About shape of giant breather

V. E. Zakharov; A. I. Dyachenko

doi:10.1016/j.euromechflu.2009.10.003

About shape of giant breather

V. E. Zakharov, A. I. Dyachenko

Mathematics

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

32 Scopus citations

Abstract

The pulse of freak waves on the surface of deep water can be a breather-type solution of the Euler equation. The shape of surface is periodic function of time in a moving frame. Only in the limit of very small steepness its shape is described by the Nonlinear Shredinger Equation (NLSE). For moderately small steepness we derived more exact envelope nonlocal equation similar to well-known Dysthe equation (DE), which is more convenient for analytical and numerical study. We have found approximate solution of this equation by the use of the variational approach.

Original language	English (US)
Pages (from-to)	127-131
Number of pages	5
Journal	European Journal of Mechanics, B/Fluids
Volume	29
Issue number	2
DOIs	https://doi.org/10.1016/j.euromechflu.2009.10.003
State	Published - Mar 2010

Keywords

Dysthe equation
freak wave
free surface

ASJC Scopus subject areas

Mathematical Physics
General Physics and Astronomy

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10.1016/j.euromechflu.2009.10.003

Cite this

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title = "About shape of giant breather",

abstract = "The pulse of freak waves on the surface of deep water can be a breather-type solution of the Euler equation. The shape of surface is periodic function of time in a moving frame. Only in the limit of very small steepness its shape is described by the Nonlinear Shredinger Equation (NLSE). For moderately small steepness we derived more exact envelope nonlocal equation similar to well-known Dysthe equation (DE), which is more convenient for analytical and numerical study. We have found approximate solution of this equation by the use of the variational approach.",

keywords = "Dysthe equation, freak wave, free surface",

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

note = "Funding Information: This work was supported by the US Army Corps of Engineers Grant W912-BU-08-P-0143, by ONR Grant N00014-06-C-0130, NSF Grant DMS 0404577, RFBR Grant 09-01-00631 and RFBR Grant 07-01-92165-CNRS, NOPP Grant “TSA-a two scale approximation for wind-generated ocean surface waves”, the Program “Fundamental Problems in Nonlinear Dynamics” from the RAS Presidium, and Grant “Leading Scientific Schools of Russia”.",

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doi = "10.1016/j.euromechflu.2009.10.003",

language = "English (US)",

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AU - Dyachenko, A. I.

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N2 - The pulse of freak waves on the surface of deep water can be a breather-type solution of the Euler equation. The shape of surface is periodic function of time in a moving frame. Only in the limit of very small steepness its shape is described by the Nonlinear Shredinger Equation (NLSE). For moderately small steepness we derived more exact envelope nonlocal equation similar to well-known Dysthe equation (DE), which is more convenient for analytical and numerical study. We have found approximate solution of this equation by the use of the variational approach.

AB - The pulse of freak waves on the surface of deep water can be a breather-type solution of the Euler equation. The shape of surface is periodic function of time in a moving frame. Only in the limit of very small steepness its shape is described by the Nonlinear Shredinger Equation (NLSE). For moderately small steepness we derived more exact envelope nonlocal equation similar to well-known Dysthe equation (DE), which is more convenient for analytical and numerical study. We have found approximate solution of this equation by the use of the variational approach.

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KW - free surface

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About shape of giant breather

Abstract

Keywords

ASJC Scopus subject areas

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