Thermodynamics of MHD flows with axial symmetry

Abstract

We present strategies based upon extremization principles, in the case of the axisymmetric equations of magnetohydrodynamics (MHD). We study the equilibrium shape 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 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.

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Cited by in corpus (7)

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• Long-range correlations and coherent structures in magnetohydrodynamic equilibria
• Strong vorticity fluctuations and antiferromagnetic correlations in axisymmetric fluid equilibria
• Statistical equilibrium principles in 2D fluid flow: from geophysical fluids to the solar tachocline