dorsal/arxiv
View SchemaSimplified Variational Principles for Barotropic Magnetohydrodynamics
| Authors | Asher Yahalom, Donald Lynden-Bell |
|---|---|
| Categories | |
| ArXiv ID | physics/0603115 |
| URL | https://arxiv.org/abs/physics/0603115 |
| DOI | 10.1017/S0022112008002024 |
| Journal | Journal of Fluid Mechanics Volume 607 (25 July 2008), pp. 235-265 |
Abstract
Variational principles for magnetohydrodynamics were introduced by previous authors both in Lagrangian and Eulerian form. In this paper we introduce simpler Eulerian variational principles from which all the relevant equations of barotropic magnetohydrodynamics can be derived. The variational principle is given in terms of six independent functions for non-stationary barotropic flows and three independent functions for stationary barotropic flows. This is less then the seven variables which appear in the standard equations of barotropic magnetohydrodynamics which are the magnetic field $\vec B$ the velocity field $\vec v$ and the density $\rho$. The equations obtained for non-stationary barotropic magnetohydrodynamics resemble the equations of Frenkel, Levich & Stilman \cite{FLS}. The connection between the Hamiltonian formalism introduced in \cite{FLS} and the present Lagrangian formalism (with Eulerian variables) will be discussed. Finally the relations between barotropic magnetohydrodynamics topological constants and the functions of the present formalism will be elucidated.
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"abstract": "Variational principles for magnetohydrodynamics were introduced by previous\nauthors both in Lagrangian and Eulerian form. In this paper we introduce\nsimpler Eulerian variational principles from which all the relevant equations\nof barotropic magnetohydrodynamics can be derived. The variational principle is\ngiven in terms of six independent functions for non-stationary barotropic flows\nand three independent functions for stationary barotropic flows. This is less\nthen the seven variables which appear in the standard equations of barotropic\nmagnetohydrodynamics which are the magnetic field $\\vec B$ the velocity field\n$\\vec v$ and the density $\\rho$. The equations obtained for non-stationary\nbarotropic magnetohydrodynamics resemble the equations of Frenkel, Levich \u0026\nStilman \\cite{FLS}. The connection between the Hamiltonian formalism introduced\nin \\cite{FLS} and the present Lagrangian formalism (with Eulerian variables)\nwill be discussed. Finally the relations between barotropic\nmagnetohydrodynamics topological constants and the functions of the present\nformalism will be elucidated.",
"arxiv_id": "physics/0603115",
"authors": [
"Asher Yahalom",
"Donald Lynden-Bell"
],
"categories": [
"physics.plasm-ph",
"astro-ph",
"math-ph",
"math.MP",
"physics.flu-dyn"
],
"doi": "10.1017/S0022112008002024",
"journal_ref": "Journal of Fluid Mechanics Volume 607 (25 July 2008), pp. 235-265",
"title": "Simplified Variational Principles for Barotropic Magnetohydrodynamics",
"url": "https://arxiv.org/abs/physics/0603115"
},
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