Extreme wave phenomena in down-stream running modulated waves

A. Andonowati, N. Karjanto, Embrecht W.C. van Groesen

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    Abstract

    Modulational, Benjamin-Feir, instability is studied for the down-stream evolution of surface gravity waves. An explicit solution, the soliton on finite background, of the NLS equation in physical space is used to study various phenomena in detail. It is shown that for sufficiently long modulation lengths, at a unique position where the largest waves appear, phase singularities are present in the time signal. These singularities are related to wave dislocations and lead to a discrimination between successive ‘extreme’ waves and much smaller intermittent waves. Energy flow in opposite directions through successive dislocations at which waves merge and split, causes the large amplitude difference. The envelope of the time signal at that point is shown to have a simple phase plane representation, and will be described by a symmetry breaking unfolding of the steady state solutions of NLS. The results are used together with the maximal temporal amplitude MTA, to design a strategy for the generation of extreme (freak, rogue) waves in hydrodynamic laboratories.
    Original languageEnglish
    Pages (from-to)1425-1443
    Number of pages19
    JournalApplied mathematical modelling
    Volume31
    Issue number500-266
    DOIs
    Publication statusPublished - Jul 2007

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    Keywords

    • Extreme waves Rogue waves Phase singularity Freak waves Wave dislocation

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