title: Thermodynamics of magnetohydrodynamic flows with axial symmetry.
abstract: We present strategies based upon optimization principles in the case of the axisymmetric equations of magnetohydrodynamics (MHD). We derive the equilibrium state by using a minimum energy principle under the constraints of the MHD axisymmetric equations. We also propose a numerical algorithm based on a maximum energy dissipation principle to compute in a consistent way the nonlinearly dynamically stable equilibrium states. Then, we develop the statistical mechanics of such flows and recover the same equilibrium states giving a justification of the minimum energy principle. We find that fluctuations obey a Gaussian shape and we make the link between the conservation of the Casimirs on the coarse-grained scale and the process of energy dissipation. We contrast these results with those of two-dimensional hydrodynamical turbulence where the equilibrium state maximizes a H function at fixed energy and circulation and where the fluctuations are nonuniversal.
authors.affiliation: DRECAM/SPEC/CEA Saclay, and CNRS (URA2464), Gif sur Yvette, France. nicolas.leprovost@cea.fr
authors.forename: N
authors.initials: N
authors.lastname: Leprovost
authors.forename: B
authors.initials: B
authors.lastname: Dubrulle
authors.forename: P-H
authors.initials: PH
authors.lastname: Chavanis