A General Metriplectic Framework with Application to Dissipative Extended Magnetohydrodynamics

Abstract

General equations for conservative yet dissipative (entropy producing) extended magnetohydrodynamics are derived from two-fluid theory. Keeping all terms generates unusual cross-effects, such as thermophoresis and a current viscosity that mixes with the usual velocity viscosity. While the Poisson bracket of the ideal version of this model have already been discovered, we determine its metriplectic counterpart that describes the dissipation. This is done using a new and general thermodynamic point of view for deriving dissipative brackets, a means of derivation that is natural for understanding and creating dissipative brackets. Finally the formalism is used to study dissipation in the Lagrangian variable picture where, in the context of extended magnetohydrodynamics, nonlocal dissipative brackets naturally emerge.

arXiv comment32 pages

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Cited by in corpus (8)

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• A Collision Operator for Describing Dissipation in Noncanonical Phase Space
• Collisional Gyrokinetics Teases the Existence of Metriplectic Reduction
• Dissipative Brackets for the Fokker-Planck Equation in Hamiltonian Systems and Characterization of Metriplectic Manifolds
• A class of three-dimensional gyroviscous magnetohydrodynamic models
• Metriplectic foundations of gyrokinetic Vlasov-Maxwell-Landau theory
• Singular cotangent models and complexity in fluids with dissipation
• Structure-preserving and thermodynamically consistent finite element discretization for visco-resistive MHD with thermoelectric effect