Abstract.
The recently suggested theoretical model for highly nonlinear potential long-crested water waves is discussed, where weak three-dimensional effects are included as small corrections to exact two-dimensional equations written in terms of the conformal variables [V.P. Ruban, Phys. Rev. E 71, 055303(R) (2005)]. Some numerical results based on this theory are presented, which describe spontaneous formation of rogue waves on the deep water for different initial conditions. In particular, the given numerical examples describe: (i) nonlinear stage of the modulational instability, (ii) breathing rogue wave in a random wave field, and (iii) freak wave in a weakly crossing sea state.
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C. Kharif, E. Pelinovsky, Eur. J. Mech. B/Fluids 22Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 603 (2003)
K. Dysthe, H.E. Krogstad, P. Muller, Ann. Rev. Fluid Mech. 40Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 287 (2008)
Special Issue: Eur. J. Mech. B/Fluids 25Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 535 (2006)
P.A.E.M. Janssen, J. Phys. Oceanogr. 33Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 863 (2003)
M.A. Tayfun, J. Geophys. Res. 85 C3Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 1548 (1980)
F. Fedele, M.A. Tayfun, J. Fluid Mech. 620Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 221 (2009)
D.H. Peregrine, Adv. Appl. Mech. 16Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 9 (1976)
I.V. Lavrenov, A.V. Porubov, Eur. J. Mech. B/Fluids 25Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 574 (2006)
C. Fochesato, S. Grilli, F. Dias, Wave Motion 44Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 395 (2007)
H. Socquet-Juglard, K. Dysthe, K. Trulsen, et al., J. Fluid Mech. 542Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 195 (2005)
O. Gramstad, K. Trulsen, J. Fluid Mech. 582Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 463 (2007)
M. Onorato, T. Waseda, A. Toffoli, et al., Phys. Rev. Lett. 102Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 114502 (2009)
M. Onorato, A.R. Osborne, M. Serio, Phys. Rev. Lett. 96Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 014503 (2006)
P.K. Shukla, I. Kourakis, B. Eliasson, et al., Phys. Rev. Lett. 97Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 094501 (2006)
T.B. Benjamin, J.E. Feir, J. Fluid Mech. 27Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 417 (1967)
V.E. Zakharov, Sov. Phys. JETP 24Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 455 (1967)
V.E. Zakharov, J. Appl. Mech. Tech. Phys. 9Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 190 (1968)
J.W. McLean, Y.C. Ma, D.U. Martin, P.G. Saffman, H.C. Yuen, Phys. Rev. Lett. 46Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 817 (1981)
V.I. Shrira, S.I. Badulin, C. Kharif, J. Fluid Mech. 318Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 375 (1996)
F. Collard, G. Caulliez, Phys. Fluids 11Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 3195 (1999)
F. Dias, C. Kharif, Annu. Rev. Fluid Mech. 31Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 301 (1999)
A.I. Dyachenko, E.A. Kuznetsov, M.D. Spector, V.E. Zakharov, Phys. Lett. A 221Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 73 (1996)
A.I. Dyachenko, V.E. Zakharov, E.A. Kuznetsov, Fiz. Plazmy 22Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 916 (1996)
A.I. Dyachenko, V.E. Zakharov, E.A. Kuznetsov, Plasma Phys. Rep. 22Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 829 (1996)
A.I. Dyachenko, Doklady Akademii Nauk 376Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 27 (2001)
A.I. Dyachenko, Doklady Mathematics 63Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 115 (2001)
W. Choi, R. Camassa, J. Engrg. Mech. ASCE 125Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 756 (1999)
V.E. Zakharov, A.I. Dyachenko, O.A. Vasilyev, Eur. J. Mech. B/Fluids 21Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 283 (2002)
A.I. Dyachenko, V.E. Zakharov, Pis’ma v ZhETF 81Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 318 (2005)
A.I. Dyachenko, V.E. Zakharov, JETP Letters 81Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 255 (2005)
V.E. Zakharov, A.I. Dyachenko, A.O. Prokofiev, Eur. J. Mech. B/Fluids 25Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 677 (2006)
A.I. Dyachenko, V.E. Zakharov, JETP Lett. 88Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 307 (2008)
V.P. Ruban, Phys. Rev. E 70Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 066302 (2004)
V.P. Ruban, Phys. Lett. A 340Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 194 (2005)
N. Akhmediev, A. Ankiewicz, J.M. Soto-Crespo, Phys. Rev. E 80Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 026601 (2009)
N. Akhmediev, A. Ankiewicz, M. Taki, Phys. Lett. A 373Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 675 (2009)
N. Akhmediev, J.M. Soto-Crespo, A. Ankiewicz, Phys. Lett. A 373Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 2137 (2009)
D. Clamond, J. Grue, J. Fluid Mech. 447Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 337 (2001)
D. Fructus, D. Clamond, J. Grue, Ø. Kristiansen, J. Comput. Phys. 205Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 665 (2005)
F. Dias, T.J. Bridges, Fluid Dyn. Res. 38Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 803 (2006)
C. Fochesato, F. Dias, Proc. Roy. Soc. A - Math. Phys. Eng. Sci. 462Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 2715 (2006)
S.T. Grilli, F. Dias, P. Guyenne, C. Fochesato, F. Enet, Progress in Fully Nonlinear Potential Flow Modeling of 3D Extreme Ocean Waves. Chapter 3 in Advances in Numerical Simulation of Nonlinear Water Waves (ISBN: 978-981-283-649-6, edited by Q.W. Ma) (Vol. 11 in Series in Advances in Coastal and Ocean Engineering) (World Scientific Publishing Co. Pte. Ltd., 2010), p. 75
P. Guyenne, S.T. Grilli, J. Fluid Mech. 547Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 361 (2006)
S.T. Grilli, http://www.oce.uri.edu/~grilli/
K.B. Dysthe, Proc. R. Soc. London, Ser. A 369Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 105 (1979)
K. Trulsen, K.B. Dysthe, Wave Motion 24Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 281 (1996)
K. Trulsen, I. Kliakhandler, K.B. Dysthe, et al., Phys. Fluids 12Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 2432 (2000)
V.P. Ruban, Phys. Rev. E 71Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 055303(R) (2005)
V.P. Ruban, J. Dreher, Phys. Rev. E 72Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 066303 (2005)
V.P. Ruban, Phys. Rev. E 74Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 036305 (2006)
V.P. Ruban, Phys. Rev. Lett. 99Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 044502 (2007)
V.P. Ruban, Phys. Rev. E 79Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 065304(R) (2009)
V.P. Ruban, JETP 110Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 529 (2010)
V.E. Zakharov, Eur. J. Mech. B/Fluids 18Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 327 (1999)
V.P. Ruban, J.J. Rasmussen, Phys. Rev. E 68Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 056301 (2003)
P.M. Lushnikov, V.E. Zakharov, Physica D 203Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 9 (2005)
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Ruban, V. Conformal variables in the numerical simulations of long-crested rogue waves. Eur. Phys. J. Spec. Top. 185, 17–33 (2010). https://doi.org/10.1140/epjst/e2010-01235-x
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DOI: https://doi.org/10.1140/epjst/e2010-01235-x