Instability and evolution of nonlinearly interacting water waves

P.K. Shukla, I. Kourakis, B. Eliasson, M. Marklund, L. Stenflo

Research output: Contribution to journalArticle

109 Citations (Scopus)

Abstract

We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schrödinger equations. We derive a nonlinear dispersion relation. The latter is numerically analyzed to obtain the regions and the associated growth rates of the modulational instability. Furthermore, we follow the long term evolution of the latter by means of computer simulations of the governing nonlinear equations and demonstrate the formation of localized coherent wave envelopes. Our results should be useful for understanding the formation and nonlinear propagation characteristics of large-amplitude freak waves in deep water.
LanguageEnglish
Article number094501
Number of pages4
JournalPhysical Review Letters
Volume97
Issue number9
DOIs
Publication statusPublished - 1 Sep 2006

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water waves
deep water
nonlinear equations
envelopes
computerized simulation
propagation

Keywords

  • water waves
  • modulational instability
  • deep water

Cite this

Shukla, P.K. ; Kourakis, I. ; Eliasson, B. ; Marklund, M. ; Stenflo, L. / Instability and evolution of nonlinearly interacting water waves. In: Physical Review Letters. 2006 ; Vol. 97, No. 9.
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Instability and evolution of nonlinearly interacting water waves. / Shukla, P.K.; Kourakis, I.; Eliasson, B.; Marklund, M.; Stenflo, L.

In: Physical Review Letters, Vol. 97, No. 9, 094501, 01.09.2006.

Research output: Contribution to journalArticle

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T1 - Instability and evolution of nonlinearly interacting water waves

AU - Shukla, P.K.

AU - Kourakis, I.

AU - Eliasson, B.

AU - Marklund, M.

AU - Stenflo, L.

PY - 2006/9/1

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N2 - We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schrödinger equations. We derive a nonlinear dispersion relation. The latter is numerically analyzed to obtain the regions and the associated growth rates of the modulational instability. Furthermore, we follow the long term evolution of the latter by means of computer simulations of the governing nonlinear equations and demonstrate the formation of localized coherent wave envelopes. Our results should be useful for understanding the formation and nonlinear propagation characteristics of large-amplitude freak waves in deep water.

AB - We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schrödinger equations. We derive a nonlinear dispersion relation. The latter is numerically analyzed to obtain the regions and the associated growth rates of the modulational instability. Furthermore, we follow the long term evolution of the latter by means of computer simulations of the governing nonlinear equations and demonstrate the formation of localized coherent wave envelopes. Our results should be useful for understanding the formation and nonlinear propagation characteristics of large-amplitude freak waves in deep water.

KW - water waves

KW - modulational instability

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