Shear-driven dynamo waves at high magnetic Reynolds number

Nature ◽  
2013 ◽  
Vol 497 (7450) ◽  
pp. 463-465 ◽  
Author(s):  
S. M. Tobias ◽  
F. Cattaneo
Keyword(s):  
Reynolds Number ◽  
Magnetic Reynolds Number ◽  
Dynamo Waves

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).

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.

2-D numerical simulation of electron MHD acceleration under low magnetic Reynolds number

2021 ◽  
Author(s):  
Xu Pan ◽  
Sheng-Wu Zhang ◽  
Wei Xu ◽  
Zhi-Wen Ding ◽  
Yuan-Ran Qiu
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Magnetic Reynolds Number

A magneto-hydrodynamic Stokes flow

1961 ◽  
Vol 260 (1300) ◽  
pp. 79-90 ◽  
Keyword(s):  
Reynolds Number ◽  
Stokes Flow ◽  
Hartmann Number ◽  
Magnetic Reynolds Number ◽  
Conducting Fluid ◽  
Slow Flow ◽  
Magnetic Pole ◽  
Total Drag ◽  
Conducting Sphere ◽  
Stokes Drag

This paper considers the slow flow of a viscous, conducting fluid past a non-conducting sphere at whose centre is a magnetic pole. The magnetic Reynolds number is assumed to be small, and the modifications to the classical Stokes flow and the free magnetic pole field are obtained for an arbitrary Hartmann number. The total drag D on the sphere has been calculated, and the ratio D / D s determined as a function of the Hartmann number M , where D s is the Stokes drag. In particular ( D — D s )/ D s = 37/210 M 2 + O ( M 4 ) for small M and ( D — D s )/ Ds ~ 0·7205 M - 1 as M → ∞.

ADOMIAN DECOMPOSITION METHOD (ADM) SIMULATION OF MAGNETO-BIO-TRIBOLOGICAL SQUEEZE FILM WITH MAGNETIC INDUCTION EFFECTS

2015 ◽  
Vol 15 (05) ◽  
pp. 1550072 ◽  
Author(s):  
O. ANWAR BÉG ◽  
D. TRIPATHI ◽  
T. SOCHI ◽  
P. K. GUPTA
Keyword(s):  
Reynolds Number ◽  
Magnetic Induction ◽  
Decomposition Method ◽  
Magnetic Force ◽  
Adomian Decomposition Method ◽  
Magnetic Reynolds Number ◽  
Squeeze Film ◽  
Strength Parameter ◽  
Numerical Verification ◽  
Adomian Decomposition

The Adomian decomposition method (ADM) is applied to analyze Newtonian bio-magneto-tribological squeeze film flow with magnetic induction effects incorporated. Robust solutions are developed for the transformed radial and tangential momentum and radial and tangential induced magnetic field conservation equations. The effects of squeeze Reynolds number (N1= Rem/ Bt where Bt = Batchelor number), dimensionless axial magnetic force strength parameter (N2), dimensionless tangential magnetic force strength parameter (N3), magnetic Reynolds number ( Rem) are depicted graphically. ADM is observed to demonstrate excellent convergence, stability and versatility in simulating both magnetic squeeze film problems. Numerical verification is achieved with Nakamura's tridiagonal finite difference method (NTM). The simulations are relevant to "smart" biological bearings and prosthetics (e.g., "smart knees") exploiting magnetic fluids.

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