Metriplectic framework for dissipative magneto-hydrodynamics

PHYSICA D-NONLINEAR PHENOMENA

卷:241

Article

Materassi, Massimo¹  Tassi, Emanuele² 

[1] CNR, ISC, I-50019 Sesta Fiorentino, Italy

[2] Aix Marseille Univ, Ctr Phys Theor, CNRS, F-13288 Marseille 09, France

关键词: Magneto-hydrodynamics;    Hamiltonian systems;    Dissipative systems;    Metriplectic systems;   

DOI  :  10.1016/j.physd.2011.12.013

来源: Elsevier

【 摘 要 】

The metriplectic framework, which allows for the formulation of an algebraic structure for dissipative systems, is applied to visco-resistive Magneto-Hydrodynamics (MHD), adapting what had already been done for non-ideal Hydrodynamics (HD). The result is obtained by extending the HD symmetric bracket and free energy to include magnetic field dynamics and resistive dissipation. The correct equations of motion are obtained once one of the Casimirs of the Poisson bracket for ideal MHD is identified with the total thermodynamic entropy of the plasma. The metriplectic framework of MHD is shown to be invariant under the Galileo Group. The metriplectic structure also permits us to obtain the asymptotic equilibria toward which the dynamics of the system evolves. This scheme is finally adapted to the two-dimensional incompressible resistive MHD, that is of major use in many applications. (C) 2012 Published by Elsevier B.V.

【 授权许可】

Free