DOCSLIB.ORG

Predicting Ocean Rogue Waves from Point Measurements: an Experimental Study for Unidirectional Waves

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Predicting Ocean Rogue Waves from Point Measurements: an Experimental Study for Unidirectional Waves Predicting ocean rogue waves from point measurements: An experimental study for unidirectional waves The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Cousins, Will et al. "Predicting ocean rogue waves from point measurements: An experimental study for unidirectional waves." Physical Review E, 99, 3 (March 2019): 032201 © 2019 The Author(s) As Published http://dx.doi.org/10.1103/PhysRevE.99.032201 Publisher American Physical Society Version Final published version Citable link http://hdl.handle.net/1721.1/120744 Terms of Use Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. PHYSICAL REVIEW E 99, 032201 (2019) Predicting ocean rogue waves from point measurements: An experimental study for unidirectional waves Will Cousins,1 Miguel Onorato,2,3 Amin Chabchoub,4 and Themistoklis P. Sapsis1,* 1Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 2Dipartimento di Fisica, Università degli Studi di Torino, 10125 Torino, Italy 3Istituto Nazionale di Fisica Nucleare, INFN, Sezione di Torino, 10125 Torino, Italy 4School of Civil Engineering, The University of Sydney, Sydney NSW 2006, Australia (Received 29 April 2018; published 4 March 2019) Rogue waves are strong localizations of the wave field that can develop in different branches of physics and engineering, such as water or electromagnetic waves. Here, we experimentally quantify the prediction potentials of a comprehensive rogue-wave reduced-order precursor tool that has been recently developed to predict extreme events due to spatially localized modulation instability. The laboratory tests have been conducted in two different water wave facilities and they involve unidirectional water waves; in both cases we show that the deterministic and spontaneous emergence of extreme events is well predicted through the reported scheme. Due to the interdisciplinary character of the approach, similar studies may be motivated in other nonlinear dispersive media, such as nonlinear optics, plasma, and solids, governed by similar equations, allowing the early stage of extreme wave detection. DOI: 10.1103/PhysRevE.99.032201 I. INTRODUCTION of wave height or wave crest for the given sea state. This allows one to calculate the probability of encountering a wave Rogue waves, also known as freak waves, are abnormally whose height is larger than a certain threshold (usually 2 large waves with crest-to-trough height exceeding two times times the significant wave height); see, for example, [14]. the significant wave height [1–5]. Although rare (approxi- On shorter timescales, a deterministic prediction of rogue mately three waves per day in a single point measurement, waves is generally possible. In [15] a predictability time scale using linear theory, and an average wave period of 10 s), for rogue waves was estimated through extensive numerical these waves can have dramatic effects on ships and other simulations using a phase-resolved high-order spectral tech- ocean structures [6,7]. Therefore, predicting such extreme nique [16,17]. It was demonstrated that a timescale for reliable events is an important challenging topic in the field of ocean prediction can be O(10T ), where T is the peak period of the engineering, as well as other fields of wave physics, including p p spectrum. plasma [8], solids [9], and optics [10–12]. In addition, from a For long-crested water waves, statistics are far from Gaus- mathematical viewpoint the short-term prediction problem of sian, with heavy tails [18–21]. In this case, the dominant extreme events in nonlinear waves presents particular interest mechanism for the formation of large waves is finite-time in- due to the stochastic character of water waves and also the stabilities rising in the form of a spatially localized modulation inherent complexity of the governing equations. instability [14,22,23]. For deep water waves, a manifestation Before discussing in detail the emphasized prediction tool of this focusing is the well-known modulation instability for rogue waves, we find it relevant to make a general state- of a plane wave to small sideband perturbations [24,25]. ment on the predictability of surface gravity waves. In [13]it This instability, which has been demonstrated experimentally has been shown numerically that 2D (i.e., in two horizontal since the 1960s [26,27] and its limiting case more recently dimensions) ocean waves are described by a chaotic system; [28,29], generates significantly focused coherent structures this implies that due to positive Lyapunov exponents, after by soaking up energy from the nearby field [30–32]. In this some time (space) the system loses memory of the initial context it is possible and more advantageous to study the condition and any attempt to perform a deterministic forecast dynamics of wave groups (in contrast to individual waves) will generally fail. Annenkov and Shrira [13] found that through reduced-order representations [23,33,34], alleviating a timescale of predictability for typical steepness of ocean the direct numerical treatment of the full equations. Depend- waves is of the order of 1000 wave periods. For larger times, ing on the typical dimensions (length, width, height) of the predictions, including rogue-wave forecast, can be made only wave group, we may have subsequent modulation instability, on a statistical basis, i.e., given a wave spectrum and its which leads to further significant magnification of the wave evolution, the goal is to establish the probability distribution group height. Such critical wave groups can be formed by the random superposition of different harmonics, see Fig. 1. If a wave group has appropriate characteristics, it will amplify *Corresponding author: [email protected] due to modulation instability. Such nonlinear evolution can be 2470-0045/2019/99(3)/032201(9) 032201-1 ©2019 American Physical Society COUSINS, ONORATO, CHABCHOUB, AND SAPSIS PHYSICAL REVIEW E 99, 032201 (2019) is the modified nonlinear Schrödinger equation (MNLS) [38], formulated as an evolution equation in space rather than in time [41]. The analysis of this universal equation, that can be also applied to a wide range of physical media (for instance, in optics [42]), allows for the characterization of wave groups or pulses as critical to become either rogue or not through single point measurements of the time series of the surface elevation. We demonstrate the effectiveness of the developed scheme through experimental hydrodynamic data in the form of time series of water wave profiles. Using multiple realizations of rogue waves, we statistically quantify the accuracy of the developed scheme. The main distinction of the present work is that in prior work the predictive scheme was applied only in the context of forecasting the propagation of a wave field through numerical FIG. 1. In the typical regime the dominant mechanism for the simulations of the MNLS. It is true that the laboratory exper- wave group formation is the superposition of linear waves. If a iments considered here are overly simplistic representations critical wave group is formed, i.e., one with sufficiently large length of realistic ocean dynamics. However, the work presented and amplitude, the strongly nonlinear dynamics associated with here represents a significant step forward in reduced-order modulation instability can be foreseen through simple precursors. forecasting of extreme events, demonstrating that this scheme can provide accurate spatiotemporal predictions in an experi- foreseen using simple precursors that quantify the conditions mental environment with noisy measurements. for modulation instability of the wave group, as shown in Fig. 1. II. PRECURSORS BASED ON POINT MEASUREMENTS A reduced-order precursor for the prediction of rogue waves, caused by spatially localized modulation instability, Our goal is to predict extreme waves in unidirectional wave has been proposed for unidirectional [35,36] as well as direc- fields on the surface of deep water using time measurements tional [37] surface gravity waves. The idea behind it comes at a single point with satisfactory high sampling frequency. from combining spectral information for the sea state and The developed scheme consists of an offline, as well as an information involving the evolution of isolated wave groups online, real-time component. For the offline component, we to rogue waves. The derived precursors have the form of quantify the critical wave groups that evolve to rogue waves using direct numerical solutions of the MNLS equation. Here characteristic patterns that precede rogue waves O(10Tp) ahead. Using field information (i.e., wave measurements with we employed the MNLS equation for demonstration purposes; spatial extend) for the region of interest, the predictive scheme the fully nonlinear water wave equations could also be used, quickly identifies locations where these patterns are present but the offline component would be computationally more and provides the estimated magnitude of a rogue wave that expensive. In the online, real-time component, we identify the will occur in the near future, close to this location. The coherent wave groups in measurements of a physical, irregular developed scheme is particularly robust, given that it relies wave time-series. We then use the results from the offline on the detection of large-scale features (having the size of component to predict how the measured groups will evolve. the wave group) utilizing either temporal or spatial mea- The scheme we discuss here closely follows the ideas surements. For this reason the scheme does not depend on presented in [35]. In this case the prediction analysis was small-scale measurement errors. In addition, it is extremely based on the availability of field measurements. The algorithm fast due to the fact that there is no need to calculate any reported in this work predicts future extreme waves from solution of any evolution equation involved in the prediction time-series measurements of the wave field at a single point.
Load more

Recommended publications
  • High-Throughput Biological Cell Classification Featuring Real-Time Optical Data Compression
    Conference on Information Sciences and Systems, CISS 2015, Baltimore, MD, USA, March 18-20 2015 High-throughput Biological Cell Classification Featuring Real-time Optical Data Compression Bahram Jalali*, Ata Mahjoubfar, and Claire L. Chen Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA Plenary Talk *Email: [email protected] Abstract—High throughput real-time instruments are needed the current gold standard in high-speed fluorescence imaging to acquire large data sets for detection and classification of rare [16]. events. Enabled by the photonic time stretch digitizer, a new class of instruments with record throughputs have led to the discovery Producing data rates as high as one tera bit per second, of optical rogue waves [1], detection of rare cancer cells [2], and these real-time instruments pose a big data challenge that the highest analog-to-digital conversion performance ever overwhelms even the most advanced computers [17]. Driven achieved [3]. Featuring continuous operation at 100 million by the necessity of solving this problem, we have recently frames per second and shutter speed of less than a nanosecond, introduced and demonstrated a categorically new data the time stretch camera is ideally suited for screening of blood compression technology [18, 19]. The so called Anamorphic and other biological samples. It has enabled detection of breast (warped) Stretch Transform is a physics based data processing cancer cells in blood with record, one-in-a-million, sensitivity [2]. technique that aims to mitigate the big data problem in real- Owing to their high real-time throughput, instruments produce a time instruments, in digital imaging, and beyond [17-21].
    [Show full text]
  • Dissipative Rogue Waves Generated by Chaotic Pulse Bunching in a Mode-Locked Laser
    week ending PRL 108, 233901 (2012) PHYSICAL REVIEW LETTERS 8 JUNE 2012 Dissipative Rogue Waves Generated by Chaotic Pulse Bunching in a Mode-Locked Laser C. Lecaplain,1 Ph. Grelu,1 J. M. Soto-Crespo,2 and N. Akhmediev3 1Laboratoire Interdisciplinaire Carnot de Bourgogne, U.M.R. 6303 C.N.R.S., Universite´ de Bourgogne, 9 avenue A. Savary, BP 47870 Dijon Cedex 21078, France 2Instituto de O´ ptica, C.S.I.C., Serrano 121, 28006 Madrid, Spain 3Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200, Australia (Received 14 December 2011; published 5 June 2012) Rare events of extremely high optical intensity are experimentally recorded at the output of a mode- locked fiber laser that operates in a strongly dissipative regime of chaotic multiple-pulse generation. The probability distribution of these intensity fluctuations, which highly depend on the cavity parameters, features a long-tailed distribution. Recorded intensity fluctuations result from the ceaseless relative motion and nonlinear interaction of pulses within a temporally localized multisoliton phase. DOI: 10.1103/PhysRevLett.108.233901 PACS numbers: 42.65.Tg, 47.20.Ky Waves of extreme amplitude, or ‘‘rogue waves,’’ have satisfying the criteria of rogue waves [17,18]. In order to been the subject of intense research activity during the past strongly interact, the multiplicity of pulses should be con- decade [1,2]. Initiated first in the context of oceanic waves, fined within a relatively tight temporal domain. The two where the induced stakes and consequences are the most predictions also stressed the dominant impact of dissipa- critical, the notion of ‘‘rogue waves’’ or ‘‘freak waves’’ is tive effects on the involved nonlinear dynamics.
    [Show full text]
  • The Universal Route to Rogue Waves
    PHYSICAL REVIEW X 9, 041057 (2019) Featured in Physics Experimental Evidence of Hydrodynamic Instantons: The Universal Route to Rogue Waves Giovanni Dematteis ,1,2 Tobias Grafke,3 Miguel Onorato ,2,4 and Eric Vanden-Eijnden5 1Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy 2Dipartimento di Fisica, Universit`a degli Studi di Torino, Via Pietro Giuria 1, 10125 Torino, Italy 3Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom 4INFN, Sezione di Torino, Via Pietro Giuria 1, 10125 Torino, Italy 5Courant Institute, New York University, 251 Mercer Street, New York, New York 10012, USA (Received 3 July 2019; revised manuscript received 2 October 2019; published 18 December 2019) A statistical theory of rogue waves is proposed and tested against experimental data collected in a long water tank where random waves with different degrees of nonlinearity are mechanically generated and free to propagate along the flume. Strong evidence is given that the rogue waves observed in the tank are hydrodynamic instantons, that is, saddle point configurations of the action associated with the stochastic model of the wave system. As shown here, these hydrodynamic instantons are complex spatiotemporal wave field configurations which can be defined using the mathematical framework of large deviation theory and calculated via tailored numerical methods. These results indicate that the instantons describe equally well rogue waves created by simple linear superposition (in weakly nonlinear conditions) or by nonlinear focusing (in strongly nonlinear conditions), paving the way for the development of a unified explanation to rogue wave formation. DOI: 10.1103/PhysRevX.9.041057 Subject Areas: Fluid Dynamics, Nonlinear Dynamics, Statistical Physics I.
    [Show full text]
  • Optical Rogue Wave in Random Distributed Feedback Fiber Laser Jiangming Xu1,2, Jian Wu1,2, Jun Ye1, Pu Zhou1,2,*, Hanwei Zhang1,2, Jiaxin Song1, & Jinyong Leng1,2
    Optical rogue wave in random distributed feedback fiber laser Jiangming Xu1,2, Jian Wu1,2, Jun Ye1, Pu Zhou1,2,*, Hanwei Zhang1,2, Jiaxin Song1, & Jinyong Leng1,2 The famous demonstration of optical rogue wave (RW)-rarely and unexpectedly event with extremely high intensity-had opened a flourishing time for temporal statistic investigation as a powerful tool to reveal the fundamental physics in different laser scenarios. However, up to now, optical RW behavior with temporally localized structure has yet not been presented in random fiber laser (RFL) characterized with mirrorless open cavity, whose feedback arises from distinctive distributed multiple scattering. Here, thanks to the participation of sustained and crucial stimulated Brillouin scattering (SBS) process, experimental explorations of optical RW are done in the highly-skewed transient intensity of an incoherently-pumped standard-telecom-fiber-constructed RFL. Furthermore, threshold-like beating peak behavior can also been resolved in the radiofrequency spectroscopy. Bringing the concept of optical RW to RFL domain without fixed cavity may greatly extend our comprehension of the rich and complex kinetics such as photon propagation and localization in disordered amplifying media with multiple scattering. 1 College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China . 2 Hunan Provincial Collaborative Innovation Center of High Power Fiber Laser, Changsha 410073, China. J. X. and J. W. contributed equally to this paper. Correspondence and requests for materials should be addressed to P. Z. (email: [email protected]). The concept of random laser employing multiple scattering of photons in an amplifying disordered material to achieve coherent light has attracted increasing attention due to its special features, such as cavity-free, structural simplicity, and promising applications in imaging, medical diagnostics, and other scientific or industrial fields [1-3].
    [Show full text]
  • Optical Rogue Waves in Integrable Turbulence
    Optical Rogue Waves in Integrable Turbulence Pierre Suret et Stéphane Randoux Postdoc : F. Gustave PhD : R. El Koussaifi, A. Tikan, P. Walczak (2016) Collaborators : Fast Measurement : S. Bielawski, C. Szwaj, C. Evain (Phlam) Oceanography : M. Onorato (Turin, Italie) Integrable Systems : G. El (Loughbourough, UK) 1. Context 2. Experiments 3. Theoretical approach Optical Rogue Waves in Wave Turbulence Integrable Turbulence ü Waves ubiquitous phenomena in Physics ü Dispersion ü Nonlinearity ü Often, randomness plays a significant role Wave turbulence = nonlinear dispersive random waves hydrodynamics, oceanography, optics, mechanics, plasma physics… Optical Rogue Waves in Nonlinear Statistical OpticsIntegrable Turbulence Statistical Optics (linear) ü XXth century Random / partially coherent light (spatial or temporal fluctuation, coherence / spectrum…) Nonlinear Statistical (fiber) Optics ü 1960s Lasers / nonlinear optics ü 1990s Supercontinuum (ps, cw) : nonlinear + incoherent A.Kudlinski and A. Mussot, Opt. Lett., 33, (2008) J. M. Dudley et al., Opt. Express 17, (2009) ü 2000s Challenge : statistical description of nonlinear random waves A. Picozzi et al., Optical wave turbulence : Toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics Physics Reports, (2014) Optical Rogue Waves in “Turbulence” in Optical fibersIntegrable Turbulence Optical fibers : tabletop laboratories of hydrodynamical phenomena ü Turbulence E.G. Turitsyna et al., « The laminar–turbulent transition in a fibre laser », Nat. Photonics,
    [Show full text]
  • Time Stretch and Its Applications Ata Mahjoubfar1,2, Dmitry V
    REVIEW ARTICLE PUBLISHED ONLINE: 1 JUNE 2017 | DOI: 10.1038/NPHOTON.2017.76 Time stretch and its applications Ata Mahjoubfar1,2, Dmitry V. Churkin3,4,5, Stéphane Barland6, Neil Broderick7, Sergei K. Turitsyn3,5 and Bahram Jalali1,2,8,9* Observing non-repetitive and statistically rare signals that occur on short timescales requires fast real-time measurements that exceed the speed, precision and record length of conventional digitizers. Photonic time stretch is a data acquisition method that overcomes the speed limitations of electronic digitizers and enables continuous ultrafast single-shot spectroscopy, imaging, reflectometry, terahertz and other measurements at refresh rates reaching billions of frames per second with non-stop recording spanning trillions of consecutive frames. The technology has opened a new frontier in measurement science unveiling transient phenomena in nonlinear dynamics such as optical rogue waves and soliton molecules, and in relativistic electron bunching. It has also created a new class of instruments that have been integrated with artificial intelligence for sensing and biomedical diagnostics. We review the fundamental principles and applications of this emerging field for continuous phase and amplitude characterization at extremely high repetition rates via time-stretch spectral interferometry. he Shannon–Hartley theorem provides a tool to quantify the in instrumentation have led to new science. We anticipate that a new information content of analog data. The theorem prescribes that type of instrument that performs time-resolved single-shot measure- Tunpredictability — the element of surprise — is the property that ments of ultrafast events and that makes continuous measurements defines information. No information is carried by a periodic signal, over long timescales spanning trillions of pulses will unveil previously such as a sinusoidal wave, because its evolution is entirely predictable.
    [Show full text]
  • Extreme Value Phenomena in Optics: Origins and Links with Oceanic Rogue Waves
    Extreme value phenomena in optics: origins and links with oceanic rogue waves John Dudley1, Go¨ery Genty2, Fr´ed´eric Dias3, & Benjamin Eggleton4 1Institut FEMTO-ST, Universit´ede Franche-Comt´e, Besan¸con, France 2Optics Laboratory, Tampere University of Technology, Tampere, Finland 3Centre de Mathematiques et de leurs Applications, ENS Cachan, Cachan, France 4CUDOS, School of Physics, University of Sydney, NSW 2006, Australia [email protected], [email protected],[email protected], [email protected] Abstract. 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 highly nonlinear fibers. 1 Introduction A central challenge in understanding extreme events is to develop rigorous mod- els linking the complex generation dynamics and the associated statistical be- haviour. Quantitative studies of extreme value phenomena, however, are often hampered in two ways: (i) the intrinsic scarcity of the events under study and (ii) the fact that such events often appear in environments where measurements are difficult. In this context, highly significant experiments were reported by Solli et al. in late 2007, where a novel wavelength-to-time detection technique has allowed the direct characterization of the shot-to-shot statistics in the extreme nonlinear optical spectral broadening process known as supercontinuum (SC) generation when launching pulses of long duration into a fiber with high nonlin- earity [1]. Although this regime of SC generation is known to exhibit fluctuations on the SC long wavelength edge [2], it was shown that these fluctuations contain a small number of statistically-rare “rogue” events associated with an enhanced red-shift and a greatly increased intensity.
    [Show full text]
  • Rogue Waves – Towards a Unifying Concept?: Discussions and Debates
    Eur. Phys. J. Special Topics 185, 5–15 (2010) c EDP Sciences, Springer-Verlag 2010 THE EUROPEAN DOI: 10.1140/epjst/e2010-01234-y PHYSICAL JOURNAL SPECIAL TOPICS Regular Article Rogue waves – towards a unifying concept?: Discussions and debates V. Ruban1,a,Y.Kodama2,b, M. Ruderman3,c, J. Dudley4,d,R.Grimshaw5,e, P. McClintock6,f ,M.Onorato7,g, C. Kharif8,h,E.Pelinovsky9,i,T.Soomere10,j, G. Lindgren11,k, N. Akhmediev12,l,A.Slunyaev9,m, D. Solli13, C. Ropers14, B. Jalali13,n, F. Dias15, and A. Osborne16,17,o 1 L. D. Landau Institute for Theoretical Physics RAS, 2 Kosygin Street, 119334 Moscow, Russia 2 Department of Mathematics, Ohio State University, Columbus, OH 43210 3 School of Mathematics and Statistics, University of Sheffield, Hounsfield Road, Hicks Building, Sheffield S3 7RH, UK 4 Depart´ement d’Optique P. M. Duffieux, Institut FEMTO-ST, UMR 6174 CNRS-Universit´ede Franche-Comt´e, 25030 Besan¸con, France 5 Loughborough University, UK 6 Department of Physics, Lancaster University, Lancaster LA1 4YB, UK 7 Dipartimento di Fisica Generale, Universit`a di Torino, Via P. Giuria, 1, 10125 Torino, Italy 8 IRPHE, 49 rue F. Joliot-Curie 13384 Marseille Cedex 13, France 9 Department of Nonlinear Geophysical Processes, Institute of Applied Physics, Nizhny Novgorod, Russia 10 Centre for Non-linear Studies, Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn, Estonia 11 Mathematical Statistics, Lund University, Box 118, SE-221 00 Lund, Sweden 12 Optical Sciences Group, Research School of Physics and Engineering, Institute of Advanced Studies, The Australian National University, Canberra ACT 0200, Australia 13 Photonics Laboratory, UCLA, 420 Westwood Blvd., Los Angeles, CA 90095-1594 14 Courant Res.
    [Show full text]
  • Instabilities, Breathers and Rogue Waves in Optics
    Instabilities, breathers and rogue waves in optics John M. Dudley1, Frédéric Dias2, Miro Erkintalo3, Goëry Genty4 1. Institut FEMTO-ST, UMR 6174 CNRS-Université de Franche-Comté, Besançon, France 2. School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland 3. Department of Physics, University of Auckland, Auckland, New Zealand 4. Department of Physics, Tampere University of Technology, Tampere, Finland Optical rogue waves are rare yet extreme fluctuations in the value of an optical field. The terminology was first used in the context of an analogy between pulse propagation in optical fibre and wave group propagation on deep water, but has since been generalized to describe many other processes in optics. This paper provides an overview of this field, concentrating primarily on propagation in optical fibre systems that exhibit nonlinear breather and soliton dynamics, but also discussing other optical systems where extreme events have been reported. Although statistical features such as long-tailed probability distributions are often considered the defining feature of rogue waves, we emphasise the underlying physical processes that drive the appearance of extreme optical structures. Many physical systems exhibit behaviour associated with the emergence of high amplitude events that occur with low probability but that have dramatic impact. Perhaps the most celebrated examples of such processes are the giant oceanic “rogue waves” that emerge unexpectedly from the sea with great destructive power [1]. There is general agreement that 1 the emergence of giant waves involves physics different from that generating the usual population of ocean waves, but equally there is a consensus that one unique causative mechanism is unlikely.
    [Show full text]
  • Rogue Waves and Their Generating Mechanisms in Different Physical Contexts
    Physics Reports 528 (2013) 47–89 Contents lists available at SciVerse ScienceDirect Physics Reports journal homepage: www.elsevier.com/locate/physrep Rogue waves and their generating mechanisms in different physical contexts M. Onorato a,b, S. Residori c,∗, U. Bortolozzo c, A. Montina d, F.T. Arecchi e,f a Dipartimento di Fisica Generale, Università degli Studi di Torino, Via Pietro Giuria 1, 10125 Torino, Italy b INFN, Sezione di Torino, Via Pietro Giuria 1, 10125 Torino, Italy c INLN, Université de Nice Sophia-Antipolis, CNRS, 1361 route des Lucioles, 06560 Valbonne, France d Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5 Canada e Dipartimento di Fisica, Università di Firenze, Italy f CNR-INO, largo E. Fermi 6, 50125 Firenze, Italy article info a b s t r a c t Article history: Rogue waves is the name given by oceanographers to isolated large amplitude waves, Accepted 19 December 2012 that occur more frequently than expected for normal, Gaussian distributed, statistical Available online 14 March 2013 events. Rogue waves are ubiquitous in nature and appear in a variety of different contexts. editor: G.I. Stegeman Besides water waves, they have been recently reported in liquid Helium, in nonlinear optics, microwave cavities, etc. The first part of the review is dedicated to rogue waves in the oceans and to their laboratory counterpart with experiments performed in water basins. Most of the work and interpretation of the experimental results will be based on the nonlinear Schrödinger equation, an universal model, that rules the dynamics of weakly nonlinear, narrow band surface gravity waves.
    [Show full text]
  • Bright-Dark Rogue Wave in Mode-Locked Fibre Laser Rogue
    Conference 10228: Nonlinear Optics and Applications amplification. Under beam shaping technique, achieving high energy We present the results of an experimental and theoretical study of square pulses can be realized by exploiting the dissipative soliton the complex nonlinear polarization dynamics leading to rogue wave’s resonance theory where the energy is not limited by the soliton area emergence. The theoretical model consists of seven coupled non-linear theorem and it increases proportionally with allows the pulse width to equations and takes in account both orthogonal states of polarizations widen linearly. (SOPs) in the fiber [1, 2]. The model predicts the existence of seven Dissipative soliton resonance square pulses were experimentally observed eigenfrequencies in the cavity due to polarization instability near lasing in setups consisting on the nonlinear polarization evolution mechanism in threshold. By adjusting the laser parameters (the power and the SOP normal and anomalous dispersion regimes. It has also been demonstrated of the pump wave and in-cavity birefringence) we can tune some in mode-locked figure-of-eight fiber lasers using optical circulators and eigenfrequencies from completely different (non-degenerate states) to dual pumping. These results highlighted the fact that the high non- coinciding (degenerated states). The experiments were performed with a linearity plays an important role in widening the pulse. passively self-mode-locked erbium-doped fiber oscillator implemented in a ring configuration and operating near the lasing threshold. The obtained In this work, we present a widely adjustable high energy square pulse experimental results are in a good correspondence with the theory. laser operating in dissipative soliton resonance in a passively mode- Moreover, it was observed that non-degenerate states of oscillator lead locked figure-of-eight fiber configuration using dual Er:Yb co-doped to L-shaped probability distribution function (PDF) and true rogue waves double clad amplifiers.
    [Show full text]
  • An Adaptive Filter for Studying the Life Cycle of Optical Rogue Waves
    An adaptive filter for studying the life cycle of optical rogue waves Chu Liu1, 2, 4, Eric J. Rees2, 4, Toni Laurila2, Shuisheng Jian1, and Clemens F. Kaminski 2, 3,* 1Institute of Lightwave Technology, Key Lab of All Optical Network and Advanced Telecommunication Network of EMC, Beijing Jiaotong University, Beijing 100044, China 2Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, CB2 3RA, UK 3SAOT School of Advanced Optical Technologies, Friedrich Alexander University, D-91058 Erlangen, Germany 4These authors contributed equally to this work *[email protected] Abstract: 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. 2010 Optical Society of America OCIS codes: (060.5530) Fiber optics and optical communications: Pulse propagation and temporal solitons; (190.4370) Nonlinear optics: Nonlinear optics, fibers. References and links 1. J. M. Dudley, and J. R. Taylor, Supercontinuum Generation in Optical Fibers, (Cambridge University Press, Cambridge, 2010) 2. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006). 3. J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt.
    [Show full text]