Influence of equilibrium shear flow along the magnetic field on the resistive tearing instability

1983 ◽  
Vol 26 (10) ◽  
pp. 2966 ◽  
Author(s):  
R. B. Paris
Keyword(s):  
Magnetic Field ◽  
Shear Flow ◽  
Tearing Instability ◽  
The Magnetic Field

Compressible magnetoconvection in three dimensions: planforms and nonlinear behaviour

1995 ◽  
Vol 305 ◽  
pp. 281-305 ◽  
Author(s):  
P. C. Matthews ◽  
M. R. E. Proctor ◽  
N. O. Weiss
Keyword(s):  
Magnetic Field ◽  
Shear Flow ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Nonlinear Behaviour ◽  
Two Dimensional ◽  
Horizontal Shear ◽  
Mean Flow ◽  
The Magnetic Field

Convection in a compressible fiuid with an imposed vertical magnetic field is studied numerically in a three-dimensional Cartesian geometry with periodic lateral boundary conditions. Attention is restricted to the mildly nonlinear regime, with parameters chosen first so that convection at onset is steady, and then so that it is oscillatory.Steady convection occurs in the form of two-dimensional rolls when the magnetic field is weak. These rolls can become unstable to a mean horizontal shear flow, which in two dimensions leads to a pulsating wave in which the direction of the mean flow reverses. In three dimensions a new pattern is found in which the alignment of the rolls and the shear flow alternates.If the magnetic field is sufficiently strong, squares or hexagons are stable at the onset of convection. Both the squares and the hexagons have an asymmetrical topology, with upflow in plumes and downflow in sheets. For the squares this involves a resonance between rolls aligned with the box and rolls aligned digonally to the box. The preference for three-dimensional flow when the field is strong is a consequence of the compressibility of the layer- for Boussinesq magnetoconvection rolls are always preferred over squares at onset.In the regime where convection is oscillatory, the preferred planform for moderate fields is found to be alternating rolls - standing waves in both horizontal directions which are out of phase. For stronger fields, both alternating rolls and two-dimensional travelling rolls are stable. As the amplitude of convection is increased, either by dcereasing the magnetic field strength or by increasing the temperature contrast, the regular planform structure seen at onset is soon destroyed by secondary instabilities.

Transport Coefficients and Orientational Distributions of a Dilute Colloidal Dispersion Composed of Hematite Particles: Analysis for an Applied Magnetic Field Parallel to the Angular Velocity Vector of Simple Shear Flow

2006 ◽  
Author(s):  
Ryo Hayasaka ◽  
Akira Satoh ◽  
Tamotsu Majima
Keyword(s):  
Magnetic Field ◽  
Shear Flow ◽  
Magnetic Moment ◽  
Flow Direction ◽  
Transport Coefficients ◽  
Colloidal Dispersion ◽  
Field Direction ◽  
Simple Shear Flow ◽  
Magnetic Field Direction ◽  
The Magnetic Field

We have studied the influences of the magnetic field, shear rate, and random forces on transport coefficients such as viscosity and diffusion coefficient, and also on the orientational distributions of hematite particles composed of a dilute colloidal dispersion. Hematite particles are modeled as spheroids with a magnetic moment normal to the particle axis. In the present analysis, these particles are assumed to conduct the rotational Brownian motion in a simple shear flow as well as an external magnetic field. The basic equation of the orientational distribution function has been derived from the balance of the torques and solved by the numerical analysis method. The results obtained here are summarized as follows. With increasing the magnetic field, since the magnetic moment is strongly restricted to the magnetic field direction, the motion of the particle is forced to rotate in directions normal to the shear flow direction. In the case of a strong magnetic field and a smaller shear rate, the rodlike particles can freely rotate in the xy-plane with the magnetic moment remaining pointing to the magnetic field direction. On the other hand, for a strong shear flow, the particle has a tendency to incline in the flow direction with the magnetic moment pointing to the magnetic field direction. Additionaly, the diffusion coefficient gives rise to smaller values than expected, since the rodlike particle sediments with the particle inclining toward directions normal to the moment direction.

DOMAIN STRUCTURE AND MR EFFECT OF FERROFLUID EMULSION

2001 ◽  
Vol 15 (06n07) ◽  
pp. 859-863 ◽  
Author(s):  
CHIKARA OGAWA ◽  
YUICHI MASUBUCHI ◽  
JUN-ICHI TAKIMOTO ◽  
KIYOHITO KOYAMA
Keyword(s):  
Magnetic Field ◽  
Shear Flow ◽  
Domain Structure ◽  
Silicone Oil ◽  
Dielectric Constants ◽  
Immiscible Liquids ◽  
Water Based ◽  
Mr Effect ◽  
Er Fluids ◽  
The Magnetic Field

Blends of immiscible liquids with different dielectric constants and viscosities were known to show the ER effect due to the change of the domain structure by the electric field. In this paper, we report on our attempt to explore the possibility of the magnetic analog of these blend-type ER fluids. Water-based ferrofluid was blended with silicone oil with higher viscosity than the ferrofluid, in order to see whether the negative MR effect can be induced. The domain structure and the viscosity under the magnetic field and shear flow were studied. Growth of the droplet due to coalescence was observed under the field, which resulted in the gradual decrease of the shear viscosity.

On the Behavior of an Oblate Spheroidal Hematite Particle in a Simple Shear Flow Under a Uniform Magnetic Field Applied in the Flow Direction

2013 ◽  
Author(s):  
Haruka Yokoyama ◽  
Akira Satoh
Keyword(s):  
Magnetic Field ◽  
Brownian Motion ◽  
Shear Flow ◽  
Field Strength ◽  
Flow Direction ◽  
Hematite Particle ◽  
Oblate Spheroidal ◽  
Orientational Distribution ◽  
The Magnetic Field ◽  
Rotational Brownian Motion

We discuss the orientational properties of an oblate spheroidal hematite particle and also its influence on the rheological characteristics of a dilute suspension of these magnetic particles, by means of an analytical approach based on the orientational distribution function. An oblate spheroidal hematite particle has an important characteristic that it is magnetized in a direction normal to the particle axis. This particle is assumed to conduct the rotational Brownian motion including both the usual and spin Brownian motion in a simple shear flow under a uniform magnetic field applied in the shear flow direction. In the present analysis, we have taken into account only the friction force (torque) with neglecting the hydrodynamic interactions among particles. From the balance of the torques acting on a particle, we have developed the basic equation of the orientational distribution function. This basic equation has been numerically solved in order to investigate the dependence of the orientational distribution on the magnetic field strength, shear rate and rotational Brownian motion, and also the relationship between the orientational distribution and the transport coefficients such as viscosity and diffusion coefficient. The results obtained here are summarized as follows. If both the magnetic field and the shear flow are weak, the particle does not exhibit specific directional characteristics under the influence of rotational Brownian motion. If the magnetic field is more dominant, the particle inclines such that the oblate surface is parallel to the magnetic field direction. If the Peclet number increases and the shear flow becomes more dominant, the particle shows a sharper peak of the orientational distribution in the shear flow direction. The viscosity due to the magnetic torque increases and finally converges to a constant value as the magnetic field increases. The viscosity curve has an overshoot profile and this overshoot appears at a larger value of the magnetic field strength for the case of a larger Peclet number. Moreover, the viscosity increases more significantly for a larger aspect ratio or for a more oblate hematite particle. In a sedimentation process under the gravitational field, the translational diffusion coefficient decreases with increasing magnetic field strength in the present case of the magnetic field direction.

scholarly journals On the connection between the magneto-elliptic and magneto-rotational instabilities

2012 ◽  
Vol 698 ◽  
pp. 358-373 ◽  
Author(s):  
Krzysztof A. Mizerski ◽  
Wladimir Lyra
Keyword(s):  
Magnetic Field ◽  
Angular Velocity ◽  
Shear Flow ◽  
Growth Rates ◽  
Radial Profile ◽  
Rotational Instability ◽  
Horizontal Instability ◽  
Flow Limit ◽  
Limiting Case ◽  
The Magnetic Field

AbstractIt has recently been suggested that the magneto-rotational instability (MRI) is a limiting case of the magneto-elliptic instability (MEI). This limit is obtained for horizontal modes in the presence of rotation and an external vertical magnetic field, when the aspect ratio of the elliptic streamlines tends to infinite. In this paper we unveil the link between these previously unconnected mechanisms, explaining both the MEI and the MRI as different manifestations of the same magneto-elliptic-rotational instability (MERI). The growth rates are found and the influence of the magnetic and rotational effects is explained, in particular the effect of the magnetic field on the range of negative Rossby numbers at which the horizontal instability is excited. Furthermore, we show how the horizontal rotational MEI in the rotating shear flow limit is linked to the MRI by the use of the local shearing box model, typically used in the study of accretion discs. In such a limit the growth rates of the two instability types coincide for any power-law-type background angular velocity radial profile with negative exponent corresponding to the value of the Rossby number of the rotating shear flow. The MRI requirement for instability is that the background angular velocity profile is a decreasing function of the distance from the centre of the disc, which corresponds to the horizontal rotational MEI requirement of negative Rossby numbers. Finally a physical interpretation of the horizontal instability, based on a balance between the strain, the Lorentz force and the Coriolis force, is given.

Tearing instability inside a 2D current sheet with a normal magnetic field

2021 ◽  
Author(s):  
Chen Shi ◽  
Anton Artemyev ◽  
Marco Velli ◽  
Anna Tenerani
Keyword(s):  
Magnetic Field ◽  
Magnetic Reconnection ◽  
Current Sheet ◽  
Normal Component ◽  
Field Energy ◽  
Tearing Mode ◽  
Magnetic Field Energy ◽  
Tearing Instability ◽  
The Magnetic Field ◽  
Normal Magnetic Field

<p>Magnetic reconnection converts the magnetic field energy into thermal and kinetic energies of the plasma. This process usually happens at extremely fast speed and is therefore believed to be a fundamental mechanism to explain various explosive phenomena such as coronal mass ejections and planetary magnetospheric storms. How magnetic reconnection is triggered from the large magnetohydrodynamic (MHD) scales remains an open question, with some theoretical and numerical studies showing the tearing instability to be involved. Observations in the Earth’s magnetotail and near the magnetopause show that a finite normal magnetic field is usually present inside the reconnecting current sheet. Besides, such a normal field may also exist in the solar corona. However, how this normal magnetic field modifies the tearing instability is not thoroughly studied. Here we discuss the linear tearing instability inside a two-dimensional current sheet with a normal component of magnetic field where the magnetic tension force is balanced by ion flows parallel and anti-parallel to the magnetic field. We solve the dispersion relation of the tearing mode with wave vector parallel to the reconnecting magnetic field. Our results confirm that the finite normal magnetic field stabilizes the tearing mode and makes the mode oscillatory instead of purely growing.</p>

scholarly journals Ferrocholesteric–ferronematic transitions induced by shear flow and magnetic field

2017 ◽  
Vol 8 ◽  
pp. 2552-2561 ◽  
Author(s):  
Dmitriy V Makarov ◽  
Alexander A Novikov ◽  
Alexander N Zakhlevnykh
Keyword(s):  
Magnetic Field ◽  
Shear Flow ◽  
Velocity Gradient ◽  
Orientation Angle ◽  
Helical Structure ◽  
Shear Velocity ◽  
Critical Magnetic Field ◽  
Field Orientation ◽  
Magnetic Field Orientation ◽  
The Magnetic Field

We study the unwinding of the ferrocholesteric helical structure induced by a combined action of a magnetic field and a shear flow. Both influences are able to induce the ferrocholesteric–ferronematic transition independently; however, the differences between the magnetic field orientation and the flow alignment direction lead to a competition between magnetic and hydrodynamic mechanisms of influence on the ferrocholesteric structure. We analyze various orientations of a magnetic field relative to the direction of a shear flow. The pitch of the ferrocholesteric helix is obtained as function of the strength and the orientation angle of the magnetic field, the shear velocity gradient and a reactive parameter. Phase diagrams of ferrocholesteric–ferronematic transition and the pitch of the ferrocholesteric helix as functions of the material and the governing parameters are calculated. We find out that imposing a shear flow leads to a shift of the magnetic field threshold. The value of the critical magnetic field depends on the magnetic field orientation, the velocity gradient, and the viscous coefficients. We show that the interplay of a magnetic field and a shear flow can induce reentrant orientational transitions that are ferrocholesteric–ferronematic–ferrocholesteric.

Sign in / Sign up

Export Citation Format

Share Document