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| Titel |
Benjamin–Feir instability of waves in the presence of current |
| VerfasserIn |
I. V. Shugan, H. H. Hwung, R. Y. Yang |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
2198-5634
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics Discussions ; 1, no. 2 ; Nr. 1, no. 2 (2014-12-05), S.1803-1832 |
| Datensatznummer |
250115135
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| Publikation (Nr.) |
 copernicus.org/npgd-1-1803-2014.pdf |
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| Zusammenfassung |
| 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. |
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