Minimal atmospheric finite-mode models preserving symmetry and generalized Hamiltonian structures

PHYSICA D-NONLINEAR PHENOMENA

卷:240

Article

Bihlo, Alexander¹  Staufer, Johannes¹ 

[1] Univ Vienna, Fac Math, A-1090 Vienna, Austria

关键词: Finite-mode models;    Hamiltonian mechanics;    Nambu mechanics;    Symmetries;   

DOI  :  10.1016/j.physd.2010.11.011

来源: Elsevier

【 摘 要 】

A typical problem with the conventional Galerkin approach for the construction of finite-mode models is to keep structural properties unaffected in the process of discretization. We present two examples of finite-mode approximations that in some respect preserve the geometric attributes inherited from their continuous models: a three-component model of the barotropic vorticity equation known as Lorenz' maximum simplification equations [EN. Lorenz, Maximum simplification of the dynamic equations, Tellus 12 (3) (1960) 243-254] and a six-component model of the two-dimensional Rayleigh-Benard convection problem. It is reviewed that the Lorenz-1960 model respects both the maximal set of admitted point symmetries and an extension of the noncanonical Hamiltonian form (Nambu form). In a similar fashion, it is proved that the famous Lorenz-1963 model violates the structural properties of the Saltzman equations and hence cannot be considered as the maximum simplification of the Rayleigh-Benard convection problem. Using a six-component truncation, we show that it is again possible to retain both symmetries and the Nambu representation in the course of discretization. The conservative part of this six-component reduction is related to the Lagrange top equations. Dissipation is incorporated using a metric tensor. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

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