Freak waves as nonlinear stage of Stokes wave modulation instability

V. E. Zakharov; A. I. Dyachenko; A. O. Prokofiev

doi:10.1016/j.euromechflu.2006.03.004

Freak waves as nonlinear stage of Stokes wave modulation instability

V. E. Zakharov, A. I. Dyachenko, A. O. Prokofiev

Mathematics

Research output: Contribution to journal › Article › peer-review

181 Scopus citations

Abstract

Numerical simulation of evolution of nonlinear gravity waves is presented. Simulation is done using two-dimensional code, based on conformal mapping of the fluid to the lower half-plane. We have considered two problems: (i) modulation instability of wave train and (ii) evolution of NLSE solitons with different steepness of carrier wave. In both cases we have observed formation of freak waves.

Original language	English (US)
Pages (from-to)	677-692
Number of pages	16
Journal	European Journal of Mechanics, B/Fluids
Volume	25
Issue number	5
DOIs	https://doi.org/10.1016/j.euromechflu.2006.03.004
State	Published - Sep 2006

Keywords

Freak wave
Free surface
Modulation instability

ASJC Scopus subject areas

Mathematical Physics
General Physics and Astronomy

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10.1016/j.euromechflu.2006.03.004

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title = "Freak waves as nonlinear stage of Stokes wave modulation instability",

abstract = "Numerical simulation of evolution of nonlinear gravity waves is presented. Simulation is done using two-dimensional code, based on conformal mapping of the fluid to the lower half-plane. We have considered two problems: (i) modulation instability of wave train and (ii) evolution of NLSE solitons with different steepness of carrier wave. In both cases we have observed formation of freak waves.",

keywords = "Freak wave, Free surface, Modulation instability",

author = "Zakharov, {V. E.} and Dyachenko, {A. I.} and Prokofiev, {A. O.}",

note = "Funding Information: This work was supported by the US Army Corps of Engineers Grant W912HZ-05-P-0351, by ONR Grant N00014-03-1-0648, NSF Grant DMS 0404577, RFBR Grant 06-01-00665, the Program “Fundamental Problems in Nonlinear Dynamics” from the RAS Presidium, and Grant “Leading Scientific Schools of Russia”.",

year = "2006",

month = sep,

doi = "10.1016/j.euromechflu.2006.03.004",

language = "English (US)",

volume = "25",

pages = "677--692",

journal = "European Journal of Mechanics, B/Fluids",

issn = "0997-7546",

publisher = "Elsevier B.V.",

number = "5",

}

TY - JOUR

T1 - Freak waves as nonlinear stage of Stokes wave modulation instability

AU - Zakharov, V. E.

AU - Dyachenko, A. I.

AU - Prokofiev, A. O.

N1 - Funding Information: This work was supported by the US Army Corps of Engineers Grant W912HZ-05-P-0351, by ONR Grant N00014-03-1-0648, NSF Grant DMS 0404577, RFBR Grant 06-01-00665, the Program “Fundamental Problems in Nonlinear Dynamics” from the RAS Presidium, and Grant “Leading Scientific Schools of Russia”.

PY - 2006/9

Y1 - 2006/9

N2 - Numerical simulation of evolution of nonlinear gravity waves is presented. Simulation is done using two-dimensional code, based on conformal mapping of the fluid to the lower half-plane. We have considered two problems: (i) modulation instability of wave train and (ii) evolution of NLSE solitons with different steepness of carrier wave. In both cases we have observed formation of freak waves.

AB - Numerical simulation of evolution of nonlinear gravity waves is presented. Simulation is done using two-dimensional code, based on conformal mapping of the fluid to the lower half-plane. We have considered two problems: (i) modulation instability of wave train and (ii) evolution of NLSE solitons with different steepness of carrier wave. In both cases we have observed formation of freak waves.

KW - Freak wave

KW - Free surface

KW - Modulation instability

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U2 - 10.1016/j.euromechflu.2006.03.004

DO - 10.1016/j.euromechflu.2006.03.004

M3 - Article

AN - SCOPUS:33747140354

SN - 0997-7546

VL - 25

SP - 677

EP - 692

JO - European Journal of Mechanics, B/Fluids

JF - European Journal of Mechanics, B/Fluids

IS - 5

ER -

Freak waves as nonlinear stage of Stokes wave modulation instability

Abstract

Keywords

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