Simplified variational principles for non-barotropic magnetohydrodynamics

Yahalom, Asher

doi:10.1017/s0022377816000222

Cited by 21 publications

(52 citation statements)

References 41 publications

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“…Magnetic helicity is an invariant of MHD (e.g. Elsässer (1956), Woltjer (1958), Moffatt (1969Moffatt ( , 1978). In (1.7) it is assumed that the normal magnetic field component B n = B·n vanishes on the boundary ∂V .…”

Section: Introductionmentioning

confidence: 99%

On magnetohydrodynamic gauge field theory

Webb

Anco

2017

J. Phys. A: Math. Theor.

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Clebsch potential gauge field theory for magnetohydrodynamics is developed based in part on the theory of Calkin (1963). It is shown how the polarization vector P in Calkin's approach naturally arises from the Lagrange multiplier constraint equation for Faraday's equation for the magnetic induction B, or alternatively from the magnetic vector potential form of Faraday's equation. Gauss's equation, (divergence of B is zero) is incorporated in the variational principle by means of a Lagrange multiplier constraint. Noether's theorem coupled with the gauge symmetries is used to derive the conservation laws for (a) magnetic helicity, (b) cross helicity, (c) fluid helicity for non-magnetized fluids, and (d) a class of conservation laws associated with curl and divergence equations which applies to Faraday's equation and Gauss's equation. The magnetic helicity conservation law is due to a gauge symmetry in MHD and not due to a fluid relabelling symmetry. The analysis is carried out for the general case of a nonbarotropic gas in which the gas pressure and internal energy density depend on both the entropy S and the gas density ρ. The cross helicity and fluid helicity conservation laws in the non-barotropic case are nonlocal conservation laws that reduce to local conservation laws for the case of a barotropic gas. The connections between gauge symmetries, Clebsch potentials and Casimirs are developed. It is shown that the gauge symmetry functionals in the work of Henyey (1982) satisfy the Casimir determining equations.PACS numbers: 95.30. Qd,47.35.Tv,52.30.Cv,45.20.Jj,96.60.j,96.60.Vg P·dS = P x dy ∧ dz + P y dz ∧ dx + P z dx ∧ dy,( 1.5) is the polarization 2-form. In the usual MHD, non-relativistic limit ∇·P = 0 (i..e. ρ c = 0), and (1.2) simplifies to:

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Section: Introductionmentioning

confidence: 99%

On magnetohydrodynamic gauge field theory

Webb

Anco

2017

J. Phys. A: Math. Theor.

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“…which is just the circulation of the topological velocity along the magnetic field lines. This quantity can be written in terms of the generalized Clebsch representation of the velocity [18]:…”

Section: Metage Translationsmentioning

confidence: 99%

“…Yahalom & Lynden-Bell [4] has also shown that the translation group of the magnetic metage is connected to Woltjer [5,6] conservation of cross helicity for barotropic MHD. Recently the concept of metage was generalized also for non barotropic MHD in which magnetic field lines lie on entropy surfaces [7]. This was later generalized by dropping the entropy condition on magnetic field lines [8].…”

Section: Introductionmentioning

confidence: 99%

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A New Diffeomorphism Symmetry Group of Non-Barotropic Magnetohydrodynamics

Yahalom

2019

J. Phys.: Conf. Ser.

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The theorem of Noether dictates that for every continuous symmetry group of an Action the system must possess a conservation law. In this paper we discuss some subgroups of Arnold's labelling symmetry diffeomorphism related to non-barotropic magnetohydrodynamics (MHD) and the conservations laws associated with them. Those include but are not limited to the metage translation group and the associated topological conservations law of non-barotropic cross helicity.

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“…Both conservation laws for the helicity in the fluid dynamics case and the barotropic MHD case were shown to originate from a relabelling symmetry through the Noether theorem [4][5][6][7]. Consider the equations of non-barotropic MHD [8,9]:…”

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confidence: 99%

A conserved local cross helicity for non-barotropic MHD

Yahalom

2017

Geophysical & Astrophysical Fluid Dynamics

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Cross helicity is not conserved in non-barotropic magnetohydrodynamics (MHD) (as opposed to barotropic or incompressible MHD). Here we show that variational analysis suggests a new kind of cross helicity which is conserved in the non barotropic case. The non barotropic cross helicity reduces to the standard cross helicity under barotropic assumptions. The new cross helicity is conserved even for topologies for which the variational principle does not apply.

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Simplified variational principles for non-barotropic magnetohydrodynamics

Cited by 21 publications

References 41 publications

On magnetohydrodynamic gauge field theory

On magnetohydrodynamic gauge field theory

A New Diffeomorphism Symmetry Group of Non-Barotropic Magnetohydrodynamics

A conserved local cross helicity for non-barotropic MHD

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