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| Titel |
Three-dimensional freak waves and higher-order wave-wave resonances |
| VerfasserIn |
S. I. Badulin, D. V. Ivonin, V. A. Dulov |
| Konferenz |
EGU General Assembly 2012
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 14 (2012) |
| Datensatznummer |
250066208
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| Zusammenfassung |
| Quite often the freak wave phenomenon is associated with the mechanism of modulational
(Benjamin-Feir) instability resulted from resonances of four waves with close directions and
scales. This weakly nonlinear model reflects some important features of the phenomenon and
is discussing in a great number of studies as initial stage of evolution of essentially nonlinear
water waves. Higher-order wave-wave resonances attract incomparably less attention. More
complicated mathematics and physics explain this disregard partially only. The true reason is
a lack of adequate experimental background for the study of essentially three-dimensional
water wave dynamics.
We start our study with the classic example of New Year Wave. Two extreme events: the
famous wave 26.5 meters and one of smaller 18.5 meters height (formally, not
freak) of the same record, are shown to have pronounced features of essentially
three-dimensional five-wave resonant interactions. The quasi-spectra approach is used for
the data analysis in order to resolve adequately frequencies near the spectral peak
fp - 0.057Hz and, thus, to analyze possible modulations of the dominant wave
component. In terms of the quasi-spectra the above two anomalous waves show
co-existence of the peak harmonic and one at frequency f5w = 3-2fp that corresponds to
maximum of five-wave instability of weakly nonlinear waves. No pronounced marks of
usually discussed Benjamin-Feir instability are found in the record that is easy to
explain: the spectral peak frequency fp corresponds to the non-dimensional depth
parameter kD - 0.92 (k – wavenumber, D - 70 meters – depth at the Statoil
platform Draupner site) that is well below the shallow water limit of the instability
kD = 1.36.
A unique data collection of wave records of the Marine Hydrophysical Institute in the
Katsiveli platform (Black Sea) has been analyzed in view of the above findings of possible
impact of the five-wave instability on freak wave occurrence. The data cover period October
14 – November 6, 2009 almost continuously. Antenna of 6 resistance wave gauges (a
pentagon with one center gauge) is used to gain information on wave directions. Wave
conditions vary from perfect still to storms with significant wave heights up to Hs = 1.7
meters and wind speeds 15m/s. Measurements with frequency 10Hz for dominant frequencies
0.1 - 0.2Hz fixed 40 freak wave events (criterium H-Hs > 2) and showed no dependence on
Hs definitely. Data processing within frequency quasi-spectra approach and directional
spectra reconstructions found pronounced features of essentially three-dimensional
anomalous waves. All the events are associated with dramatic widening of instant
frequency spectra in the range fp - f5w and stronger directional spreading. On
the contrary, the classic Benjamin-Feir modulations show no definite links with
the events and can be likely treated as dynamically neutral part of wave field. The
apparent contradiction with the recent study (Saprykina, Dulov, Kuznetsov, Smolov,
2010) based on the same data collection can be explained partially by features of
data processing. Physical roots of the inconsistency should be detailed in further
studies.
The work was supported by the Russian government contract 11.G34.31.0035 (signed 25
November 2010), Russian Foundation for Basic Research grant 11-05-01114-a, Ukrainian
State Agency of Science, Innovations and Information under Contract M/412-2011 and ONR
grant N000141010991. Authors gratefully acknowledge continuing support of these
foundations. |
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