Melnikov analysis and inverse spectral analysis of rogue waves in deep water

    Authors

    C. M. Schober

    Comments

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    Abbreviated Journal Title

    Eur. J. Mech. B-Fluids

    Keywords

    rogue waves; freak waves; homoclinic orbits; nonlinear Schrodinger; equation; nonlinear focusing; modulational instability; NONLINEAR SCHRODINGER-EQUATION; OCEANIC SEA STATES; HOMOCLINIC ORBITS; FREAK-WAVES; MODULATIONAL INSTABILITY; DYNAMICS; TRAINS; CHAOS; NLS; Mechanics; Physics, Fluids & Plasmas

    Abstract

    Rogue waves in deep water are investigated in the framework of the nonlinear Schrodinger (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(epsilon)-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. (C) 2006 Elsevier SAS. All rights reserved.

    Journal Title

    European Journal of Mechanics B-Fluids

    Volume

    25

    Issue/Number

    5

    Publication Date

    1-1-2006

    Document Type

    Article

    Language

    English

    First Page

    602

    Last Page

    620

    WOS Identifier

    WOS:000240549700007

    ISSN

    0997-7546

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