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| Titel |
Imbalance of energy and momentum source terms of the sea wave transfer equation for fully developed seas |
| VerfasserIn |
G. V. Caudal |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1812-0784
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| Digitales Dokument |
URL |
| Erschienen |
In: Ocean Science ; 8, no. 6 ; Nr. 8, no. 6 (2012-12-13), S.1085-1098 |
| Datensatznummer |
250006019
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| Publikation (Nr.) |
 copernicus.org/os-8-1085-2012.pdf |
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| Zusammenfassung |
| In the concept of full development, the sea wave spectrum is regarded as a
nearly stationary solution of the wave transfer equation, where source and
sink terms should be in balance with respect to both energy and momentum.
Using a two-dimensional empirical sea wave spectral model at full
development, this paper performs an assessment of the compatibility of the
energy and momentum budgets of sea waves over the whole spectral range. Among
the various combinations of model functions for wave breaking and wind source
terms tested, not one is found to fulfill simultaneously the energy and
momentum balance of the transfer equation. Based on experimental and
theoretical grounds, wave breaking is known to contribute to frequency
downshift of a narrow-banded wave spectrum when the modulational instability
is combined with wave breaking. On those grounds, it is assumed that, in
addition to dissipation, wave breaking produces a spectral energy flux
directed toward low wavenumbers. I show that it is then possible to remove
the energy and momentum budget inconsistency, and correspondingly the
required strength of this spectral flux is estimated. Introducing such a
downward spectral flux permits fulfilling both energy and momentum balance
conditions. Meanwhile, the consistency between the transfer equation and
empirical spectra, estimated by means of a cost function K, is either
improved or slightly reduced, depending upon the wave breaking and wind
source terms chosen. Other tests are performed in which it is further assumed
that wave breaking would also be associated with azimuthal diffusion of the
spectral energy. This would correspondingly reduce the required downward
spectral flux by a factor of up to 5, although it would not be able to remove
it entirely. |
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