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Benjamin–feir Instability of Waves in the Presence of Current : Volume 1, Issue 2 (05/12/2014)

By Shugan, I. V.

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Book Id: WPLBN0004020083
Format Type: PDF Article :
File Size: Pages 30
Reproduction Date: 2015

Title: Benjamin–feir Instability of Waves in the Presence of Current : Volume 1, Issue 2 (05/12/2014)  
Author: Shugan, I. V.
Volume: Vol. 1, Issue 2
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Copernicus GmbH
Historic
Publication Date:
2014
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications

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Hwung, H. H., Yang, R. Y., & Shugan, I. V. (2014). Benjamin–feir Instability of Waves in the Presence of Current : Volume 1, Issue 2 (05/12/2014). Retrieved from http://hawaiilibrary.net/


Description
Description: International Wave Dynamics Research Center, National Cheng Kung University, Tainan, Taiwan. The development of Benjamin–Feir instability of Stokes waves in the presence of variable current is presented. We employ a model of a resonance system having three coexisting nonlinear waves and nonuniform current. The model is free from the narrow-band approximation for surface waves and relatively weak adverse current. The modulation instability of Stokes waves in nonuniform moving media has special properties. Interaction with countercurrent accelerates the growth of sideband modes on a short spatial scale. An increase in initial wave steepness intensifies the wave energy exchange accompanied by wave breaking dissipation, results in asymmetry of sideband modes and a frequency downshift with an energy transfer jump to the lower sideband mode, and depresses the higher sideband and carrier wave. Nonlinear waves may even overpass the blocking barrier produced by strong adverse current. The frequency downshift of the energy peak is permanent and the system does not revert to its initial state. We find reasonable correspondence between the results of model simulations and available experimental results for wave interaction with blocking opposing current. Large transient or freak waves with amplitude and steepness several times those of normal waves may form during temporal nonlinear focusing of the resonant waves accompanied by energy income from sufficiently strong opposing current. We employ the resonance model for the estimation of the maximum amplification of wave amplitudes as a function of gradually increasing opposing current and compare the result obtained with recently published experimental results and modeling results obtained with the nonlinear Schrödinger equation.

Summary
Benjamin–Feir instability of waves in the presence of current

Excerpt
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