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| Titel |
On the Hamiltonian approach: Applications to geophysical flows |
| VerfasserIn |
V. Goncharov, V. Pavlov |
| 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.219-240 |
| Datensatznummer |
250002640
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| Publikation (Nr.) |
 copernicus.org/npg-5-219-1998.pdf |
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| Zusammenfassung |
| This paper presents developments of the Harniltonian
Approach to problems of fluid dynamics, and also considers some specific applications of
the general method to hydrodynamical models. Nonlinear gauge transformations are found to
result in a reduction to a minimum number of degrees of freedom, i.e. the number of pairs
of canonically conjugated variables used in a given hydrodynamical system. It is shown
that any conservative hydrodynamic model with additional fields which are in involution
may be always reduced to the canonical Hamiltonian system with three degrees of freedom
only. These gauge transformations are associated with the law of helicity conservation.
Constraints imposed on the corresponding Clebsch representation are determined for some
particular cases, such as, for example. when fluid motions develop in the absence of
helicity. For a long time the process of the introduction of canonical variables into
hydrodynamics has remained more of an intuitive foresight than a logical finding. The
special attention is allocated to the problem of the elaboration of the corresponding
regular procedure. The Harniltonian Approach is applied to geophysical models including
incompressible (3D and 2D) fluid motion models in curvilinear and lagrangian coordinates.
The problems of the canonical description of the Rossby waves on a rotating sphere and of
the evolution of a system consisting of N singular vortices are investigated. |
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