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| Titel |
A basing of the diffusion approximation derivation for the four-wave kinetic integral and properties of the approximation |
| VerfasserIn |
V. G. Polnikov |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 9, no. 3/4 ; Nr. 9, no. 3/4, S.355-366 |
| Datensatznummer |
250006549
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| Publikation (Nr.) |
 copernicus.org/npg-9-355-2002.pdf |
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| Zusammenfassung |
| A basing of the
diffusion approximation derivation for the Hasselmann kinetic integral
describing nonlinear interactions of gravity waves in deep water is
discussed. It is shown that the diffusion approximation containing the
second derivatives of a wave spectrum in a frequency and angle (or in wave
vector components) is resulting from a step-by-step analytical integration
of the sixfold Hasselmann integral without involving the quasi-locality
hypothesis for nonlinear interactions among waves. A singularity analysis
of the integrand expression gives evidence that the approximation
mentioned above is the small scattering angle approximation, in fact, as
it was shown for the first time by Hasselmann and Hasselmann (1981). But,
in difference to their result, here it is shown that in the course of
diffusion approximation derivation one may obtain the final result as a
combination of terms with the first, second, and so on derivatives. Thus,
the final kind of approximation can be limited by terms with the second
derivatives only, as it was proposed in Zakharov and Pushkarev (1999). For
this version of diffusion approximation, a numerical testing of the
approximation properties was carried out. The testing results give a basis
to use this approximation in a wave modelling practice. |
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