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)


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].


Poisson Bracket Nonlinear Stability Hamiltonian Structure Slow Manifold Nonlinear Saturation 
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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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