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| Titel |
Evaluation of kurtosis of JONSWAP spectra |
| VerfasserIn |
Sergei Annenkov, Victor Shrira |
| Konferenz |
EGU General Assembly 2013
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 15 (2013) |
| Datensatznummer |
250080427
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| Zusammenfassung |
| Typical random wind waves in the sea are characterized by broad-band spectra and
quasi-Gaussian statistics. While the evolution of wave field spectra in the ocean is well
studied, very little is known about how departure of wave statistics from Gaussian depends on
characteristics of wave spectra. This information is needed for many applications but
is very difficult to extract from observations outside laboratory. It is common to
characterize the departure of wave statistics from Gaussianity by value of kurtosis, a
fourth-order statistical moment. 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
quasi-Gaussian waves there are two contributions to kurtosis. The first one, C4(b), is due to
bound harmonics, while the second one, “dynamic kurtosis” C4(d), is linked to
nonlinear wave-wave interactions. Under standard weak turbulence assumptions Janssen
(2003) derived expressions for both components of kurtosis in terms of energy
spectra. However, since the evaluation of the resulting 6-dimensional integrals is
technically challenging, it has not been implemented for any experimental wave
spectra.
Here we evaluate C4(d) and C4(b) for the JONSWAP spectra, a widely used family of
parametrisations of the observed spectra. We choose the k-form of the JONSWAP spectrum
with the peak at k = 1. The frequency spectra are considered in the range 0.5 < Ï < 3. The
magnitude of the spectra is specified by parameter α, where α is proportional to the square of
the steepness. The range of α corresponds to the range of steepness from 0.04 to 0.3. The
JONSWAP parameter γ characterizing “peakedness“ of the spectra. γ is taken from 1 to
10. Angular distributions of the (cosθ)N type are considered for several values of
N.
Thus we find behaviour of both components of kurtosis in the three-dimensional
parameter space (α,γ,N) and their sensitivity to approximations of the spectral shape. This
provides a good idea on the degree of departure of wave statistics from Gaussian for realistic
wave fields. |
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