Hamiltonian and action formalisms for two-dimensional gyroviscous MHD

Abstract

A general procedure for constructing action principles for continuum models via a generalization of Hamilton's principle of mechanics is described. Through the procedure, an action principle for a gyroviscous magnetohydrodynamics (MHD) model is constructed. The model is shown to agree with a reduced version of Braginskii's fluid equations. The construction reveals the origin of the gyromap, a device used to derive previous gyrofluid models. Also, a systematic reduction procedure is presented for obtaining the Hamiltonian structure in terms of the noncanonical Poisson bracket. The construction procedure yields a class of Casimir invariants, which are then used to variational principles for equilibrium equations with flow and gyroviscosity. The procedure for obtaining reduced fluid models with gyroviscosity is also described.

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Cited by in corpus (9)

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• Action Principles for Extended MHD Models
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• Inertial magnetohydrodynamics
• On the structure and statistical theory of turbulence of extended magnetohydrodynamics
• The action principle for generalized fluid motion including gyroviscosity
• Hamiltonian Magnetohydrodynamics: Lagrangian, Eulerian, and Dynamically Accessible Stability -- Examples with Translation Symmetry
• Multi-region relaxed magnetohydrodynamics with flow
• Multi-region relaxed Hall magnetohydrodynamics with flow