ON THE KELVIN–HELMHOLTZ PROBLEM IN MAGNETOHYDRODYNAMICS WITH FINITE CONDUCTIVITY

1965 ◽  
Vol 43 (7) ◽  
pp. 1342-1346
Author(s):  
R. A. Wentzell
Keyword(s):  
Magnetic Field ◽  
Finite Conductivity ◽  
Type Problem ◽  
Horizontal Magnetic Field ◽  
Helmholtz Problem ◽  
Infinite Conductivity ◽  
The Magnetic Field

A study has been made of the effect of large but finite conductivity upon Kelvin–Helmholtz-type instabilities in the presence of a horizontal magnetic field. For finite conductivity, the selected Kelvin–Helmholtz-type problem which is stable at infinite conductivity is stable no matter how large the magnetic field. These instabilities grow aperiodically at a rate proportional to (resistivity)[Formula: see text].

THE EFFECT OF FINITE CONDUCTIVITY ON GRAVITY WAVES IN A HORIZONTAL MAGNETIC FIELD

1965 ◽  
Vol 43 (4) ◽  
pp. 645-652 ◽  
Author(s):  
R. A. Wentzell ◽  
J. H. Blackwell
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Gravity Waves ◽  
Gravitational Force ◽  
Finite Conductivity ◽  
Horizontal Magnetic Field ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Infinite Conductivity ◽  
Mode Solution

A study has been made of the behavior of the plane interface between a vacuum and an electrically conducting fluid subject to a normal gravitational force and a magnetic field parallel to the interface. The system is examined for perturbations which bend the lines of force, without restriction to the extensively used idealization of infinite electrical conductivity. The eigenvalue spectra obtained, which are surprisingly different from the simpler ones corresponding to infinite conductivity, are examined by approximate and numerical techniques over the complete range of electrical conductivity from infinity to zero. The disappearance of a normal mode solution above a critical value of conductivity is an interesting feature of the effect of finite conductivity on magnetohydrodynamic stability.

The propagation of small disturbances in hydromagnetics

1959 ◽  
Vol 5 (3) ◽  
pp. 387-400 ◽  
Author(s):  
G. S. S. Ludford
Keyword(s):  
Magnetic Field ◽  
Fourth Order ◽  
Plane Waves ◽  
Perfect Conductor ◽  
Finite Conductivity ◽  
Infinite Conductivity ◽  
Fourth Order Equations ◽  
Weak Fields ◽  
The Magnetic Field ◽  
Small Disturbances

This paper is concerned with the propagation of small initial disturbances in a conducting gas under the influence of a uniform external magnetic field.For a perfect conductor, there are three types of plane waves, each of which depends strongly on the angle at which the magnetic field is crossed. The modifying effects of finite conductivity are determined and, in the case of these waves, this is done uniformly for all angles. A general disturbance may be resolved into two parts, one of which satisfies a fourth-order equation and the other a fifth; for a perfect conductor these reduce to second-and fourth-order equations, respectively.The free oscillations of the gas are examined when it is contained in a rectangular box, and, in particular, when the external field is very weak or very strong. For vanishingly weak fields the idealization of infinite conductivity proves to be inadequate. Finally, the initial-value problem is discussed.

The Magnetic Anisotropy of Stretched Rubber as a Function of the Tension to Which It Is Subjected

1945 ◽  
Vol 18 (1) ◽  
pp. 8-9 ◽  
Author(s):  
Eugénie Cotton-Feytis
Keyword(s):  
Magnetic Field ◽  
Magnetic Anisotropy ◽  
Uniaxial Crystal ◽  
Horizontal Magnetic Field ◽  
First Approximation ◽  
The Difference ◽  
The Times ◽  
Angular Displacements ◽  
The Magnetic Field ◽  
Oscillation Method

Abstract From the standpoint of its magnetic anisotropy, stretched rubber is comparable in a first approximation to a uniaxial crystal, in which the direction of the axis is the same as the direction of elongation. It is possible to measure this anisotropy by means of the oscillation method used by Krishnan, Guha and Banerjee in studying crystals. The sample to be examined is suspended in a uniform horizontal magnetic field in such a manner that its axis is horizontal. It is then so arranged that the torsion of the suspension wire is zero when the rubber sample is in a position of equilibrium in the field. The times of oscillation T′ and T for very small angular displacements around this position, in the presence and then in the absence of the magnetic field, are then recorded. In this way the difference between the specific susceptibilities in the direction of the axis and in the horizontal direction perpendicular to the axis is calculated by application of the equation:

Kinematic dynamo problem in a linear velocity field

1984 ◽  
Vol 144 ◽  
pp. 1-11 ◽  
Author(s):  
Ya. B. Zel'Dovich ◽  
A. A. Ruzmaikin ◽  
S. A. Molchanov ◽  
D. D. Sokoloff
Keyword(s):  
Magnetic Field ◽  
Spatial Distribution ◽  
Velocity Field ◽  
Random Matrix ◽  
Magnetic Energy ◽  
Linear Velocity ◽  
Finite Conductivity ◽  
Kinematic Dynamo ◽  
Linear Velocity Field ◽  
The Magnetic Field

A magnetic field is shown to be asymptotically (t → ∞) decaying in a flow of finite conductivity with v = Cr, where C = Cζ(t) is a random matrix. The decay is exponential, and its rate does not depend on the conductivity. However, the magnetic energy increases exponentially owing to growth of the domain occupied by the field. The spatial distribution of the magnetic field is a set of thin ropes and (or) layers.

Magnetohydrodynamic convection in a vertical slot with horizontal magnetic field

2003 ◽  
Vol 475 ◽  
pp. 21-40 ◽  
Author(s):  
ULRICH BURR ◽  
LEOPOLD BARLEON ◽  
PAUL JOCHMANN ◽  
ARKADY TSINOBER
Keyword(s):  
Magnetic Field ◽  
Heat Transport ◽  
Convective Heat ◽  
Convective Motion ◽  
Vortex Structures ◽  
Test Fluid ◽  
Local Anisotropy ◽  
Horizontal Magnetic Field ◽  
Vertical Slot ◽  
The Magnetic Field

This article presents an experimental study of magnetohydrodynamic convection in a tall vertical slot under the influence of a horizontal magnetic field. The test fluid is an eutectic sodium potassium Na22K78 alloy with a small Prandtl number of Pr ≈ 0:02. The experimental setup covers Rayleigh numbers in the range 103 [lsim ] Ra [lsim ] 8×104 and Hartmann numbers 0 < M < 1600. The effect of the magnetic field on the convective heat transport is determined not only by damping as expected from Joule dissipation but also, for magnetic fields not too strong, the convective heat transfer may be considerably enhanced compared to ordinary hydrodynamic (OHD) flow. Estimates of the isotropy properties of the flow by a four-element temperature probe demonstrate that the increase in convective heat transport accompanies the formation of strong local anisotropy of the turbulent eddies in the sense of an alignment of the main direction of vorticity with the magnetic field. The reduced three-dimensional nonlinearities in non-isotropic flow favour the formation of largescale vortex structures compared to OHD flow, which are more effective for convective heat transport. Along with the formation of quasi-two-dimensional vortex structures, temperature fluctuations may be considerably enhanced in a magnetic field that is not too strong. However, above Hartmann numbers M [gsim ] 400 the formerly strongly time-dependent flow suddenly becomes stationary with an extended region of high convective heat transport at stationary flow. Finally, for very high Hartmann numbers the convective motion is strongly suppressed and the heat transport is reduced to a state close to pure heat conduction.

scholarly journals Large-scale dynamos in rapidly rotating plane layer convection

2018 ◽  
Vol 612 ◽  
pp. A97 ◽  
Author(s):  
P. J. Bushby ◽  
P. J. Käpylä ◽  
Y. Masada ◽  
A. Brandenburg ◽  
B. Favier ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Plane Layer ◽  
Cycle Period ◽  
Dynamo Action ◽  
Horizontal Magnetic Field ◽  
Vortex Instability ◽  
Large Scale Vortex ◽  
The Mean ◽  
The Magnetic Field

Context.Convectively driven flows play a crucial role in the dynamo processes that are responsible for producing magnetic activity in stars and planets. It is still not fully understood why many astrophysical magnetic fields have a significant large-scale component.Aims.Our aim is to investigate the dynamo properties of compressible convection in a rapidly rotating Cartesian domain, focusing upon a parameter regime in which the underlying hydrodynamic flow is known to be unstable to a large-scale vortex instability.Methods.The governing equations of three-dimensional non-linear magnetohydrodynamics (MHD) are solved numerically. Different numerical schemes are compared and we propose a possible benchmark case for other similar codes.Results.In keeping with previous related studies, we find that convection in this parameter regime can drive a large-scale dynamo. The components of the mean horizontal magnetic field oscillate, leading to a continuous overall rotation of the mean field. Whilst the large-scale vortex instability dominates the early evolution of the system, the large-scale vortex is suppressed by the magnetic field and makes a negligible contribution to the mean electromotive force that is responsible for driving the large-scale dynamo. The cycle period of the dynamo is comparable to the ohmic decay time, with longer cycles for dynamos in convective systems that are closer to onset. In these particular simulations, large-scale dynamo action is found only when vertical magnetic field boundary conditions are adopted at the upper and lower boundaries. Strongly modulated large-scale dynamos are found at higher Rayleigh numbers, with periods of reduced activity (grand minima-like events) occurring during transient phases in which the large-scale vortex temporarily re-establishes itself, before being suppressed again by the magnetic field.

Hydromagnetic Stability of Two Rivlin-Ericksen Elastico-Viscous Superposed Conducting Fluids

1997 ◽  
Vol 52 (6-7) ◽  
pp. 528-532
Author(s):  
R. C. Sharma ◽  
P. Kumar
Keyword(s):  
Magnetic Field ◽  
Wave Number ◽  
Horizontal Magnetic Field ◽  
Number Range ◽  
Wave Number Range ◽  
Unstable Configuration ◽  
The Stability ◽  
Superposed Fluids ◽  
The Magnetic Field ◽  
Conducting Fluids

Abstract The stability of the plane interface separating two Rivlin-Ericksen elastico-viscous superposed fluids of uniform densities when the whole system is immersed in a uniform horizontal magnetic field has been studied. The stability analysis has been carried out, for mathematical simplicity, for two highly viscous fluids of equal kinematic viscosities and equal kinematic viscoelasticities. It is found that the stability criterion is independent of the effects of viscosity and viscoelasticity and is dependent on the orientation and magnitude of the magnetic field. The magnetic field is found to stabilize a certain wave-number range of the unstable configuration. The behaviour of growth rates with respect to kinematic viscosity and kinematic viscoelasticity parameters are examined numerically.

Magnetohydrodynamic Stability of Two Streaming Superposed Viscoelastic Conducting Fluids

2001 ◽  
Vol 56 (6-7) ◽  
pp. 416-439
Author(s):  
Mohamed Fahmy El
Keyword(s):  
Magnetic Field ◽  
Stable Configuration ◽  
Retardation Time ◽  
Horizontal Magnetic Field ◽  
Fluid Velocities ◽  
Unstable Configuration ◽  
The Stability ◽  
The Magnetic Field ◽  
Conducting Fluids ◽  
Alfven Velocity

Abstract The stability of the plane interface separating two Oldroydian viscoelastic superposed moving fluids of uniform densities when immersed in a uniform horizontal magnetic field has been in­ vestigated. The stability analysis has been carried out, for mathematical simplicity, for two highly viscous fluids of equal kinematic viscosities. It is found that the potentially stable configuration remains stable if the fluids are at rest, while it becomes unstable if the fluids move. The stability criterion is found to be independent of the viscosity and viscoelasticity, and to be dependent on the orientation of the magnetic field and the magnitudes of the fluids and Alfven velocities. It is also found that the potentially unstable configuration remains unstable in the absence of average fluid velocities, or in the presence of fluid velocities and absence of a magnetic field. The magnetic field is found to stabilize a certain wavenumbers range of the unstable configuration even in the presence of the effects of viscoelasticity. The behaviour of growth rates with respect to the stress relaxation time, strain retardation time, fluid and Alfven velocity parameters is examined analytically, and the stability conditions are obtained and discussed. -Pacs: 47.20.-k; 47.50.+d; 47.65.+a.

RESPONSE OF DYKE TO OSCILLATING DIPOLE

Geophysics ◽  
1958 ◽  
Vol 23 (1) ◽  
pp. 128-133 ◽  
Author(s):  
James Paul Wesley
Keyword(s):  
Magnetic Field ◽  
Closed Form ◽  
Scalar Potential ◽  
Three Dimensions ◽  
Electromagnetic Response ◽  
Dipole Source ◽  
First Approximation ◽  
Sulfide Ore ◽  
Infinite Conductivity ◽  
The Magnetic Field

A dyke of sulfide ore may be geophysically prospected by observing its electromagnetic response to a slowly oscillating magnetic dipole source. An excellent first approximation of the fields generated is obtained by considering the idealized case of a dyke of infinite conductivity and vanishing thickness in a vacuum. Surprisingly, this idealized problem can be solved exactly in terms of a newly discovered Green’s function for Laplace’s equation (in three dimensions) which is simply expressed in closed form. The magnetic scalar potential and the magnetic field are given for final results.

Nonlinear compressible magnetoconvection. Part 3. Travelling waves in a horizontal field

1995 ◽  
Vol 300 ◽  
pp. 287-309 ◽  
Author(s):  
D. P. Brownjohn ◽  
N. E. Hurlburt ◽  
M. R. E. Proctor ◽  
N. O. Weiss
Keyword(s):  
Magnetic Field ◽  
Numerical Experiments ◽  
Strong Field ◽  
Travelling Waves ◽  
Standing Waves ◽  
Weak Field ◽  
Horizontal Magnetic Field ◽  
Weakly Nonlinear ◽  
Physical Mechanisms ◽  
The Magnetic Field

We present results of numerical experiments on two-dimensional compressible convection in a polytropic layer with an imposed horizontal magnetic field. Our aim is to determine how far this geometry favours the occurrence of travelling waves. We therefore delineate the region of parameter space where travelling waves are stable, explore the ways in which they lose stability and investigate the physical mechanisms that are involved. In the magnetically dominated regime (with the plasma beta, $\hat{\beta}$ = 8), convection sets in at an oscillatory bifurcation and travelling waves are preferred to standing waves. Standing waves are stable in the strong-field regime ($\hat{\beta}$ = 32) but travelling waves are again preferred in the intermediate region ($\hat{\beta}$ = 128), as suggested by weakly nonlinear Boussinesq results. In the weak-field regime ($\hat{\beta}$ ≥ 512) the steady nonlinear solution undergoes symmetry-breaking bifurcations that lead to travelling waves and to pulsating waves as the Rayleigh number, $\circ{R}$, is increased. The numerical experiments are interpreted by reference to the bifurcation structure in the ($\hat{\beta}$, $\circ{R}$)-plane, which is dominated by the presence of two multiple (Takens-Bogdanov) bifurcations. Physically, the travelling waves correspond to slow magnetoacoustic modes, which travel along the magnetic field and are convectively excited. We conclude that they are indeed more prevalent when the field is horizontal than when it is vertical.

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