Influence of magnetic reynolds number on the current distribution in a magnetohydrodynamic channel with allowance for the Hall effect

1973 ◽  
Vol 6 (3) ◽  
pp. 496-500
Author(s):  
A. L. Levin
Keyword(s):  
Reynolds Number ◽  
Hall Effect ◽  
Current Distribution ◽  
Magnetic Reynolds Number ◽  
Magnetohydrodynamic Channel

scholarly journals Second-order Solutions for Steady Magnetohydrodynamic Channel Flow with Anisotropic Conductivity

1972 ◽  
Vol 25 (6) ◽  
pp. 719
Author(s):  
DM Panton
Keyword(s):  
Reynolds Number ◽  
Perturbation Expansion ◽  
Magnetic Reynolds Number ◽  
Arbitrary Cross Section ◽  
Second Order ◽  
Anisotropic Conductivity ◽  
Square Channel ◽  
Flow Parameters ◽  
Flow Through ◽  
Magnetohydrodynamic Channel

Further investigation of steady magnetohydrodynamic flow through a straight channel of arbitrary cross section with nonconducting walls is considered, in the presence of anisotropic conductivity due to the Hall effect, where no restriction is made on the Reynolds number or magnetic Reynolds number. An approximate solution is provided by a perturbation expansion in terms of the Hall parameter, assumed small. Corrections are made to the first-order solutions established by Panton and Hosking (1971) and the solutions are then extended to the second order for a square channel. It is found that both the Reynolds number and magnetic Reynolds number terms have a significant influence on the mass transport, the former far outweighing the contribution to the flow established by Tani (1962) for the values of the flow parameters assumed.

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.

On dynamo action in a steady flow at large magnetic reynolds number

1989 ◽  
Vol 49 (1-4) ◽  
pp. 3-22 ◽  
Author(s):  
A. M. Soward
Keyword(s):  
Reynolds Number ◽  
Steady Flow ◽  
Magnetic Reynolds Number ◽  
Dynamo Action

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.

Fully developed MHD turbulence near critical magnetic Reynolds number

1981 ◽  
Vol 104 ◽  
pp. 419-443 ◽  
Author(s):  
J. Léorat ◽  
A. Pouquet ◽  
U. Frisch
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Isotropic Turbulence ◽  
Magnetic Energy ◽  
Reynolds Numbers ◽  
Magnetic Reynolds Number ◽  
Mhd Equations ◽  
Liquid Sodium ◽  
Turbulent Heat ◽  
Mhd Turbulence

Liquid-sodium-cooled breeder reactors may soon be operating at magnetic Reynolds numbers RM where magnetic fields can be self-excited by a dynamo mechanism (as first suggested by Bevir 1973). Such flows have kinetic Reynolds numbers RV of the order of 107 and are therefore highly turbulent.This leads us to investigate the behaviour of MHD turbulence with high RV and low magnetic Prandtl numbers. We use the eddy-damped quasi-normal Markovian closure applied to the MHD equations. For simplicity we restrict ourselves to homogeneous and isotropic turbulence, but we do include helicity.We obtain a critical magnetic Reynolds number RMc of the order of a few tens (non-helical case) above which magnetic energy is present. RMc is practically independent of RV (in the range 40 to 106). RMc can be considerably decreased by the presence of helicity: when the overall size of the flow L is much larger than the integral scale l0, RMc can drop below unity as suggested by an α-effect argument. When L ≈ l0 the drop can still be substantial (factor of 6) when helicity is a maximum. We examine how the turbulence is modified when RM crosses RMc: presence of magnetic energy, decreased kinetic energy, steepening of kinetic-energy spectrum, etc.We make no attempt to obtain quantitative estimates for a breeder reactor, but discuss some of the possible consequences of exceeding RMc, such as decreased turbulent heat transport. More precise information may be obtained from numerical simulations and experiments (including some in the subcritical regime).

A note on the magnetic Reynolds number

1986 ◽  
Vol 19 (7) ◽  
pp. L133-L135 ◽  
Author(s):  
J E Allen
Keyword(s):  
Reynolds Number ◽  
Magnetic Reynolds Number

The boundary layer in crossed-fields m.h.d.

1966 ◽  
Vol 25 (2) ◽  
pp. 229-240 ◽  
Author(s):  
W. R. Sears
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Flat Plate ◽  
Flow Problem ◽  
Inviscid Flow ◽  
Magnetic Reynolds Number ◽  
Large Reynolds Number ◽  
Zero Values ◽  
Plate Solution ◽  
A Current

This study of the boundary layer of steady, incompressible, plane, crossed-fields m.h.d. flow at large Reynolds numberReand magnetic Reynolds numberRmbegins with a review of Hartmann's case, where a boundary layer occurs whose thickness is proportional to (Re Rm)−½. Following this clue, it is shown that in general the boundary layer is a ‘local Hartmann boundary layer’. Its profiles are always exponential and it is determined completely by local quantities. The skin friction and the total electric current in the layer are proportional to the square root of the magnetic Prandtl number, i.e. to (Rm/Re)½. Thus the exterior-flow problem, the solution of which precedes a boundary-layer solution, generally involves a current sheet at the fluid-solid interface.This inviscid-flow problem becomes tractable if (Rm/Re)½is small enough to permit a linearized solution. The flow field about a flat plate at zero incidence is calculated in this approximation. It is pointed out that the thin-cylinder solutions of Sears & Resler (1959), which pertain toRm/Re= 0, can immediately be extended to small, non-zero values of this parameter by linear combination with this flat-plate solution.

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