Evolution of rogue waves in interacting wave systems

Anders Grönlund, Bengt Eliasson, Mattias Marklund

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

Large-amplitude water waves on deep water have long been known in the seafaring community, and are the cause of great concern for, e.g., oil platform constructions. The concept of such freak waves is nowadays, thanks to satellite and radar measurements, well established within the scientific community. There are a number of important models and approaches for the theoretical description of such waves. By analyzing the scaling behavior of freak wave formation in a model of two interacting waves, described by two coupled non-linear Schrödinger equations, we show that there are two different dynamical scaling behaviors above and below a critical angle θc of the direction of the interacting waves, below which all wave systems evolve and display statistics similar to a wave system of non-interacting waves. The results equally apply to other systems described by the non-linear Schrödinger equations, and should be of interest when designing optical wave guides.
Original languageEnglish
Article number24001
Number of pages5
JournalEPL: A Letters Journal Exploring the Frontiers of Physics
Volume86
Issue number2
DOIs
Publication statusPublished - 24 Apr 2009

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nonlinear equations
scaling
radar measurement
water waves
deep water
platforms
oils
statistics
causes

Keywords

  • water waves
  • rogue waves
  • fluid dynamics

Cite this

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title = "Evolution of rogue waves in interacting wave systems",
abstract = "Large-amplitude water waves on deep water have long been known in the seafaring community, and are the cause of great concern for, e.g., oil platform constructions. The concept of such freak waves is nowadays, thanks to satellite and radar measurements, well established within the scientific community. There are a number of important models and approaches for the theoretical description of such waves. By analyzing the scaling behavior of freak wave formation in a model of two interacting waves, described by two coupled non-linear Schr{\"o}dinger equations, we show that there are two different dynamical scaling behaviors above and below a critical angle θc of the direction of the interacting waves, below which all wave systems evolve and display statistics similar to a wave system of non-interacting waves. The results equally apply to other systems described by the non-linear Schr{\"o}dinger equations, and should be of interest when designing optical wave guides.",
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Evolution of rogue waves in interacting wave systems. / Grönlund, Anders; Eliasson, Bengt; Marklund, Mattias.

In: EPL: A Letters Journal Exploring the Frontiers of Physics, Vol. 86, No. 2, 24001, 24.04.2009.

Research output: Contribution to journalArticle

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AU - Grönlund, Anders

AU - Eliasson, Bengt

AU - Marklund, Mattias

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AB - Large-amplitude water waves on deep water have long been known in the seafaring community, and are the cause of great concern for, e.g., oil platform constructions. The concept of such freak waves is nowadays, thanks to satellite and radar measurements, well established within the scientific community. There are a number of important models and approaches for the theoretical description of such waves. By analyzing the scaling behavior of freak wave formation in a model of two interacting waves, described by two coupled non-linear Schrödinger equations, we show that there are two different dynamical scaling behaviors above and below a critical angle θc of the direction of the interacting waves, below which all wave systems evolve and display statistics similar to a wave system of non-interacting waves. The results equally apply to other systems described by the non-linear Schrödinger equations, and should be of interest when designing optical wave guides.

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