Thermodynamics of MHD flows with axial symmetry
Fluid Dynamics
2007-05-23 v1 Plasma Physics
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.
Keywords
Cite
@article{arxiv.physics/0407025,
title = {Thermodynamics of MHD flows with axial symmetry},
author = {Nicolas Leprovost and Pierre-Henri Chavanis and Berengere Dubrulle},
journal= {arXiv preprint arXiv:physics/0407025},
year = {2007}
}