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| Titel |
On the problem of optimal approximation of the four-wave kinetic integral |
| VerfasserIn |
V. G. Polnikov, L. Farina |
| 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. 5/6 ; Nr. 9, no. 5/6, S.497-512 |
| Datensatznummer |
250006564
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| Publikation (Nr.) |
 copernicus.org/npg-9-497-2002.pdf |
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| Zusammenfassung |
| The problem of
optimization of analytical and numerical approximations of Hasselmann's
nonlinear kinetic integral is discussed in general form. Considering the
general expression for the kinetic integral, a principle to obtain the
optimal approximation is formulated. From this consideration it follows
that the most well-accepted approximations, such as Discrete Interaction
Approximation (DIA) (Hasselmann et al., 1985), Reduced Integration
Approximation (RIA) (Lin and Perry, 1999), and the Diffusion Approximation
proposed recently in Zakharov and Pushkarev (1999) (ZPA), have the same
roots. The only difference among them is, essentially, the choice of the
4-wave configuration for the interacting waves. To evaluate a quality of
any approximation for the 2-D nonlinear energy transfer, a mathematical
measure of relative error is constructed and the meaning of approximation
efficiency is postulated. By the use of these features it is shown that
DIA has better accuracy and efficiency than ZPA. Following to the general
idea of optimal approximation and by using the measures introduced, more
efficient and faster versions of DIA are proposed. |
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