Related papers: Potential Vorticity in Magnetohydrodynamics
Conservation laws in ideal gas dynamics and magnetohydrodynamics (MHD) associated with fluid relabelling symmetries are derived using Noether's first and second theorems. Lie dragged invariants are discussed in terms of the MHD Casimirs. A…
A multi-symplectic formulation of ideal magnetohydrodynamics (MHD) is developed based on a Clebsch variable variational principle in which the Lagrangian consists of the kinetic minus the potential energy of the MHD fluid modified by…
The conservation of the recently formulated relativistic canonical helicity [Yoshida Z, Kawazura Y, and Yokoyama T 2014 J. Math. Phys. 55 043101] is derived from Noether's theorem by constructing an action principle on the relativistic…
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…
In this paper we discuss conservation laws in ideal magnetohydrodynamics (MHD) and gas dynamics associated with advected invariants. The invariants in some cases, can be related to fluid relabelling symmetries associated with the Lagrangian…
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 ${\bf P}$ in Calkin's approach, naturally arises from the Lagrange multiplier…
We outline how discrete analogues of the conservation of potential vorticity may be achieved in Finite Element numerical schemes for a variational system which has the particle relabelling symmetry, typically shallow water equations. We…
Using a four-dimensional manifestly covariant formalism suitable for classical fluid dynamics, it is shown that the conservation of potential vorticity is not associated with any symmetry of the equations of motion but is instead a trivial…
The Lagrangian, multi-dimensional, ideal, compressible gasdynamic equations are written in a multi-symplectic form, in which the Lagrangian fluid labels, $m^i$ (the Lagrangian mass coordinates) and time $t$ are the independent variables,…
The paper considers the plane one-dimensional flows for magnetohydrodynamics in the mass Lagrangian coordinates. The inviscid, thermally non-conducting medium is modeled by a polytropic gas. The equations are examined for symmetries and…
A recent paper arXiv:1312.4890 on multi-symplectic magnetohydrodynamics (MHD) using Clebsch variables in an Eulerian action principle with constraints is further extended. We relate a class of symplecticity conservation laws to a vorticity…
Two applications of the Noether method for fluids and plasmas are presented based on the Euler-Lagrange and Euler-Poincare variational principles, which depend on whether the dynamical fields are to be varied independently or not,…
A recent paper considered symmetries and conservation laws of the plane one-dimensional flows for magnetohydrodynamics in the mass Lagrangian coordinates. This paper analyses the one-dimensional magnetohydrodynamics flows with cylindrical…
The exact law for fully developed homogeneous compressible magnetohydrodynamics (CMHD) turbulence is derived. For an isothermal plasma, without the assumption of isotropy, the exact law is expressed as a function of the plasma velocity…
Based on the Newton's second law and the Maxwell equations for the electromagnetic fields, we establish a new 3D incompressible magneto-hydrodynamics(MHD) equations for the motion of plasma under the standard Coulomb gauge. By using the…
We show that relativistic magnetohydrodynamics (MHD) can be recast as a novel theory of superfluidity. This new theory formulates MHD just in terms of conservation equations, including dissipative effects, by introducing appropriate…
Compressible ideal magnetohydrodynamics (MHD) is formulated in terms of the time evolution of potential vorticity and magnetic flux per unit mass using a compact Lie bracket notation. It is demonstrated that this simplifies analytic…
Parker's formulation of isotopological plasma relaxation process in magnetohydrodynamics (MHD) is extended to Hall MHD. The torsion coefficient alpha in the Hall MHD Beltrami condition turns out now to be proportional to the "potential…
Symmetries of the one-dimensional shallow water magnetohydrodynamics equations (SMHD) in Gilman's approximation are studied. The SMHD equations are considered in case of a plane and uneven bottom topography in Lagrangian and Eulerian…
We present a variational approach for relativistic ideal hydrodynamics interacting with electromagnetic fields. The momentum of fluid is introduced as the canonical conjugate variable of the position of a fluid element, which coincides with…