The investigation of dynamics of intense solitary wave groups of collinear surface waves is performed by means of numerical simulations of the Euler equations and laboratory experiments. The processes of solitary wave generation, reflection from a wall, and collisions are considered. Steep solitary wave groups with characteristic steepness up to kAcr ≈ 0.3 (where k is the dominant wavenumber and Acr is the crest amplitude) are concerned. They approximately restore the structure after the interactions. In the course of the interaction with the wall and collisions, the maximum amplitude of the wave crests is shown to enhance up to 2.5 times. A standing-wave-like structure occurs in the vicinity of the wall, with certain locations of nodes and antinodes regardless the particular phase of the reflecting wave group. A strong asymmetry of the maximal wave groups due to an anomalous setup is shown in situations of collisions of solitons with different frequencies of the carrier. In some situations of head-on collisions, the amplitude of the highest wave is larger than in overtaking collisions of the same solitons. The discovered effects in interactions of intense wave groups are important in the context of mechanisms and manifestations of oceanic rogue waves.
REFERENCES
1.
Ablowitz
, M. J.
and Horikis
, T. P.
, “Interacting nonlinear wave envelopes and rogue wave formation in deep water
,” Phys. Fluids
27
, 012107
(2015
).2.
Ablowitz
, M. J.
and Segur
, H.
, “On the evolution of packets of water waves
,” J. Fluid Mech.
92
, 691
–715
(1979
).3.
Adcock
, T. A. A.
, “A note on the set-up under the Draupner wave
,” J. Ocean Eng. Mar. Energy
3
, 89
(2017
).4.
Adcock
, T. A. A.
, Taylor
, P. H.
, Yan
, S.
, Ma
, Q. W.
, and Janssen
, P. A. E. M.
, “Did the Draupner wave occur in a crossing sea?
,” Proc. R. Soc. A
467
, 3004
–3021
(2011
).5.
Akrish
, G.
, Rabinovitch
, O.
, and Agnon
, Y.
, “Extreme run-up events on a vertical wall due to nonlinear evolution of incident wave groups
,” J. Fluid Mech.
797
, 644
–664
(2016
).6.
Alber
, I. E.
, “The effects of randomness on the stability of two-dimensional surface wavetrain
,” Proc. R. Soc. A
363
, 525
–546
(1978
).7.
Benjamin
, T. B.
and Feir
, J. E.
, “The disintegration of wave trains on deep water. Part 1. Theory
,” J. Fluid Mech.
27
, 417
–430
(1967
).8.
Biesel
, F.
and Suquet
, F.
, “Les apparails geenerateurs de houle en laboratoire
,” Houille Blanche
2
, 147
(1951
).9.
Carbone
, F.
, Dutykh
, D.
, Dudley
, J. M.
, and Dias
, F.
, “Extreme wave runup on a vertical cliff
,” Geophys. Res. Lett.
40
, 3138
–3143
, doi:10.1002/grl.50637 (2013
).10.
Chabchoub
, A.
and Grimshaw
, R. H. J.
, “The hydrodynamic nonlinear Schrödinger equation: Space and time
,” Fluids
1
, 23
(2016
).11.
Chen
, Y. Y.
, Kharif
, C.
, Yang
, J. H.
, Hsu
, H. C.
, Touboul
, J.
, and Chambarel
, J.
, “An experimental study of steep solitary wave reflection at a vertical wall
,” Eur. J. Mech. B/Fluids
49
, 20
–28
(2015
).12.
Costa
, A.
, Osborne
, A. R.
, Resio
, D. T.
, Alessio
, S.
, Chrivi
, E.
, Saggese
, E.
, Bellomo
, K.
, and Long
, C. E.
, “Soliton turbulence in shallow water ocean surface waves
,” Phys. Rev. Lett.
113
, 108501
(2014
).13.
Deconinck
, B.
, Pelinovsky
, D.
, and Carter
, J. D.
, “Transverse instabilities of deep-water solitary waves
,” Proc. R. Soc. A
462
, 2039
–2061
(2006
).14.
Dyachenko
, A. I.
, Kachulin
, D. I.
, and Zakharov
, V. E.
, “New compact equation for numerical simulation of freak waves on deep water
,” J. Phys.: Conf. Ser.
681
, 012028
(2016
).15.
Dyachenko
, A. I.
and Zakharov
, V. E.
, “On the formation of freak waves on the surface of deep water
,” JETP Lett.
88
, 307
(2008
).16.
Hasimoto
, H.
and Ono
, H.
, “Nonlinear modulation of gravity waves
,” J. Phys. Soc. Jpn.
33
, 805
–811
(1972
).17.
Kharif
, C.
, Pelinovsky
, E.
, and Slunyaev
, A.
, Rogue Waves in the Ocean
(Springer-Verlag
, Berlin, Heidelberg
, 2009
).18.
Klein
, M.
, Clauss
, G. F.
, Rajendran
, S.
, Soares
, C. G.
, and Onorato
, M.
, “Peregrine breathers as design waves for wave-structure interaction
,” Ocean Eng.
(in press)19.
Onorato
, M.
, Osborne
, A. R.
, and Serio
, M.
, “Modulational instability in crossing sea states: A possible mechanism for the formation of freak waves
,” Phys. Rev. Lett.
96
, 014503
(2006
).20.
Onorato
, M.
, Osborne
, A. R.
, Serio
, M.
, and Bertone
, S.
, “Freak waves in random oceanic sea states
,” Phys. Rev. Lett.
86
, 5831
–5834
(2001
).21.
Onorato
, M.
, Proment
, D.
, Clauss
, G.
, and Klein
, M.
, “Rogue waves: From nonlinear Schrodinger breather solutions to sea-keeping test
,” PLOS One
8
, e54629
(2013
).22.
Onorato
, M.
, Waseda
, T.
, Toffoli
, A.
, Cavaleri
, L.
, Gramstad
, O.
, Janssen
, P. A.
, Kinoshita
, T.
, Monbaliu
, J.
, Mori
, N.
, Osborne
, A. R.
, Serio
, M.
, Stansberg
, C. T.
, Tamura
, H.
, and Trulsen
, K.
, “Statistical properties of directional ocean waves: The role of the modulational instability in the formation of extreme events
,” Phys. Rev. Lett.
102
, 114502
(2009
).23.
Pelinovsky
, E. N.
, Shurgalina
, E. G.
, Sergeeva
, A. V.
, Talipova
, T. G.
, El
, G.
, and Grimshaw
, R. H. J.
, “Two-soliton interaction as an elementary act of soliton turbulence in integrable systems
,” Phys. Lett. A
377
, 272
–275
(2013
).24.
Roskes
, G. J.
, “Nonlinear multiphase deep-water wavetrains
,” Phys. Fluids
19
, 1253
–1254
(1976
).25.
Satsuma
, J.
and Yajima
, N.
, “Initial value problems of one-dimensional self-modulation of nonlinear waves in dispersive media
,” Prog. Theor. Phys. Suppl.
55
, 284
–306
(1974
).26.
Sergeeva
, A.
and Slunyaev
, A.
, “Rogue waves, rogue events and extreme wave kinematics in spatio-temporal fields of simulated sea states
,” Nat. Hazards Earth Syst. Sci.
13
, 1759
–1771
(2013
).27.
Shemer
, L.
and Sergeeva
, A.
, “An experimental study of spatial evolution of statistical parameters in a unidirectional narrow-banded random wavefield
,” J. Geophys. Res.
114
, C01015
, doi:10.1029/2008JC005077 (2009
).28.
Shemer
, L.
, Sergeeva
, A.
, and Liberzon
, D.
, “Effect of the initial spectral shape on spatial evolution of the statistics of unidirectional nonlinear random waves
,” J. Geophys. Res.
115
, 12039
, doi:10.1029/2010JC006326 (2010a
).29.
Shemer
, L.
, Sergeeva
, A.
, and Slunyaev
, A.
, “Applicability of envelope model equations for simulation of narrow-spectrum unidirectional random field evolution: Experimental validation
,” Phys. Fluids
22
, 016601
(2010b
).30.
Slunyaev
, A.
, “Nonlinear analysis and simulations of measured freak wave time series
,” Eur. J. Mech. B/Fluids
25
, 621
–635
(2006
).31.
Slunyaev
, A.
, Clauss
, G. F.
, Klein
, M.
, and Onorato
, M.
, “Simulations and experiments of short intense envelope solitons of surface water waves
,” Phys. Fluids
25
, 067105
(2013a
).32.
Slunyaev
, A.
, Pelinovsky
, E.
, Sergeeva
, A.
, Chabchoub
, A.
, Hoffmann
, N.
, Onorato
, M.
, and Akhmediev
, N.
, “Super rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations
,” Phys. Rev. E
88
, 012909
(2013b
).33.
Slunyaev
, A.
, Pelinovsky
, E.
, and Soares
, C. G.
, “Modeling freak waves from the north sea
,” Appl. Ocean Res.
27
, 12
–22
(2005
).34.
Slunyaev
, A. V.
, “A high-order nonlinear envelope equation for gravity waves in finite-depth water
,” JETP
101
, 926
–941
(2005
).35.
Slunyaev
, A. V.
, “Numerical simulation of ‘limiting’ envelope solitons of gravity waves on deep water
,” JETP
109
, 676
–686
(2009
).36.
Slunyaev
, A. V.
and Pelinovsky
, E. N.
, “The role of multiple soliton interactions in generation of rogue waves: The mKdV framework
,” Phys. Rev. Lett.
117
, 214501
(2016
).37.
Slunyaev
, A. V.
and Shrira
, V. I.
, “On the highest non-breaking wave in a group: Fully nonlinear water wave breathers vs weakly nonlinear theory
,” J. Fluid Mech.
735
, 203
–248
(2013
).38.
Sun
, Y.-H.
, “Soliton synchronization in the focusing nonlinear Schrödinger equation
,” Phys. Rev. E
93
, 052222
(2016
).39.
Tanaka
, M.
, “Maximum amplitude of modulated wavetrain
,” Wave Motion
12
, 559
–568
(1990
).40.
Viotti
, C.
, Carbone
F.
, and Dias
, F.
, “Conditions for extreme wave runup on a vertical barrier by nonlinear dispersion
,” J. Fluid Mech.
748
, 768
–788
(2014
).41.
West
, B. J.
, Brueckner
, K. A.
, Janda
, R. S.
, Milder
, D. M.
, and Milton
, R. L.
, “A new numerical method for surface hydrodynamics
,” J. Geophys. Res.
92
, 11803
–11824
, doi:10.1029/jc092ic11p11803 (1987
).42.
Yuen
, H. C.
and Lake
, B. M.
, “Nonlinear deep water waves: Theory and experiment
,” Phys. Fluids
18
, 956
–960
(1975
).43.
Zakharov
, V.
, “Stability of periodic waves of finite amplitude on a surface of deep fluid
,” J. Appl. Mech. Tech. Phys.
2
, 190
–194
(1968
).44.
Zakharov
, V. E.
, Dyachenko
, A. I.
, and Prokofiev
, A. O.
, “Freak waves as nonlinear stage of Stokes wave modulation instability
,” Eur. J. Mech. B/Fluids
25
, 677
–692
(2006
).45.
Zakharov
, V. E.
and Ostrovsky
, L. A.
, “Modulation instability: The beginning
,” Physica D
238
, 540
–548
(2009
).46.
Zakharov
, V. E.
and Rubenchik
, A. M.
, “Instability of waveguides and solitons in nonlinear media
,” Sov. Phys. JETP
38
, 494
–500
(1974
).© 2017 Author(s).
2017
Author(s)
You do not currently have access to this content.
