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| Titel |
The modified Korteweg - de Vries equation in the theory of large - amplitude internal waves |
| VerfasserIn |
R. Grimshaw, E. Pelinovsky, T. Talipova |
| 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 ; 4, no. 4 ; Nr. 4, no. 4, S.237-250 |
| Datensatznummer |
250001812
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| Publikation (Nr.) |
 copernicus.org/npg-4-237-1997.pdf |
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| Zusammenfassung |
| The propagation of large- amplitude
internal waves in the ocean is studied here for the case when the nonlinear effects are of
cubic order, leading to the modified Korteweg - de Vries equation. The coefficients of
this equation are calculated analytically for several models of the density
stratification. It is shown that the coefficient of the cubic nonlinear term may have
either sign (previously only cases of a negative cubic nonlinearity were known). Cubic
nonlinear effects are more important for the high modes of the internal waves. The
nonlinear evolution of long periodic (sine) waves is simulated for a three-layer model of
the density stratification. The sign of the cubic nonlinear term influences the character
of the solitary wave generation. It is shown that the solitary waves of both polarities
can appear for either sign of the cubic nonlinear term; if it is positive the solitary
waves have a zero pedestal, and if it is negative the solitary waves are generated on the
crest and the trough of the long wave. The case of a localised impulsive initial
disturbance is also simulated. Here, if the cubic nonlinear term is negative, there is no
solitary wave generation at large times, but if it is positive solitary waves appear as
the asymptotic solution of the nonlinear wave evolution. |
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