TY - JOUR

T1 - On Benjamin-Feir instability and evolution of a nonlinear wave with finite-amplitude sidebands

AU - Shemer, L.

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=78649720466&partnerID=8YFLogxK

U2 - 10.5194/nhess-10-2421-2010

DO - 10.5194/nhess-10-2421-2010

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AN - SCOPUS:78649720466

VL - 10

SP - 2421

EP - 2427

JO - Natural Hazards and Earth System Sciences

JF - Natural Hazards and Earth System Sciences

SN - 1561-8633

IS - 11

ER -