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| Titel |
Hamiltonian approach to the derivation of evolution equations for wave trains in weakly unstable media |
| VerfasserIn |
N. N. Romanova |
| 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 ; 5, no. 4 ; Nr. 5, no. 4, S.241-253 |
| Datensatznummer |
250002641
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| Publikation (Nr.) |
 copernicus.org/npg-5-241-1998.pdf |
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| Zusammenfassung |
| The dynamics of weakly nonlinear wave trains in unstable
media is studied. This dynamics is investigated in the framework of a broad class of
dynamical systems having a Hamiltonian structure. Two different types of instability are
considered. The first one is the instability in a weakly supercritical media. The simplest
example of instability of this type is the Kelvin-Helmholtz instability. The second one is
the instability due to a weak linear coupling of modes of different nature. The simplest
example of a geophysical system where the instability of this and only of this type takes
place is the three-layer model of a stratified shear flow with a continuous velocity
profile. For both types of instability we obtain nonlinear evolution equations describing
the dynamics of wave trains having an unstable spectral interval of wavenumbers. The transformation
to appropriate canonical variables turns out to be different for each case, and equations
we obtained are different for the two types of instability we considered. Also obtained
are evolution equations governing the dynamics of wave trains in weakly subcritical media
and in media where modes are coupled in a stable way. Presented results do not depend on a
specific physical nature of a medium and refer to a broad class of dynamical systems
having the Hamiltonian structure of a special form. |
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