On Benjamin-Feir instability and evolution of a nonlinear wave with finite-amplitude sidebands

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Abstract

In the past decade it became customary to relate the probability of appearance of extremely steep (the so-called freak, or rogue waves) to the value of the Benjamin-Feir Index (BFI) that represents the ratio of wave nonlinearity to the spectral width. This ratio appears naturally in the cubic Schröpara;dinger equation that describes evolution of unidirectional narrow-banded wave field. The notion of this index stems from the Benjamin-Feir linear stability analysis of Stokes wave. The application of BFI to evaluate the evolution of wave fields, with non-vanishing amplitudes of sideband disturbances, is investigated using the Zakharov equation as the theoretical model. The present analysis considers a 3-wave system for which the exact analytical solution of the model equations is available.

Original languageEnglish
Pages (from-to)2421-2427
Number of pages7
JournalNatural Hazards and Earth System Sciences
Volume10
Issue number11
DOIs
StatePublished - 2010

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