Title

Melnikov Analysis And Inverse Spectral Analysis Of Rogue Waves In Deep Water

Keywords

Freak waves; Homoclinic orbits; Modulational instability; Nonlinear focusing; Nonlinear Schrödinger equation; Rogue waves

Abstract

Rogue waves in deep water are investigated in the framework of the nonlinear Schrödinger (NLS) and the modified Dysthe (MD) equations. We observe that a chaotic regime increases the likelihood of rogue wave formation and that enhanced focusing occurs due to chaotic evolution of the phases. A Melnikov analysis indicates persistence of a homoclinic solution in the MD system which is O (ε{lunate})-close to an optimally phase modulated solution of the NLS. The correlation of the Melnikov analysis and the numerical experiments indicates that one approach to predicting rogue waves in realistic oceanic states is to determine the proximity of a sea state to homoclinic data of the NLS. Using the inverse spectral theory of the NLS equation, we show that the development of extreme waves in random oceanic sea states characterized by JONSWAP power spectra is well predicted by the proximity to homoclinic data of the NLS. © 2006 Elsevier SAS. All rights reserved.

Publication Date

9-1-2006

Publication Title

European Journal of Mechanics, B/Fluids

Volume

25

Issue

5

Number of Pages

602-620

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.euromechflu.2006.02.005

Socpus ID

33747141704 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/33747141704

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