Magnetic Shear Flow Research Articles

VIOLATION OF RICHARDSON'S CRITERION VIA INTRODUCTION OF A MAGNETIC FIELD

Shear flow instabilities can profoundly affect the diffusion of momentum in jets, stars, and disks. The Richardson criterion gives a sufficient condition for instability of a shear flow in a stratified medium. The velocity gradient $V'$ can only destabilize a stably stratified medium with squared Brunt-Vaisala frequency $N^2$ if $V'^2/4>N^2$. We find this is no longer true when the medium is a magnetized plasma. We investigate the effect of stable stratification on magnetic field and velocity profiles unstable to magneto-shear instabilities, i.e., instabilities which require the presence of both magnetic field and shear flow. We show that a family of profiles originally studied by Tatsuno & Dorland (2006) remain unstable even when $V'^2/4<N^2$, violating the Richardson criterion. However, not all magnetic fields can result in a violation of the Richardson criterion. We consider a class of flows originally considered by Kent (1968), which are destabilized by a constant magnetic field, and show that they become stable when $V'^2/4<N^2$, as predicted by the Richardson criterion. This suggests that magnetic free energy is required to violate the Richardson criterion. This work implies that the Richardson criterion cannot be used when evaluating the ideal stability of a sheared, stably stratified, and magnetized plasma. We briefly discuss the implications for astrophysical systems.

On the linear stability of weakly ionized, magnetized planar shear flows

We investigate the effects of ambipolar diffusion and the Hall effect on the stability of weakly-ionized, magnetized planar shear flows. Employing a local approach similar to the shearing-sheet approximation, we solve for the evolution of linear perturbations in both streamwise-symmetric and non-streamwise-symmetric geometries using WKB techniques and/or numerical methods. We find that instability arises from the combination of shear and non-ideal magnetohydrodynamic processes, and is a result of the ability of these processes to influence the free energy path between the perturbations and the shear. They turn what would be simple linear-in-time growth due to current and vortex stretching from shear into exponentially-growing instabilities. Our results aid in understanding previous work on the behaviour of weakly-ionized accretion discs. In particular, the recent finding that the Hall effect and ambipolar diffusion destabilize both positive and negative angular velocity gradients acquires a natural explanation in the more general context of this paper. We construct a simple toy model for these instabilities based upon transformation operators (shears, rotations, and projections) that captures both their qualitative and, in certain cases, exact quantitative behaviour.

Overreflection and Generation of Gravito‐Alfven Waves in Solar‐Type Stars

The dynamics of linear perturbations is studied in magnetized plasma shear flows with a constant shearing rate and with gravity-induced stratification. The general set of linearized equations is derived, and the two-dimensional case is considered in detail. The Boussinesq approximation is used in order to examine relatively small scale perturbations of low-frequency modes: gravito-Alfven waves (GAWs) and entropy-mode (EM) perturbations. It is shown that for flows with arbitrary shearing rate, there exists a finite time interval of nonadiabatic evolution of the perturbations. The nonadiabatic behavior manifests itself in a twofold way, viz., by the overreflection of the GAWs and by the generation of GAWs from EM perturbations. It is shown that these phenomena act as efficient transformers of the equilibrium flow energy into the energy of the perturbations for moderate and high shearing rate solar plasma flows. Efficient generation of GAWs by EM perturbations takes place for shearing rates about an order of magnitude smaller than necessary for development of a shear instability. The latter fact could have important consequences for the problem of angular momentum redistribution within the Sun and solar-type stars.

The mean electro-motive force and current helicity under the influence of rotation, magnetic field and shear

The mean electromotive force (MEMF) in a rotating stratified magnetohydrodynamical turbulence is studied. Our study is based on the mean-field magnetohydrodynamics framework and τ approximation. We compute the effects of the large-scale magnetic fields (LSMF), global rotation and large-scale shear flow on the different parts of the MEMF (such as α-effect, turbulent diffusion, turbulent transport, etc.) in an explicit form. The influence of the helical magnetic fluctuations which stem from the small-scale dynamo is taken into account, as well. In the article, we derive the equation governing the current helicity evolution. It is shown that the joint effect of the differential rotation and magnetic fluctuations in the stratified media can be responsible for the generation, maintenance and redistribution of the current helicity. The implication of the obtained results to astrophysical dynamos is considered.

Structure and rheology of model-ferrofluids under shear flow

Nonequilibrium simulations of ferromagnetic colloids in the presence of a magnetic field and plane shear flow are performed. Results for the nonequilibrium magnetization and the nonequilibrium structure factor are presented. We observe that the nonequilibrium magnetization and the magnetoviscosity are enhanced due to dipolar interactions. Structure formation due to magnetic field and shear flow are observed in qualitative agreement with experimental results.

Aqueous cholesteric liquid crystals using uncharged rodlike polypeptides.

The aqueous, lyotropic liquid-crystalline phase behavior of the alpha-helical polypeptide, poly(N(epsilon)-2-[2-(2-methoxyethoxy)ethoxy]acetyl-lysine) (1), has been studied using optical microscopy and X-ray scattering. Solutions of optically pure 1 were found to form cholesteric liquid crystals at volume fractions that decreased with increasing average chain length. At very high volume fractions, the formation of a hexagonal mesophase was observed. The pitch of the cholesteric phase could be varied by a mixture of enantiomeric samples L-1 and D-1, where the pitch increased as the mixture approached equimolar. The cholesteric phases could be untwisted, using either magnetic field or shear flow, into nematic phases, which relaxed into cholesterics upon removal of field or shear. We have found that the phase diagram of 1 in aqueous solution parallels that of poly(gamma-benzyl glutamate) in organic solvents, thus providing a useful system for liquid-crystal applications requiring water as solvent.

How Can Jets Survive MHD Instabilities?

We present the main findings of two recent studies using high-resolution MHD simulations of supersonic magnetized shear flow layers. First, a strong large-scale coalescence effect partially countered by small-scale reconnection events is shown to dominate the dynamics in a two-dimensional layer subject to Kelvin-Helmholtz (KH) instabilities. Second, an interaction mechanism between two different types of instabilities (KH and current-driven modes) is shown to occur in a cylindrical jet configuration embedded in an helical magnetic field. Finally, we discuss the implications of these results for astrophysical jets survival.

The two-dimensional magnetohydrodynamic Kelvin–Helmholtz instability: Compressibility and large-scale coalescence effects

The Kelvin–Helmholtz (KH) instability occurring in a single shear flow configuration that is embedded in a uniform flow-aligned magnetic field, is revisited by means of high resolution two-dimensional magnetohydrodynamic simulations. First, the calculations extend previous studies of magnetized shear flows to a higher compressibility regime. The nonlinear evolution of an isolated KH billow emerging from the fastest growing linear mode for a convective sonic Mach number Mcs=0.7 layer is in many respects similar to its less compressible counterpart (Mach Mcs=0.5). In particular, the disruptive regime where locally amplified, initially weak magnetic fields, control the nonlinear saturation process is found for Alfvén Mach numbers 4≲MA≲30. The most notable difference between Mcs=0.7 vs Mcs=0.5 layers is that higher density contrasts and fast magnetosonic shocklet structures are observed. Second, the use of adaptive mesh refinement allows to parametrically explore much larger computational domains, including up to 22 wavelengths of the linearly dominant mode. A strong process of large-scale coalescence is found, whatever the magnetic field regime. It proceeds through continuous pairing/merging events between adjacent vortices up to the point where the final large-scale vortical structure reaches the domain dimensions. This pairing/merging process is attributed to the growth of subharmonic modes and is mainly controlled by relative phase differences between them. These grid-adaptive simulations demonstrate that even in very weak magnetic field regimes (MA≃30), the large-scale KH coalescence process can trigger tearing-type reconnection events previously identified in cospatial current–vortex sheets.

A rheometer for the investigation of structure formation in ferrofluids under magnetic field and shear flow

A rheometer for the investigation of structure formation in ferrofluids under magnetic field and shear flow

Nonlinear dust Alfvén waves in plasmas with shear flow

In the presence of a nonuniform magnetic field and shear flow, two coupled nonlinear equations for perturbed electromagnetic fields are derived in a dusty plasma. A linear instability of dust Alfvén waves is discussed and the analytical solution of the nonlinear equations is found in the form of tripolar vortices.

Comment on “Effect of flow profile on low frequency drift-type waves in a dusty plasma” [Phys. Plasmas 8, 3150 (2001)

It is pointed out that a recently published study [Phys. Plasmas 8, 3150 (2001)] of the effects of magnetic shear and shear flow on dust-drift waves has already been studied earlier. Further, the results obtained in Phys. Plasmas 8, 3150 (2001) are erroneous as the shear flow effect has been included in an inappropriate manner.

Local Buoyant Instability of Magnetized Shear Flows

The effect of magnetic shear and shear flow on local buoyant instabilities is investigated. A simple model is constructed allowing for an arbitrary entropy gradient and a shear plasma flow in the Boussinesq approximation. A transformation to shearing magnetic coordinates achieves a model with plasma flow along the magnetic field lines where the coordinate lines are coincident with the field lines. The solution for the normal modes of the system depends on two parameters: the Alfven Mach number of the plasma flow and the entropy gradient. The behavior of the unstable normal modes of this system is summarized by a stability diagram. Important characteristics of this stability diagram are the following: magnetic shear is stabilizing, and the entropy gradient must exceed a threshold value for unstable mode growth to occur; flow acts to suppress mode growth in a substantially unstable regime as expected, yet near marginal stability it can lessen the stabilizing effect of magnetic shear and enhance the growth rates of the instability; and, as the Alfven Mach number approaches 1, the instability is completely stabilized. Analytical work is presented supporting the characteristics of the stability diagram and illuminating the physical mechanisms controlling the behavior of the model. A derivation of the stability criterion for the case without shear flow, asymptotic solutions in the limit that the Alfven Mach number approaches 1 and in the limit of zero growth rate, a complete WKB solution for large growth rates, an exactly soluble bounded straight field case, and energy conservation relations are all presented. The implications of this work for astrophysical and fusion applications and the potential for future research extending the results to include compressibility are discussed.

DOMAIN STRUCTURE AND MR EFFECT OF FERROFLUID EMULSION

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.

Acoustic phenomena in electrostatic dusty plasma shear flows

Recent studies of nonmodal phenomena in two-component plasma flows revealed that the velocity shear induces a number of new effects both in electrostatic and magnetized shear flows. It can be expected that dusty plasmas also host shear-modified and shear-induced modes of collective behavior, which may be found by means of the nonmodal approach and which are inaccessible by means of the standard normal mode analysis. In this paper, considering the simple electrostatic dusty plasma case, a general mathematical formalism is developed for studying how velocity shear affects the evolution of dust-acoustic waves (DAWs) and ion-acoustic waves (IAWs). In the limiting (very low-frequency) case when Boltzmann distributions are used both for the electrons and the ions it is found that the velocity shear enables the extraction of kinetic energy of the background flow by the dust-acoustic waves. It is also shown that the velocity shear leads to the appearance of a new collective mode of the dust particles—shear dust vortices. In the general case it is demonstrated that the velocity shear couples DAWs and IAWs and under suitable conditions may cause their mutual transformation into each other. The flow also sustains shear ion-dust vortices—nonperiodic patterns, which may eventually acquire oscillating features and generate both DAWs and IAWs. The inverse regime, which is called evanescence of acoustic waves, can also occur: the initial blend of DAWs and IAWs can fade away degenerating into the nonperiodic, evanescent perturbation.