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| Titel |
Scales of nonlinear relaxation and balance of wind-driven seas |
| VerfasserIn |
Sergei I. Badulin, Vladimir E. Zakharov |
| 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 |
250047148
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| Zusammenfassung |
| We present analytical and numerical arguments that support the fact of leading role of
nonlinear transfer in balance of wind-driven seas. The argumentation is based on a
decomposition of the collision integral Snl in the kinetic equation for deep water waves. This
term describes the effect of four-wave resonant interactions and can be presented as a sum of
nonlinear damping ÎkNk and forcing Fk as follows
Snl = Fk - Î kNk
(1)
Here Îk – positive nonlinear damping decrement, Nk – spectral density of wave action. Both
terms ÎkNk and Fk surpass conventional parameterizations of input and dissipation of
wind-driven waves by, at least, one order of magnitude, as our numerical and analytical
results show. For wind-wave community, this basic (and, to some extent, trivial) fact is
masked by a number of stereotypes. First, conventional scaling of relaxation time Ï due to
nonlinear transfer claims proportionality Ï = Cnlμ-4 (μ = akp – characteristic steepness of
water waves, kp – wavenumber of spectral peak) implying the multiplier Cnl = O(1). In fact,
Cnl appears to be a huge value in our estimates for directionally narrow (Cnl = 36Ï) and
isotropic spectra (Cnl = 45Ï-2). The second stereotype comes from numerical algorithms
for Snl where annihilation of huge terms is considered as a good luck for accelerating
calculations the collision term Snl. As a result, the problem of wind-wave balance is
usually treated as comparison of the whole Snl with terms of wave input Sin and
dissipation Sdiss. Such approach belittles the role of the strong inherent relaxation
mechanism due to four-wave resonant interactions and overestimates dramatically
the effect of wind input and wave dissipation on spectral balance of wind-driven
waves.
The key message of the leading role of the nonlinear transfer is illustrated by analysis of
cases of fully developed (see the milestone paper by Komen et al. 1984) and the mixed
sea.
The work was supported by the Russian government contract 11.G34.31.0035 (signed 25
November 2010) and Russian Foundation for Basic Research grant 11-05-01114-a. |
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