Shear-driven Hall-magnetohydrodynamic dynamos

2021 ◽  
Vol 932 ◽  
Author(s):  
Kengo Deguchi
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Hall Effect ◽  
Shear Flows ◽  
Skin Depth ◽  
Magnetic Reynolds Number ◽  
Matched Asymptotic Expansion ◽  
Simple Shear Flow ◽  
Magnetic Field Generation ◽  
The Magnetic Field

Nonlinear Hall-magnetohydrodynamic dynamos associated with coherent structures in subcritical shear flows are investigated by using unstable invariant solutions. The dynamo solution found has a relatively simple structure, but it captures the features of the typical nonlinear structures seen in simulations, such as current sheets. As is well known, the Hall effect destroys the symmetry of the magnetohydrodynamic equations and thus modifies the structure of the current sheet and mean field of the solution. Depending on the strength of the Hall effect, the generation of the magnetic field changes in a complex manner. However, a too strong Hall effect always acts to suppress the magnetic field generation. The hydrodynamic/magnetic Reynolds number dependence of the critical ion skin depth at which the dynamos start to feel the Hall effect is of interest from an astrophysical point of view. An important consequence of the matched asymptotic expansion analysis of the solution is that the higher the Reynolds number, the smaller the Hall current affects the flow. We also briefly discuss how the above results for a relatively simple shear flow can be extended to more general flows such as infinite homogeneous shear flows and boundary layer flows. The analysis of the latter flows suggests that interestingly a strong induction of the generated magnetic field might occur when there is a background shear layer.

scholarly journals The effect of velocity shear on dynamo action due to rotating convection

2013 ◽  
Vol 717 ◽  
pp. 395-416 ◽  
Author(s):  
D. W. Hughes ◽  
M. R. E. Proctor
Keyword(s):  
Magnetic Field ◽  
Velocity Field ◽  
Large Scale ◽  
Mean Field ◽  
Magnetic Reynolds Number ◽  
Velocity Shear ◽  
Magnetic Field Generation ◽  
Dynamo Action ◽  
Rotating Convection ◽  
The Magnetic Field

AbstractRecent numerical simulations of dynamo action resulting from rotating convection have revealed some serious problems in applying the standard picture of mean field electrodynamics at high values of the magnetic Reynolds number, and have thereby underlined the difficulties in large-scale magnetic field generation in this regime. Here we consider kinematic dynamo processes in a rotating convective layer of Boussinesq fluid with the additional influence of a large-scale horizontal velocity shear. Incorporating the shear flow enhances the dynamo growth rate and also leads to the generation of significant magnetic fields on large scales. By the technique of spectral filtering, we analyse the modes in the velocity that are principally responsible for dynamo action, and show that the magnetic field resulting from the full flow relies crucially on a range of scales in the velocity field. Filtering the flow to provide a true separation of scales between the shear and the convective flow also leads to dynamo action; however, the magnetic field in this case has a very different structure from that generated by the full velocity field. We also show that the nature of the dynamo action is broadly similar irrespective of whether the flow in the absence of shear can support dynamo action.

The magneto-hydrodynamic boundary layer in the two-dimensional steady flow past a semi-infinite flat plate. I. Uniform conditions at infinity

1963 ◽  
Vol 273 (1355) ◽  
pp. 496-508 ◽  
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Drag Coefficient ◽  
Flat Plate ◽  
Magnetic Reynolds Number ◽  
Linear Ordinary Differential Equations ◽  
Electrically Conducting ◽  
The Magnetic Field ◽  
Conditions At Infinity

The problem investigated is the flow of a viscous, electrically conducting liquid past a fixed, semi-infinite, unmagnetized but conducting flat plate. The liquid flow U and also the magnetic field H 0 at a distance from the plate are both assumed to be uniform and parallel to the plate. It is assumed that the Reynolds number R and magnetic Reynolds number R m are large enough for momentum and magnetic boundary layers to have developed. The standard boundary-layer techniques as used in the Blasius solution then apply and the problem reduces to the solution of two simultaneous non-linear ordinary differential equations. These are examined by the use of an iteration method suggested in the non ­ magnetic problem by Weyl and a solution of reasonable accuracy has been obtained for the drag coefficient. This confirms a similar result obtained in a different way by Carrier & Greenspan. The principal result of the paper is that the boundary layer thickens and drag coefficient diminishes steadily as the parameter S = µH 2 0 / 4πρU 2 increases. When S attains the finite value of unity the drag coefficient obtained here actually vanishes with the flow having been reduced to rest by the action of the magnetic field. This result might be inferred qualitatively since a finite amount of work has to be done in conveying liquid particles across the lines of magnetic force.

On one-dimensional flow of a conducting gas between electrodes – with application to MHD thrusters

1994 ◽  
Vol 266 ◽  
pp. 147-173 ◽  
Author(s):  
M. D. Cowley ◽  
J. H. Horlock
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Mass Flow ◽  
Magnetic Reynolds Number ◽  
Magnetic Pressure ◽  
Chamber Pressure ◽  
One Dimensional ◽  
Plenum Chamber ◽  
Dimensional Flow ◽  
The Magnetic Field

Inviscid, adiabatic, one-dimensional flow of a conducting gas in the presence of crossed electric and magnetic fields is investigated for the case where the magnetic field is generated by the current being supplied to the gas. The electrode geometry and the connections to the electrical power supply are such that the magnetic field falls to zero at the downstream end of the MHD duct. The analysis allows for magnetic Reynolds number rm to be anywhere in the range 0 to ∞ The main part of the investigation is restricted to consideration of ducts with constant spacing between electrodes.The way in which the density of the gas varies along the duct with the changing magnetic field is analysed generally and the results are then applied to the case where gas is fed to the MHD duct from high pressure in a plenum chamber and where the duct exhausts to a region of negligible pressure. If the flow is choked by the converging entry to the duct and the magnetic Reynolds number is moderate to high, the main electromagnetic effect is for the j × B forces to accelerate the gas to supersonic speeds. As rm is reduced, ohmic heating becomes more important, and it may cause the flow to be choked at exit from the duct, giving rise to a reduction in mass flow. For certain ranges of rm and ratio of initial magnetic pressure to plenum-chamber pressure the flow may choke at a sonic point within the duct itself, while accelerating from subsonic to supersonic through the point.Some illustrative examples of how properties vary with distance along the duct have been computed and the consequences of the analysis for MHD thrusters are explored. The magnetic forces will augment thrust per unit cross-sectional area, the essential measure of this being the drop in magnetic pressure along the duct, but there is an upper limit on the ratio of magnetic pressure to plenum-chamber pressure for flows to be possible. Flow at low magnetic Reynolds number is favoured if the object is to increase specific thrust by reducing mass flow through the duct.

scholarly journals Magnetic field generation by short ultraintense laser pulse in underdense plasmas

1996 ◽  
Vol 14 (1) ◽  
pp. 55-62 ◽  
Author(s):  
V. Yu. Bychenkov ◽  
V.T. Tikhonchuk
Keyword(s):  
Magnetic Field ◽  
Laser Pulse ◽  
Laser Pulses ◽  
Skin Depth ◽  
Beam Radius ◽  
Magnetic Field Generation ◽  
Field Generation ◽  
Underdense Plasmas ◽  
Magnetic Field Magnitude ◽  
The Magnetic Field

The theory of magnetic field generation due to the interaction of short relativistic laser pulses with underdense plasmas has been developed. The magnetic field is generated due to the inverse Faraday effect occurring witha circularly polarized laser pulse. The spatial distribution of the magnetic field is investigated. It is shown that the magnetic field magnitude depends on the relationship between the laser beam radius and the plasma skin-depth.

A kinematic theory of large magnetic Reynolds number dynamos

1972 ◽  
Vol 272 (1227) ◽  
pp. 431-462 ◽  
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Hybrid Approach ◽  
Magnetic Reynolds Number ◽  
Additional Contribution ◽  
Dynamo Action ◽  
Principal Mechanism ◽  
Azimuthal Magnetic Field ◽  
Field Note ◽  
The Magnetic Field

An asymptotic analysis is made of the magnetic induction equation for certain flows characterized by a large magnetic Reynolds number R . A novel feature is the hybrid approach given to the problem. Advantage is taken of a combination of Eulerian and Lagrange coordinates. Under certain conditions the problem can be reduced to solving a pair of coupled partial differential equations dependent on only two space coordinates (cf. Braginskii 1964 a ). Two main cases are considered. First the case is examined, in which the production of azimuthal magnetic field from the meridional magnetic field by a shear in the aximuthal flow is negligible. It is shown that a term J (analogous to electric current) is related linearly to the vector B which determines the magnetic field. (Note that B is not the magnetic field vector: see (1.33) and (2.35 b ).) The current J is likely to sustain dynamo action. Secondly, the case is considered, in which shearing of meridional magnetic field is the principal mechanism for creating the azimuthal magnetic field and the effect described above is one mechanism for creating meridional magnetic field from the azimuthal magnetic field. It is shown that the term J is not only linearly related to B , but has an additional contribution P x (V x B ), where P is characterized by the flow (see (4.15)). Both these effects have been predicted previously in theories of dynamo action produced by turbulent motions. Under certain restrictive conditions the resulting equations in the second case reduce to Braginskil’s (1964 a , b ) formulation for nearly symmetric dynamos. The words azimuthal and meridional are not used here in the usual sense. The difference in terminology is a consequence of a coordinate transformation.

A re-examination of the role of magnetic field lines in electromagnetic induction

1988 ◽  
Vol 66 (3) ◽  
pp. 245-248
Author(s):  
D. H. Boteler
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Field Line ◽  
Electric Fields ◽  
Electromagnetic Induction ◽  
Magnetic Reynolds Number ◽  
Unified View ◽  
Field Lines ◽  
The Magnetic Field

By adopting a view of magnetic fields, originally proposed by Faraday, in which the magnetic field changes by a movement of field lines, it is shown that a changing magnetic field can be described by the relation [Formula: see text] where v is the velocity of the magnetic field lines. These field-line velocities are shown to be the same as material velocities in conditions of infinite magnetic Reynolds number. The "moving field-line" view provides a phenomenological model of a changing magnetic field that is useful in electromagnetic induction studies. It also allows for a unified view of electromagnetic induction in which all induced electric fields can be explained by the v × B force alone.

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.

Decay of magnetohydrodynamic turbulence at low magnetic Reynolds number

2010 ◽  
Vol 657 ◽  
pp. 502-538 ◽  
Author(s):  
P. BURATTINI ◽  
O. ZIKANOV ◽  
B. KNAEPEN
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Magnetic Interaction ◽  
Theoretical Models ◽  
Magnetic Reynolds Number ◽  
Spectral Energy ◽  
Small Scale ◽  
Short Period ◽  
Decaying Turbulence ◽  
The Magnetic Field

We report a detailed numerical investigation of homogeneous decaying turbulence in an electrically conducting fluid in the presence of a uniform constant magnetic field. The asymptotic limit of low magnetic Reynolds number is assumed. Large-eddy simulations with the dynamic Smagorinsky model are performed in a computational box sufficiently large to minimize the effect of periodic boundary conditions. The initial microscale Reynolds number is about 170 and the magnetic interaction parameter N varies between 0 and 50. We find that except for a short period of time when N = 50, the flow evolution is strongly influenced by nonlinearity and cannot be adequately described by any of the existing theoretical models. One particularly noteworthy result is the near equipartition between the rates of Joule and viscous dissipations of the kinetic energy observed at all values of N during the late stages of the decay. Further, the velocity components parallel and perpendicular to the magnetic field decay at different rates, whose value depends on the strength of the magnetic field and the stage of the decay. This leads to a complex evolution of the Reynolds stress anisotropy ellipsoid, which goes from being rod-shaped, through spherical to disc-shaped. We also discuss the possibility of the power-law decay, the comparison between computed, experimental and theoretical decay exponents, the anisotropy of small-scale fluctuations, and the evolution of the spectral energy distributions.

Research on Velocity and Inducted Magnetic Field of Conducting Flow in 2D

2013 ◽  
Vol 432 ◽  
pp. 163-167
Author(s):  
Yang Liu ◽  
Ya Ge You ◽  
Ya Qun Zhang ◽  
Xue Ling Cao
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Velocity Field ◽  
Exact Solutions ◽  
Steady Flow ◽  
Magnetic Reynolds Number ◽  
The Magnetic Field

The purpose of this paper is to present the results of velocity and inducted magnetic field based on thedimensionlessgoverning equations of the incompressible, viscous, instant fluid from equation (1) to equation (6).We assumed a full developed and steady flow so that we can get the exact solutions. Firstly, we considered the situation of low magnetic Reynolds number and inducted magnetic field being ignored. Then secondly, we considered the situation of large magnetic Reynolds number. By comparing these two situations, we found two results: (1). theelectromagnetic force produced by the magnetic field changes the original velocity field a lot (Fig.2 and Fig.3); (2). the inducted magnetic field decreases with the decrease of magnetic Reynolds number. The results also prove that the inducted magnetic field can be ignored when the magnetic Reynolds number is less than or equal to 1 (Fig.5).

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