Extreme wave phenomena in down-stream running modulated waves

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

Research output: Contribution to journalArticleAcademicpeer-review

19 Citations (Scopus)
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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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Extremes
Dislocation
Singularity
NLS Equation
Phase Plane
Gravity Waves
Gravity waves
Steady-state Solution
Surface Waves
Unfolding
Explicit Solution
Solitons
Symmetry Breaking
Surface waves
Envelope
Discrimination
Hydrodynamics
Modulation
Energy

Keywords

  • Extreme waves Rogue waves Phase singularity Freak waves Wave dislocation

Cite this

Andonowati, A. ; Karjanto, N. ; van Groesen, Embrecht W.C. / Extreme wave phenomena in down-stream running modulated waves. In: Applied mathematical modelling. 2007 ; Vol. 31, No. 500-266. pp. 1425-1443.
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Extreme wave phenomena in down-stream running modulated waves. / Andonowati, A.; Karjanto, N.; van Groesen, Embrecht W.C.

In: Applied mathematical modelling, Vol. 31, No. 500-266, 07.2007, p. 1425-1443.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - van Groesen, Embrecht W.C.

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AB - 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.

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