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| Titel |
An analytical model of the evolution of a Stokes wave and its two Benjamin–Feir sidebands on nonuniform unidirectional current |
| VerfasserIn |
I. V. Shugan, H. H. Hwung, R. Y. Yang |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 22, no. 3 ; Nr. 22, no. 3 (2015-05-21), S.313-324 |
| Datensatznummer |
250120982
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| Publikation (Nr.) |
 copernicus.org/npg-22-313-2015.pdf |
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| Zusammenfassung |
An analytical weakly nonlinear model of the Benjamin–Feir instability of a
Stokes wave on nonuniform unidirectional current is presented. The model
describes evolution of a Stokes wave and its two main sidebands propagating
on a slowly varying steady current. In contrast to the models based on
versions of the cubic Schrödinger equation, the current variations could be
strong, which allows us to examine the blockage and consider substantial
variations of the wave numbers and frequencies of interacting waves. The
spatial scale of the current variation is assumed to have the same order as
the spatial scale of the Benjamin–Feir (BF) instability. The model includes wave
action conservation law and nonlinear dispersion relation for each of the
wave's triad. The effect of nonuniform current, apart from linear
transformation, is in the detuning of the resonant interactions, which
strongly affects the nonlinear evolution of the system.
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, resulting 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 waves accompanied by energy income
from sufficiently strong opposing current. We employ the model for the
estimation of the maximum amplification of wave amplitudes as a function of
opposing current value and compare the result obtained with recently
published experimental results and modeling results obtained with the
nonlinear Schrödinger equation. |
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