Two‐dimensionality in low‐magnetic Reynolds number magnetohydrodynamic turbulence subjected to a uniform external magnetic field and randomly stirred two‐dimensional force

1992 ◽  
Vol 4 (12) ◽  
pp. 2906-2914 ◽  
Author(s):  
Norihiko Nakauchi ◽  
Hiroshi Oshima ◽  
Yoshio Saito
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
External Magnetic Field ◽  
Magnetic Reynolds Number ◽  
Two Dimensional ◽  
Magnetohydrodynamic Turbulence ◽  
Uniform External Magnetic Field

A physical description of magnetic helicity evolution in the presence of reconnection lines

1991 ◽  
Vol 46 (1) ◽  
pp. 179-199 ◽  
Author(s):  
Andrew N. Wright ◽  
Mitchell A. Berger
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Magnetic Reynolds Number ◽  
Magnetic Helicity ◽  
Two Dimensional ◽  
Flux Tubes ◽  
Physical Description ◽  
Reconnection Region ◽  
Field Geometry ◽  
Field Lines

The dissipation of relative magnetic helicity due to the presence of a resistive reconnection region is considered. We show that when the reconnection region has a vanishing cross-section, helicity is conserved, in agreement with previous studies. It is also shown that in two-dimensional systems reconnection can produce highly twisted reconnected flux tubes. Reconnection at a high magnetic Reynolds number generally conserves helicity to a good approximation. However, reconnection with a small Reynolds number can produce significant dissipation of helicity. We prove that helicity dissipation in two-dimensional configurations is associated with the retention of some of the inflowing magnetic flux by the reconnection region, vr. When the reconnection site is a simple Ohmic conductor, all of the magnetic field parallel to the reconnection line that is swept into vr is retained. (In contrast, the inflowing magnetic field perpendicular to the line is annihilated.) We are able to relate the amount of helicity dissipation to the retained flux. A physical interpretation of helicity dissipation is developed by considering the diffusion of magnetic field lines through vr. When compared with helicity-conserving reconnection, the two halves of a reconnected flux sheet appear to have slipped relative to each other parallel to the reconnection line. This provides a useful method by which the reconnected field geometry can be constructed: the incoming flux sheets are ‘cut’ where they encounter vr, allowed to slip relative to each other, and then ‘pasted’ together to form the reconnected flux sheets. This simple model yields estimates for helicity dissipation and the flux retained by vr in terms of the amount of slippage. These estimates are in agreement with those expected from the governing laws.

The annihilation of a two-dimensional jet by a transverse magnetic field

1967 ◽  
Vol 30 (1) ◽  
pp. 65-82 ◽  
Author(s):  
H. K. Moffatt ◽  
J. Toomre
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Transverse Magnetic Field ◽  
Magnetic Interaction ◽  
Transverse Magnetic ◽  
Magnetic Reynolds Number ◽  
Two Dimensional ◽  
Dimensionless Numbers ◽  
Order Unity ◽  
The Magnetic Field

The effect of an applied transverse magnetic field on the development of a two-dimensional jet of incompressible fluid is examined. The jet is prescribed in terms of its mass flux ρQ0 and its lateral scale d at an initial section x = 0. The three dimensionless numbers characterizing the problem are a Reynolds number R = Q0/ν, a magnetic Reynolds number Rm = μσQ0, and a magnetic interaction parameter N = σB20d2/ρQ0, where ρ represents density, σ conductivity, μ permeability and B0 applied field strength, and it is assumed that \[ R_m \ll 1,\quad R\gg 1,\quad N\ll 1. \] It is shown that when M2 = RN [Gt ] 1, an inviscid treatment is appropriate, and that the effect of the magnetic field is then to destroy the jet momentum within a distance of order N−1 in the downstream direction. A general solution for inviscid development is obtained, and it is shown that a large class of velocity profiles (though not all of them) are self-preserving.When M2 [Lt ] 1, it is shown that the viscous similarity solution obtained by Moreau (1963a, b) is relevant. This solution is re-derived and re-interpreted; it implies that the jet momentum is destroyed within a distance of order $R^{\frac{1}{4}}N^{-\frac{3}{4}}$ in the downstream direction.Some further aspects of the jet annihilation problem are qualitatively discussed in § 4, viz. the nature of the overall flow field, the effect of the presence of distant boundaries, the effect of increasing Rm to order unity and greater, and the effect of oblique injection. Finally the development of a jet of conducting fluid into a nonconducting environment is considered; in this case the jet is not stopped by the magnetic field unless a return path outside the fluid for the induced current is available.

Stability of a Hartmann boundary layer under the influence of a parallel magnetic field

1968 ◽  
Vol 32 (4) ◽  
pp. 721-735 ◽  
Author(s):  
S. Abas
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Asymptotic Methods ◽  
Transverse Magnetic ◽  
Magnetic Reynolds Number ◽  
Power Series Solution ◽  
Neutral Stability ◽  
Two Dimensional ◽  
Parallel Magnetic Field

Stability to infinitesimal disturbances—when a parallel magnetic field is imposed—is investigated for the flow in the boundary layer set up by two-dimensional motion between parallel planes of a viscous, incompressible, electrically conducting fluid under the influence of a transverse magnetic field. The flow is assumed to take place at low magnetic Reynolds number. The usual asymptotic methods are employed for the solution, but, apart from the Tollmientype power series solution, an exact solution of the inviscid equation is obtained in terms of the hypergeometric function and its analytic continuation. Curves of neutral stability for two-dimensional disturbances are calculated and the results for critical Reynolds number modified to take into account three-dimensional disturbances. The parallel magnetic field is found to have a strong stabilizing influence.

scholarly journals NONCOMMUTATIVE GRAPHENE

2013 ◽  
Vol 28 (16) ◽  
pp. 1350064 ◽  
Author(s):  
CATARINA BASTOS ◽  
ORFEU BERTOLAMI ◽  
NUNO COSTA DIAS ◽  
JOÃO NUNO PRATA
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Dirac Equation ◽  
Energy Levels ◽  
Dirac Fermions ◽  
Two Dimensional ◽  
Dirac System ◽  
Noncommutative Parameter

We consider a noncommutative description of graphene. This description consists of a Dirac equation for massless Dirac fermions plus noncommutative corrections, which are treated in the presence of an external magnetic field. We argue that, being a two-dimensional Dirac system, graphene is particularly interesting to test noncommutativity. We find that momentum noncommutativity affects the energy levels of graphene and we obtain a bound for the momentum noncommutative parameter.

Flow Visualization by Means of Contactless Inductive Flow Tomography in the Presence of a Magnetic Brake

2015 ◽  
Vol 15 (1) ◽  
pp. 41-48 ◽  
Author(s):  
Matthias Ratajczak ◽  
Thomas Wondrak ◽  
Klaus Timmel ◽  
Frank Stefani ◽  
Sven Eckert
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Magnetic Fields ◽  
Flow Field ◽  
Continuous Casting ◽  
Flow Structure ◽  
Cross Section ◽  
Two Dimensional ◽  
Slab Casting ◽  
Two Dimensional Flow

AbstractIn continuous casting DC magnetic fields perpendicular to the wide faces of the mold are used to control the flow in the mold. Especially in this case, even a rough knowledge of the flow structure in the mold would be highly desirable. The contactless inductive flow tomography (CIFT) allows to reconstruct the dominating two-dimensional flow structure in a slab casting mold by applying one external magnetic field and by measuring the flow-induced magnetic fields outside the mold. For a physical model of a mold with a cross section of 140 mm×35 mm we present preliminary measurements of the flow field in the mold in the presence of a magnetic brake. In addition, we show first reconstructions of the flow field in a mold with the cross section of 400 mm×100 mm demonstrating the upward scalability of CIFT.

Turbulent dynamo action at low magnetic Reynolds number

1970 ◽  
Vol 41 (2) ◽  
pp. 435-452 ◽  
Author(s):  
H. K. Moffatt
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Magnetic Energy ◽  
Magnetic Reynolds Number ◽  
Dynamo Action ◽  
Ohmic Dissipation ◽  
Magnetic Energy Density ◽  
Magnetic Diffusivity

The effect of turbulence on a magnetic field whose length-scale L is initially large compared with the scale l of the turbulence is considered. There are no external sources for the field, and in the absence of turbulence it decays by ohmic dissipation. It is assumed that the magnetic Reynolds number Rm = u0l/λ (where u0 is the root-mean-square velocity and λ the magnetic diffusivity) is small. It is shown that to lowest order in the small quantities l/L and Rm, isotropic turbulence has no effect on the large-scale field; but that turbulence that lacks reflexional symmetry is capable of amplifying Fourier components of the field on length scales of order Rm−2l and greater. In the case of turbulence whose statistical properties are invariant under rotation of the axes of reference, but not under reflexions in a point, it is shown that the magnetic energy density of a magnetic field which is initially a homogeneous random function of position with a particularly simple spectrum ultimately increases as t−½exp (α2t/2λ3) where α(= O(u02l)) is a certain linear functional of the spectrum tensor of the turbulence. An analogous result is obtained for an initially localized field.

Dispersion properties of two-dimensional plasma photonic crystals with periodically external magnetic field

2012 ◽  
Vol 152 (14) ◽  
pp. 1221-1229 ◽  
Author(s):  
Hai-Feng Zhang ◽  
Shao-Bin Liu ◽  
Xiang-Kun Kong ◽  
Bo-Rui Bian ◽  
Ya-Nan Guo
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Photonic Crystals ◽  
Two Dimensional ◽  
Dispersion Properties ◽  
Plasma Photonic Crystals
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