Metriplectic framework for dissipative magneto-hydrodynamics
نویسندگان
چکیده
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 eld dynamics and resistive dissipation. The correct equations of motion are obtained once one of the Casimirs of the Poisson bracket for ideal MHD is identi ed 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 nally adapted to the two-dimensional incompressible resistive MHD, that is of major use in many applications.
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