α≃c(g,min)/U originates from the presence of a capillary cusp angle (distinct from the usual gravity cusp angle), along which the energy radiated by the disturbance accumulates for Bond numbers of order of unity. This model, complemented by numerical simulations of the surface elevation induced by a moving Gaussian pressure disturbance, is in qualitative agreement with experimental measurements.
Mach-like capillary-gravity wakes
NASA Astrophysics Data System (ADS)
Moisy, Frédéric; Rabaud, Marc
2014-08-01
We determine experimentally the angle α of maximum wave amplitude in the far-field wake behind a vertical surface-piercing cylinder translated at constant velocity U for Bond numbers BoD=D/λc ranging between 0.1 and 4.2, where D is the cylinder diameter and λc the capillary length. In all cases the wake angle is found to follow a Mach-like law at large velocity, α ˜U-1, but with different prefactors depending on the value of BoD. For small BoD (large capillary effects), the wake angle approximately follows the law α ≃cg ,min/U, where cg ,min is the minimum group velocity of capillary-gravity waves. For larger BoD (weak capillary effects), we recover a law α ˜√gD /U similar to that found for ship wakes at large velocity [Rabaud and Moisy, Phys. Rev. Lett. 110, 214503 (2013), 10.1103/PhysRevLett.110.214503]. Using the general property of dispersive waves that the characteristic wavelength of the wave packet emitted by a disturbance is of order of the disturbance size, we propose a simple model that describes the transition between these two Mach-like regimes as the Bond number is varied. We show that the new capillary law α ≃cg ,min/U originates from the presence of a capillary cusp angle (distinct from the usual gravity cusp angle), along which the energy radiated by the disturbance accumulates for Bond numbers of order of unity. This model, complemented by numerical simulations of the surface elevation induced by a moving Gaussian pressure disturbance, is in qualitative agreement with experimental measurements.
Forecasting extreme wave events in moderate and high sea states
NASA Astrophysics Data System (ADS)
Magnusson, Anne Karin; Reistad, Magnar; Bitner-Gregersen, Elzbieta Maria
2013-04-01
Empirical studies on measurements have not yet come to conclusive relations between occurrence of rogue waves and - parameters which could be forecasted . Theoretical and tank experiments have demonstrated that high spectral peakedness and low spectral width combined (high Benjamin-Feir instability index, Onorato et al., 2006) give higher probability of rogue wave occurrence. Directional spread seems to reduce the probability of occurrence of rogue waves in these studies. Many years of experience with forecasting and discussions with people working in ocean environment indicate that rogue waves may as well occur in crossing seas. This was also indicated in a study in the Maxwave project (Toffoli et al., 2003) and the EXTREME SEAS project (Toffoli et al., 2011). We have here experimented with some indexes describing both high BFI and crossing seas and run the WAM model for some North Sea storm cases. Wave distributions measured at Ekofisk are analysed in the different cases. References • Onorato, M., Osborne, A., Serio, M., Cavaleri, L., Brandini, C., and Stansberg, C.: Extreme waves, modulational instability and second order theory: wave flume experiments on irregular waves,Europ. J. Mech. B/Fluids, 25, 586-601, 2006. • Toffoli, A., Lefevre, J.M., Monbaliu, J., Savina, H., and Bitner-Gregersen, E., "Freak Waves:Clues for Prediction in Ship Accidents?", Proc. ISOPE'2003 Conf. Hawai, USA, 2003. • Toffoli A., Bitner-Gregersen E. M., Osborne A. R., Serio M. Monbaliu J., Onorato M. (2011) Extreme Waves in Random Crossing Seas: Laboratory Experiments and Numerical Simulations. Geophys. Res. Lett., Vol. 38, L06605, 5 pp. doi: 10.1029/2011.
Multiple capillary biochemical analyzer
Dovichi, N.J.; Zhang, J.Z.
1995-08-08
A multiple capillary analyzer allows detection of light from multiple capillaries with a reduced number of interfaces through which light must pass in detecting light emitted from a sample being analyzed, using a modified sheath flow cuvette. A linear or rectangular array of capillaries is introduced into a rectangular flow chamber. Sheath fluid draws individual sample streams through the cuvette. The capillaries are closely and evenly spaced and held by a transparent retainer in a fixed position in relation to an optical detection system. Collimated sample excitation radiation is applied simultaneously across the ends of the capillaries in the retainer. Light emitted from the excited sample is detected by the optical detection system. The retainer is provided by a transparent chamber having inward slanting end walls. The capillaries are wedged into the chamber. One sideways dimension of the chamber is equal to the diameter of the capillaries and one end to end dimension varies from, at the top of the chamber, slightly greater than the sum of the diameters of the capillaries to, at the bottom of the chamber, slightly smaller than the sum of the diameters of the capillaries. The optical system utilizes optic fibers to deliver light to individual photodetectors, one for each capillary tube. A filter or wavelength division demultiplexer may be used for isolating fluorescence at particular bands. 21 figs.
Multiple capillary biochemical analyzer
Dovichi, Norman J.; Zhang, Jian Z.
1995-01-01
A multiple capillary analyzer allows detection of light from multiple capillaries with a reduced number of interfaces through which light must pass in detecting light emitted from a sample being analyzed, using a modified sheath flow cuvette. A linear or rectangular array of capillaries is introduced into a rectangular flow chamber. Sheath fluid draws individual sample streams through the cuvette. The capillaries are closely and evenly spaced and held by a transparent retainer in a fixed position in relation to an optical detection system. Collimated sample excitation radiation is applied simultaneously across the ends of the capillaries in the retainer. Light emitted from the excited sample is detected by the optical detection system. The retainer is provided by a transparent chamber having inward slanting end walls. The capillaries are wedged into the chamber. One sideways dimension of the chamber is equal to the diameter of the capillaries and one end to end dimension varies from, at the top of the chamber, slightly greater than the sum of the diameters of the capillaries to, at the bottom of the chamber, slightly smaller than the sum of the diameters of the capillaries. The optical system utilizes optic fibres to deliver light to individual photodetectors, one for each capillary tube. A filter or wavelength division demultiplexer may be used for isolating fluorescence at particular bands.
Identification of rogue datasets in serial crystallography1
Assmann, Greta; Brehm, Wolfgang; Diederichs, Kay
2016-01-01
Advances in beamline optics, detectors and X-ray sources allow new techniques of crystallographic data collection. In serial crystallography, a large number of partial datasets from crystals of small volume are measured. Merging of datasets from different crystals in order to enhance data completeness and accuracy is only valid if the crystals are isomorphous, i.e. sufficiently similar in cell parameters, unit-cell contents and molecular structure. Identification and exclusion of non-isomorphous datasets is therefore indispensable and must be done by means of suitable indicators. To identify rogue datasets, the influence of each dataset on CC1/2 [Karplus & Diederichs (2012 ▸). Science, 336, 1030–1033], the correlation coefficient between pairs of intensities averaged in two randomly assigned subsets of observations, is evaluated. The presented method employs a precise calculation of CC1/2 that avoids the random assignment, and instead of using an overall CC1/2, an average over resolution shells is employed to obtain sensible results. The selection procedure was verified by measuring the correlation of observed (merged) intensities and intensities calculated from a model. It is found that inclusion and merging of non-isomorphous datasets may bias the refined model towards those datasets, and measures to reduce this effect are suggested. PMID:27275144
Evaluation of streamflow records in Rogue River basin, Oregon
Richardson, Donald
1952-01-01
This report presents data which are, in general, supplementary to those the surface-water investigations made in the past by the U. S. Geological Survey. Those have been essentially investigations of the operation of the many gaging stations on the Rogue River and tributaries. The data presented were obtained from a detailed field investigation of the various #actors resulting from man-made structures that influence the quantity or regimen of the flow at the gaging stations. These factors include diversions from the stream, bypass channels carrying water around the gaging stations, return flow from irrigation or other projects, storage and release of flood waters, and other similar factors. Where feasible, the location, size, effect upon the streamflow periods of use, method of operation,, and similar information are. given. The information is divided into sections corresponding to areas determined by the location of gaging stations. An index of streamflow records is included. A section dealing with the adequacy of available water-resources data and containing location and period of record also is included. This information is given in general terms only, and is portrayed mainly by maps and graphs.