DOCSLIB.ORG

Dynamics of Interaction Between Solitary and Rogue Wave of the Space-Time Fractional Broer–Kaup Models Arising in Shallow Water of Harbor and Coastal Zone

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Dynamics of Interaction Between Solitary and Rogue Wave of the Space-Time Fractional Broer–Kaup Models Arising in Shallow Water of Harbor and Coastal Zone Research Article Dynamics of interaction between solitary and rogue wave of the space-time fractional Broer–Kaup models arising in shallow water of harbor and coastal zone Selina Akter1,2 · Ratan Kumar Sen1 · Harun‑Or‑ Roshid1 Received: 26 May 2020 / Accepted: 28 October 2020 / Published online: 16 November 2020 © Springer Nature Switzerland AG 2020 Abstract Under inquisition, we consider the space-time fractional Broer–Kaup model that replicate the real coastal profle to describe bidirectional wave transmission of long waves in shallow water. We integrate of the model via the unifed scheme to derive exact solitary wave solutions. The achieved results present the hyperbolic, trigonometric, and rational func- tions solutions. All of these solutions convey the periodic and solitonic natures. In particular, we present combo waves that imply a curvy periodic waves in which rogue waves occur in both sides of each waves. The dynamics of obtained nonlinear wave solutions are demonstrated in 3-D and 2-D shapes with defnite parametric values. It is shown that the obtained solutions of the model pact a very rich dynamical behavior and can be used to describe seismic type nonlinear wave motion in shallow water waves of the coastal and harbor region. Keywords The space-time fractional Broer–Kaup equation · The unifed method · Conformable derivative · Traveling wave solution 1 Introduction on numerical modeling of wave propagation [3–5]. Non- linear fractional derivatives are the appropriate tools for Generally, overall the world, configurations in the low modeling highly non-linear problems including seismic lying area of coastal region are often afected by Tsunami waves in harbor and coastal region. One of this model is wave pressure or cyclonic storm surge and such massive the space-time fractional Broer–Kaup model (FBKM) [3]. waves of the ocean and consequently damages. Mostly In this article, we shed light on the space-time fractional broken tsunami wave moves inland in the form of tur- Broer–Kaup model (FBKM) which is signifcant model to bulent hydraulic bores [1]. During tsunami type seismic describe bidirectional wave transmission of long waves in occur, region is severely damaged. Tsunamis type massive shallow water. The usual form of the space-time FBKM [3] waves create dissipated energy that travels through water is as follows medium and when the depth of the ocean decreases, the T uT u T v 0, wave height increase to higher. The velocity of tsunami t + x + x = waves depends on ocean intensity instead of the gap from � � � � � � the source of the wave [2]. It is, therefore, an important Tt v + Tx u + Tx (uv)+Tx Tx Tx u = 0, t > 0, 0 <�, � ≤ 1. event whose study will contribute to better understand- (1) ing of coastal hazards from seismic waves. Right now, such massive wave related research for the most part focuses * Harun-Or- Roshid, [email protected]; [email protected] | 1Department of Mathematics, Pabna University of Science and Technology, 6600, Pabna, Bangladesh. 2Department of Applied Mathematics, Gono Bishwabidyalay, Savar, Dhaka, Bangladesh. SN Applied Sciences (2020) 2:2000 | https://doi.org/10.1007/s42452-020-03779-8 Vol.:(0123456789) Research Article SN Applied Sciences (2020) 2:2000 | https://doi.org/10.1007/s42452-020-03779-8 Here Tt and Tx indicate conformable fractional derivative sides of each waves and express in terms of rational, trigo- [4] reverence to t and x, respectively. Besides, the seismic nometric and hyperbolic functions. (earthquake, tsunami and typhoon) waves are refect as The structure of this paper goes along with: In Sect. 2, the solitary waves. Solitons are stable and confned non- we have recalled the unifed method. In Sect. 3, we have linear wave progressed balancing between nonlinearity presented the exact solutions to the space-time fractional and dispersion in an arrangement. Due to their rising in a Broer–Kaup equations employing the unifed method. In massive diversity in media, extending from fuids [5, 6] and Sect. 4, we have discussed obtaining solutions with the astrophysical plasmas [7, 8] to semiconductors [9, 10] and graphical representation and in the last section, conclu- nonlinear optics [11, 12], solitons have converted a sensi- sions are given. ble purpose for technical exploration. Such hip in natural structures, solitons can similarly be formed in laboratories as dual plasma schemes [13, 14], Joseph-son junctions [15, 2 The unifed method 16] and so on. With this point of view, deriving soliton and its interaction solution of nonlinear wave models attract a Here, we illustrate the unifed method [29, 30] for govern- much interest of young scientist [17–19]. Currently, many ing exact solutions of nonlinear partial diferential equa- scientists are working with considerable eforts on the tions (NLPDEs) in the subsequent way. Adopt a NPDE in fractional diferential models as it gives the real proper- two independent variables x and t is given by ties of natural phenomena [20, 21]. Tozar et. al. [22], Kurt P u, u , u , u , u , u , 0, [23], Kurt et. al. [24], Tasbozan [25] and Tasbozan et. al. [26] x xxt xxx t tt … = (2) investigated new solutions for the time fractional integra- where p is a polynomial in u = u(x, t) and its several deriva- ble dispersive model that arises in ocean engineering, the tives including the highest order derivatives and non- fractional Bogoyavlensky-Konopelchenko model that linear terms. arising in fuid dynamics, the fractional coupled Burgers’ Step-1: To convert the NLPDE into Ordinary diferential equation that arises as a model of poly-dispersive sedi- equation (ODE), we operate the traveling wave variable mentation, the time fractional Benjamin-Ono model that arises internal waves in deep water and the fractional u(x, t) = U(), = kx − t, (3) Drinfeld-Sokolov-Wilson system in shallow water waves respectively. Iyiola et. al. [27] studied on the analytical where k is constant and ω is the wave velocity. Now switch- solutions of the system of conformable time-fractional ing (3) into (2) we attain an ODE Robertson equations with 1-D difusion. Cenesiz et. al. [28] R u u u uu u , , , , … = 0. (4) established new exact solutions of Burgers’ type equations with conformable derivative. Step-2: Now we integrate (4) as many times as possible. Various approaches are used to study the above frac- Keep the integrating constant to zero. tional models. Recently, Gozukizil et. al. [29] proposed a unifed scheme that receiving much attention of young Assume that the solution of ODE (4) takes the follow- researcher to handle non-linear fractional diferential mod- ing form els. Beside this, some researcher has compared the all tanh N methods [8, 9] with the unifed method [29]. Akcagil and U() = l + l S()i + m S()−i , Aydemir [30] have exemplifed that the unifed method 0 i i (5) i=1 is not only more general than the family of tanh function methods but also it gives many more general solutions whose li (i = 0, 1, 2, …, N) and mi(i = 0, 1, 2, …, N) are con- than the new members of the family of (G′/G)-expansion stants to be calculated subsequently on the situation that method. They come to verdict that the unifed method lN and mN cannot be zero at a time. The function S(ξ) satis- gives many more general solutions in an elegant way than fes the Riccati equation, the family of the tanh-function methods. S� S 2 Therefore, the aim of this paper is to solve the space- = ( ()) + , (6) time fractional Broer–Kaup equation for finding exact whose solutions are specifed as follows: solitary wave solutions via the efective unifed method Case-1: Hyperbolic function (when λ < 0): [29, 30]. This method produces combo waves that imply a curvy periodic waves in which rogue waves occur in both Vol:.(1234567890) SN Applied Sciences (2020) 2:2000 | https://doi.org/10.1007/s42452-020-03779-8 Research Article 3 Solutions for the space-time FBK model −(l2+d2)−l − cosh 2 −(+E) , via the unifed method l sinh 2√ −(+E�) √+d � ⎧ √ − −(l2+d2)�−l√ − cosh� 2 −(+E) ⎪ , Now, we apply the unifed integral scheme to extract exact ⎪ l sinh 2√−(+E)� +√d � solutions of (1). First, we consider the following transfor- S() = ⎪ √ − cosh 2 �−√(+E) −sinh� 2 −(+E) −l mation to convert (1) into ordinary diferential equation ⎪ , ⎪ √ l+�cosh �2√−(+E)�−sinh �2√−(+E)� � (ODE): ⎨ l � �E � �E ⎪ − −cosh √2 −(+ ) −sinh √2 −(+ ) t x , u x t U a b ⎪ √ l+�cosh 2� −√(+E) +�sinh 2� −√(+E) �� ( , ) = (); = + , (7) ⎪ ⎪ � √ � � √ � Case-2⎪ : Trigonometric function (when λ > 0): where a, b are constants. ⎩ Plugging (7) into (1), we have the following ODE (l2−d2)−l cos 2 (+E) , aU� + bUU� + bV � = 0. (8) l sin 2√(+E�) √+d � ⎧ √ − (l2−d2)�−√l cos� 2 (+E) � � � � 3 ��� ⎪ , aV + bU + b UV + VU + b U = 0.. (9) ⎪ l sin 2 √(+E)� +√d � S() = ⎪ √ i cos 2� √(+E) +�sin 2 (+E) −il One time integration of (8) with respect to ξ, yields ⎪ , � � � � � � ⎪ √ l+cos 2√(+E) −i sin 2√ (+E) C 2 ⎨ 1 U a −i cos� √2 (+E�) +sin� 2√ (+E�) +il V = − − U. (10) ⎪ , b 2 b ⎪ √ �l+cos �2 √(+E) �+i sin �2√(+E)� � ⎪ Switching (8) into (7) yields a unique equation ⎪ � √ � � √ � where l⎪ ≠ 0 and d, E are real arbitrary constant. b 3a a2 ⎩ b3U�� − U3 − U2 + C + b − U − C = 0, Case-3: Rational function solutions (when λ = 0) 2 2 1 b 2 (11) 1 S() =− . here C and C are integration constants. + E 1 2 Now balancing the terms U″ and U3 of (11), unknown N Step-03: By homogeneous balance principle, we deter- becomes N = 1. mine the positive integer N of (4).
Load more

Recommended publications
  • Santa Rosa County Tsunami/Rogue Wave
    SANTA ROSA COUNTY TSUNAMI/ROGUE WAVE EVACUATION PLAN Banda Aceh, Indonesia, December 2004, before/after tsunami photos 1 Table of Contents Introduction …………………………………………………………………………………….. 3 Purpose…………………………………………………………………………………………. 3 Definitions………………………………………………………………………………………… 3 Assumptions……………………………………………………………. ……………………….. 4 Participants……………………………………………………………………………………….. 4 Tsunami Characteristics………………………………………………………………………….. 4 Tsunami Warning Procedure…………………………………………………………………….. 6 National Weather Service Tsunami Warning Procedures…………………………………….. 7 Basic Plan………………………………………………………………………………………….. 10 Concept of Operations……………………………………………………………………………. 12 Public Awareness Campaign……………………………………………………………………. 10 Resuming Normal Operations…………………………………………………………………….13 Tsunami Evacuation Warning Notice…………………………………………………………….14 2 INTRODUCTION: Santa Rosa County Emergency Management developed a Santa Rosa County-specific Tsunami/Rogue wave Evacuation Plan. In the event a Tsunami1 threatens Santa Rosa County, the activation of this plan will guide the actions of the responsible agencies in the coordination and evacuation of Navarre Beach residents and visitors from the beach and other threatened areas. The goal of this plan is to provide for the timely evacuation of the Navarre Beach area in the event of a Tsunami Warning. An alternative to evacuating Navarre Beach residents off of the barrier island involves vertical evacuation. Vertical evacuation consists of the evacuation of persons from an entire area, floor, or wing of a building
    [Show full text]
  • Deep Ocean Wind Waves Ch
    Deep Ocean Wind Waves Ch. 1 Waves, Tides and Shallow-Water Processes: J. Wright, A. Colling, & D. Park: Butterworth-Heinemann, Oxford UK, 1999, 2nd Edition, 227 pp. AdOc 4060/5060 Spring 2013 Types of Waves Classifiers •Disturbing force •Restoring force •Type of wave •Wavelength •Period •Frequency Waves transmit energy, not mass, across ocean surfaces. Wave behavior depends on a wave’s size and water depth. Wind waves: energy is transferred from wind to water. Waves can change direction by refraction and diffraction, can interfere with one another, & reflect from solid objects. Orbital waves are a type of progressive wave: i.e. waves of moving energy traveling in one direction along a surface, where particles of water move in closed circles as the wave passes. Free waves move independently of the generating force: wind waves. In forced waves the disturbing force is applied continuously: tides Parts of an ocean wave •Crest •Trough •Wave height (H) •Wavelength (L) •Wave speed (c) •Still water level •Orbital motion •Frequency f = 1/T •Period T=L/c Water molecules in the crest of the wave •Depth of wave base = move in the same direction as the wave, ½L, from still water but molecules in the trough move in the •Wave steepness =H/L opposite direction. 1 • If wave steepness > /7, the wave breaks Group Velocity against Phase Velocity = Cg<<Cp Factors Affecting Wind Wave Development •Waves originate in a “sea”area •A fully developed sea is the maximum height of waves produced by conditions of wind speed, duration, and fetch •Swell are waves
    [Show full text]
  • Soliton and Rogue Wave Statistics in Supercontinuum Generation In
    Soliton and rogue wave statistics in supercontinuum generation in photonic crystal fibre with two zero dispersion wavelengths Bertrand Kibler, Christophe Finot, John M. Dudley To cite this version: Bertrand Kibler, Christophe Finot, John M. Dudley. Soliton and rogue wave statistics in supercon- tinuum generation in photonic crystal fibre with two zero dispersion wavelengths. The European Physical Journal. Special Topics, EDP Sciences, 2009, 173 (1), pp.289-295. 10.1140/epjst/e2009- 01081-y. hal-00408633 HAL Id: hal-00408633 https://hal.archives-ouvertes.fr/hal-00408633 Submitted on 17 Apr 2010 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. EPJ manuscript No. (will be inserted by the editor) Soliton and rogue wave statistics in supercontinuum generation in photonic crystal ¯bre with two zero dispersion wavelengths Bertrand Kibler,1 Christophe Finot1 and John M. Dudley2 1 Institut Carnot de Bourgogne, UMR 5029 CNRS-Universit¶ede Bourgogne, 9 Av. A. Savary, Dijon, France 2 Institut FEMTO-ST, UMR 6174 CNRS-Universit¶ede Franche-Comt¶e,Route de Gray, Besan»con, France. Abstract. Stochastic numerical simulations are used to study the statistical prop- erties of supercontinuum spectra generated in photonic crystal ¯bre with two zero dispersion wavelengths.
    [Show full text]
  • Storm, Rogue Wave, Or Tsunami Origin for Megaclast Deposits in Western
    Storm, rogue wave, or tsunami origin for megaclast PNAS PLUS deposits in western Ireland and North Island, New Zealand? John F. Deweya,1 and Paul D. Ryanb,1 aUniversity College, University of Oxford, Oxford OX1 4BH, United Kingdom; and bSchool of Natural Science, Earth and Ocean Sciences, National University of Ireland Galway, Galway H91 TK33, Ireland Contributed by John F. Dewey, October 15, 2017 (sent for review July 26, 2017; reviewed by Sarah Boulton and James Goff) The origins of boulderite deposits are investigated with reference wavelength (100–200 m), traveling from 10 kph to 90 kph, with to the present-day foreshore of Annagh Head, NW Ireland, and the multiple back and forth actions in a short space and brief timeframe. Lower Miocene Matheson Formation, New Zealand, to resolve Momentum of laterally displaced water masses may be a contributing disputes on their origin and to contrast and compare the deposits factor in increasing speed, plucking power, and run-up for tsunamis of tsunamis and storms. Field data indicate that the Matheson generated by earthquakes with a horizontal component of displace- Formation, which contains boulders in excess of 140 tonnes, was ment (5), for lateral volcanic megablasts, or by the lateral movement produced by a 12- to 13-m-high tsunami with a period in the order of submarine slide sheets. In storm waves, momentum is always im- of 1 h. The origin of the boulders at Annagh Head, which exceed portant(1cubicmeterofseawaterweighsjustover1tonne)in 50 tonnes, is disputed. We combine oceanographic, historical, throwing walls of water continually at a coastline.
    [Show full text]
  • Extreme Waves and Ship Design
    10th International Symposium on Practical Design of Ships and Other Floating Structures Houston, Texas, United States of America © 2007 American Bureau of Shipping Extreme Waves and Ship Design Craig B. Smith Dockside Consultants, Inc. Balboa, California, USA Abstract Introduction Recent research has demonstrated that extreme waves, Recent research by the European Community has waves with crest to trough heights of 20 to 30 meters, demonstrated that extreme waves—waves with crest to occur more frequently than previously thought. Also, trough heights of 20 to 30 meters—occur more over the past several decades, a surprising number of frequently than previously thought (MaxWave Project, large commercial vessels have been lost in incidents 2003). In addition, over the past several decades, a involving extreme waves. Many of the victims were surprising number of large commercial vessels have bulk carriers. Current design criteria generally consider been lost in incidents involving extreme waves. Many significant wave heights less than 11 meters (36 feet). of the victims were bulk carriers that broke up so Based on what is known today, this criterion is quickly that they sank before a distress message could inadequate and consideration should be given to be sent or the crew could be rescued. designing for significant wave heights of 20 meters (65 feet), meanwhile recognizing that waves 30 meters (98 There also have been a number of widely publicized feet) high are not out of the question. The dynamic force events where passenger liners encountered large waves of wave impacts should also be included in the (20 meters or higher) that caused damage, injured structural analysis of the vessel, hatch covers and other passengers and crew members, but did not lead to loss vulnerable areas (as opposed to relying on static or of the vessel.
    [Show full text]
  • On the Probability of Occurrence of Rogue Waves
    Nat. Hazards Earth Syst. Sci., 12, 751–762, 2012 www.nat-hazards-earth-syst-sci.net/12/751/2012/ Natural Hazards doi:10.5194/nhess-12-751-2012 and Earth © Author(s) 2012. CC Attribution 3.0 License. System Sciences On the probability of occurrence of rogue waves E. M. Bitner-Gregersen1 and A. Toffoli2 1Det Norske Veritas, Veritasveien 1, 1322 Høvik, Norway 2Swinburne University of Technology, P.O. Box 218, Hawthorn, 3122 Vic., Australia Correspondence to: E. M. Bitner-Gregersen ([email protected]) Received: 15 September 2011 – Revised: 31 January 2012 – Accepted: 5 February 2012 – Published: 23 March 2012 Abstract. A number of extreme and rogue wave studies such as the modulational instability of uniform wave pack- have been conducted theoretically, numerically, experimen- ets (see, e.g. Zakharov and Ostrovsky, 2009; Osborne, 2010, tally and based on field data in the last years, which have for a review) may give rise to substantially higher waves significantly advanced our knowledge of ocean waves. So than predicted by common second order wave models (Ono- far, however, consensus on the probability of occurrence of rato et al., 2006; Socquet-Juglard et al., 2005; Toffoli et al., rogue waves has not been achieved. The present investiga- 2008b). tion is addressing this topic from the perspective of design The recent Rogue Waves 2008 Workshop (Olagnon and needs. Probability of occurrence of extreme and rogue wave Prevosto, 2008) has brought further insight into rogue crests in deep water is here discussed based on higher order waves and their impact on marine structures, underlining time simulations, experiments and hindcast data.
    [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]
  • Measured Rogue Waves and Their Environment
    Journal of Marine Science and Engineering Article Measured Rogue Waves and Their Environment Mark D. Orzech * and David Wang Naval Research Lab, 1009 Balch Blvd, Stennis Space Ctr, MS 39529, USA; [email protected] * Correspondence: [email protected]; Tel.: +1-228-688-5974 Received: 29 September 2020; Accepted: 5 November 2020; Published: 7 November 2020 Abstract: We conduct a comprehensive analysis of over 350 years of accumulated ocean surface elevation time series and examine evidence for the effects of nonlinear frequency modulation, wave directional spread, surface current shear, and wind forcing on the likelihood of rogue wave development. Hourly sections of positional time series from 34 surface buoys are examined to identify over 8000 rogue wave events, recording wave sizes, times of occurrence, and geographic locations. The initial dataset is subjected to a quality control process to identify and remove false positives. We investigate the correlation of rogue events with the specified marine environmental factors in an attempt to validate the predictions of earlier theoretical and modeling analyses. The rogue event dataset is contrasted with a control, non-rogue dataset containing a total of nearly 510,000 hourly data segments of surface wave data. The analysis combines the wave records with surface current and wind data from state-of-the-art global coupled models. Statistics of the identified rogue events are summarized, and results of the environmental factor analysis are presented and discussed. This study finds some support for a causal connection between each of the environmental factors and the development of rogue waves. Results also suggest that localized environmental conditions at specific sites, such as seasonal variations in directional spread and/or high surface current vorticity, may provide useful signals of greater rogue wave threat.
    [Show full text]
  • Rogue Wave Phenomenon Christian Kharif, Efim Pelinovsky
    Physical Mechanisms of the Rogue Wave Phenomenon Christian Kharif, Efim Pelinovsky To cite this version: Christian Kharif, Efim Pelinovsky. Physical Mechanisms of the Rogue Wave Phenomenon. European Journal of Mechanics - B/Fluids, Elsevier, 2003, 22, n° 6, pp.603-634. hal-00000352 HAL Id: hal-00000352 https://hal.archives-ouvertes.fr/hal-00000352 Submitted on 9 May 2003 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Physical Mechanisms of the Rogue Wave Phenomenon Christian Kharif1) and Efim Pelinovsky2) 1)Institut de Recherche sur les Phenomenes Hors Equilibre (IRPHE), Technopole de Chateau-Gombert, 49 rue Joliot Curie BP 146, 13384 MARSEILLE cedex 13, France, E-mail: [email protected] 2)Laboratory of Hydrophysics and Nonlinear Acoustics, Institute of Applied Physics, 46 Uljanov Street, Nizhny Novgorod, 603950 Russia, E-mail: [email protected] Abstract: A review of physical mechanisms of the rogue wave phenomenon is given. The data of marine observations as well as laboratory experiments are briefly discussed. They demonstrate that freak waves may appear in deep and shallow waters. Simple statistical analysis of the rogue wave probability based on the assumption of a Gaussian wave field is reproduced.
    [Show full text]
  • Vector Rogue Waves and Dark Bright Boomeronic Solitons in Autonomous and Non Autonomous Settings R
    University of Massachusetts Amherst ScholarWorks@UMass Amherst Mathematics and Statistics Department Faculty Mathematics and Statistics Publication Series 2014 Vector rogue waves and dark bright boomeronic solitons in autonomous and non autonomous settings R. Babu Mareeswaran Bishop Heber College E. G. Charalampidis University of Massachusetts Amherst T. Kanna Bishop Heber College P. G. Kevrekidis University of Massachusetts Amherst D. J. Frantzeskakis University of Athens Follow this and additional works at: https://scholarworks.umass.edu/math_faculty_pubs Part of the Applied Mathematics Commons Recommended Citation Mareeswaran, R. Babu; Charalampidis, E. G.; Kanna, T.; Kevrekidis, P. G.; and Frantzeskakis, D. J., "Vector rogue waves and dark bright boomeronic solitons in autonomous and non autonomous settings" (2014). Physical Review E. 1265. Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/1265 This Article is brought to you for free and open access by the Mathematics and Statistics at ScholarWorks@UMass Amherst. It has been accepted for inclusion in Mathematics and Statistics Department Faculty Publication Series by an authorized administrator of ScholarWorks@UMass Amherst. For more information, please contact [email protected]. Vector rogue waves and dark-bright boomeronic solitons in autonomous and nonautonomous settings R. Babu Mareeswaran∗ Post Graduate and Research Department of Physics, Bishop Heber College, Tiruchirapalli{620 017, Tamil Nadu, India E. G. Charalampidisy School of Civil Engineering, Faculty of Engineering, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece and Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515, USA T. Kannaz Post Graduate and Research Department of Physics, Bishop Heber College, Tiruchirapalli{620 017, Tamil Nadu, India P. G. Kevrekidisx Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515, USA D.
    [Show full text]
  • Lifetimes of Rogue Wave Events in Direct Numerical Simulations of Deep-Water Irregular Sea Waves
    fluids Article Lifetimes of Rogue Wave Events in Direct Numerical Simulations of Deep-Water Irregular Sea Waves Anna Kokorina 1,2,* and Alexey Slunyaev 1,2,3 1 Department of Nonlinear Geophysical Processes, Institute of Applied Physics, 46 Ulyanova Street, Box-120, Nizhny Novgorod 603950, Russia; [email protected] 2 Laboratory of Modeling of Natural and Technogenic Disasters, Nizhny Novgorod State Technical University, n.a. R.E. Alekseev, 24 Minina Street, Nizhny Novgorod 603950, Russia 3 Laboratory of Topological Methods in Dynamics, National Research University-Higher School of Economics, 25 B. Pechorskaya Street, Nizhny Novgorod 603950, Russia * Correspondence: [email protected] Received: 19 March 2019; Accepted: 10 April 2019; Published: 12 April 2019 Abstract: The issue of rogue wave lifetimes is addressed in this study, which helps to detail the general picture of this dangerous oceanic phenomenon. The direct numerical simulations of irregular wave ensembles are performed to obtain the complete accurate data on the rogue wave occurrence and evolution. Purely collinear wave systems, moderately crested, and short-crested sea states have been simulated by means of the high-order spectral method for the potential Euler equations. As rogue waves are transient and poorly reflect the physical effects, we join instant abnormally high waves in close locations and close time moments to new objects, rogue events, which helps to retrieve the abnormal occurrences more stably and more consistently from the physical point of view. The rogue event lifetime probability distributions are calculated based on the simulated wave data. They show the distinctive difference between rough sea states with small directional bandwidth on one part, and small-amplitude sea states and short-crested states on the other part.
    [Show full text]
  • Rogue Waves: Rare but Damaging
    Feature: Rogue waves: rare but damaging Rogue waves: rare but damaging A recent incident highlights the danger of large waves propagating in a direction different from the mean wind and wave direction. What is the probability of encountering such waves? 2.5 metres per second, this results in a warning time of approximately Dr Johannes Gemmrich, Prof Burkard Baschek, 10 seconds before the wave hit the vessel. Prof Chris Garrett What is a rogue wave? Although ‘rogue wave’ is a popular term for an unusually large ocean n January 14, 2010, the crab fishing vessel Early Dawn wave that can cause damage to ships or endanger people, some media was hit by a very large wave coming from an unexpected accounts of rogue waves really just refer to very rough seas. In scientific direction when fishing near St. Paul, Alaska. According to terms, a ‘rogue wave’ refers to waves with height H, from trough to the Captain, the rogue wave was at least twice as high as crest, such that H/Hs ≥ α, where the significant wave height Hs is the Othe rest of the waves, if not 2.5 times as high. The Captain first saw average height of the highest one-third of the waves, and the multiplier the wave at a distance of approximately 100 metres, and immediately α is commonly chosen as either as 2.0 or 2.2. warned the crew with a buzzer. Three crew members were able to get Under maritime law, a rogue wave falls into the category of ‘perils to safety, while one crew member working at the stern of the vessel was of the sea’, which has been defined as ‘those perils which are peculiar injured by the wave.
    [Show full text]