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| Titel |
Self-similar evolution of wind wave statistical momenta |
| VerfasserIn |
Sergei Annenkov, Victor Shrira |
| Konferenz |
EGU General Assembly 2011
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 13 (2011) |
| Datensatznummer |
250047087
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| Zusammenfassung |
| The ultimate aim of studies of random wind waves is to predict probability density function
of wave characteristics, primarily wave height, at any given place and time. We study
long-term evolution of typical random wind waves, which are characterized by
broad-banded spectra and quasi-Gaussian statistics. We find the departure of wave
statistics from Gaussianity from first principles, using higher-order statistical momenta
(skewness and kurtosis) as a measure of this departure. Non-zero values of kurtosis
mean an increased or decreased probability of extreme waves (compared to that in a
Gaussian sea), which is important for assessing the risk of freak waves and other
applications.
For water waves, there are two different contributions to kurtosis. The first one is due to
bound harmonics, while the second one is linked to nonlinear wave-wave interactions. The
latter contribution requires information on the phases of interacting waves and, therefore, can
be found only with direct numerical simulation. We perform such a simulation of
wind-generated random wave fields and swell, using a specially designed algorithm based on
the Zakharov integrodifferential equation for water waves. In a generic situation, the
contribution to kurtosis due to wave interactions is shown to be small compared to the bound
harmonics contribution. This observation enables us to determine higher momenta by
calculating the bound harmonics parts directly from spectra using asymptotic expressions.
Thus, the departure of evolving wave fields from Gaussianity is explicitly contained in the
wave spectra. This enables us to broaden significantly the capability of the existing
systems for wave forecasting: in addition to simulation of spectra, it becomes possible
to simulate also higher momenta. We found that the contributions due to bound
harmonics to both skewness and kurtosis are significant for oceanic waves, and non-zero
kurtosis (typically in the range 0.1–0.3) implies a tangible increase of freak wave
probability.
From the analysis of the wave kinetic equation, it is well known that wave spectra of a
developing wind wave field and swell often evolve in a self-similar manner. For such
self-similar regimes we derive asymptotic formulas for skewness and kurtosis of a
random wave field generated by constant wind, and for swell. In particular, for the
Zakharov–Zaslavsky regime of growing wind sea, corresponding to constant momentum flux
to waves, we obtain the asymptotic decrease of kurtosis and skewness with time, proportional
to t-4-11 and t-2-11 respectively. These asymptotic properties are verified by direct
numerical simulation. |
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