On Benjamin-Feir instability and evolution of a nonlinear wave with finite-amplitude sidebands
نویسنده
چکیده
In the past decade it became customary to relate the probability of appearance of extremely steep (the socalled freak, or rogue waves) to the value of the BenjaminFeir Index (BFI) that represents the ratio of wave nonlinearity to the spectral width. This ratio appears naturally in the cubic Schrödinger 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.
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