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Success of Arnol’d’s Method in a Hierarchy of Ocean Models

Conference paper
Part of the Springer Series in Nonlinear Dynamics book series (SSNONLINEAR)

Abstract

The method of Arnol’d[l, 2] is used to derive stability conditions of Hamiltonian systems with singular Poisson brackets; notably, those of fluid mechanics:[3, 4, 5, 6, 7] Let the field(s) φ(x, t) represent the state variables, and the Hamiltonian H [φ] and Poisson bracket {. , .} be such that ∂t φ = {φ, H}. The bracket must have the usual properties;[5] in addition, it may be singular, i.e. there may exist non-trivial functional(s) of state C[φ]-called Casimir(s)- such that {C, F} a ≡ 0, for any admissible[8] functional of state F[φ].

Keywords

Poisson Bracket Nonlinear Stability Hamiltonian Structure Slow Manifold Nonlinear Saturation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References & Footnotes

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • P. Ripa
    • 1
  1. 1.C.I.C.E.S.E.EnsenadaMéxico

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