Magnetic damping of jets and vortices

1995 ◽  
Vol 299 ◽  
pp. 153-186 ◽  
Author(s):  
P. A. Davidson
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Angular Momentum ◽  
Kinetic Energy ◽  
Lorentz Force ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Magnetic Damping ◽  
Field Lines ◽  
The Magnetic Field

It is well known that the imposition of a static magnetic field tends to suppress motion in an electrically conducting liquid. Here we look at the magnetic damping of liquid-mental flows where the Reynolds number is large and the magnetic Reynolds number is small. The magnetic field is taken as uniform and the fluid is either infinite in extent or else bounded by an electrically insulating surface S. Under these conditions, we find that three general principles govern the flow. First, the Lorentz force destroys kinetic energy but does not alter the net linear momentum of the fluid, nor does it change the component of angular momentum parallel to B. In certain flows, this implies that momentum, linear or angular, is conserved. Second, the Lorentz force guides the flow in such a way that the global Joule dissipation, D, decreases, and this decline in D is even more rapid than the corresponding fall in global kinetic energy, E. (Note that both D and E are quadratic in u). Third, this decline in relative dissipation, D / E, is essential to conserving momentum, and is achieved by propagating linear or angular momentum out along the magnetic field lines. In fact, this spreading of momentum along the B-lines is a diffusive process, familiar in the context of MHD turbulence. We illustrate these three principles with the aid of a number of specific examples. In increasing order of complexity we look at a spatially uniform jet evolving in time, a three-dimensional jet evolving in space, and an axisymmetric vortex evolving in both space and time. We start with a spatially uniform jet which is dissipated by the sudden application of a transverse magnetic field. This simple (perhaps even trivial) example provides a clear illustration of our three general principles. It also provides a useful stepping-stone to our second example of a steady three-dimensional jet evolving in space. Unlike the two-dimensional jets studied by previous investigators, a three-dimensional jet cannot be annihilated by magnetic braking. Rather, its cross-section deforms in such a way that the momentum flux of the jet is conserved, despite a continual decline in its energy flux. We conclude with a discussion of magnetic damping of axisymmetric vortices. As with the jet flows, the Lorentz force cannot destroy the motion, but rather rearranges the angular momentum of the flow so as to reduce the global kinetic energy. This process ceases, and the flow reaches a steady state, only when the angular momentum is uniform in the direction of the field lines. This is closely related to the tendency of magnetic fields to promote two-dimensional turbulence.

Hydromagnetic instability of a free shear layer at small magnetic Reynolds numbers

1971 ◽  
Vol 49 (1) ◽  
pp. 21-31 ◽  
Author(s):  
Kanefusa Gotoh
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Shear Layer ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Free Shear Layer ◽  
Electrically Conducting ◽  
The Stability ◽  
The Magnetic Field

The effect of a uniform and parallel magnetic field upon the stability of a free shear layer of an electrically conducting fluid is investigated. The equations of the velocity and the magnetic disturbances are solved numerically and it is shown that the flow is stabilized with increasing magnetic field. When the magnetic field is expressed in terms of the parameter N (= M2/R2), where M is the Hartmann number and R is the Reynolds number, the lowest critical Reynolds number is caused by the two-dimensional disturbances. So long as 0 [les ] N [les ] 0·0092 the flow is unstable at all R. For 0·0092 < N [les ] 0·0233 the flow is unstable at 0 < R < Ruc where Ruc decreases as N increases. For 0·0233 < N < 0·0295 the flow is unstable at Rlc < R < Ruc where Rlc increases with N. Lastly for N > 0·0295 the flow is stable at all R. When the magnetic field is measured by M, the lowest critical Reynolds number is still due to the two-dimensional disturbances provided 0 [les ] M [les ] 0·52, and Rc is given by the corresponding Rlc. For M > 0·52, Rc is expressed as Rc = 5·8M, and the responsible disturbance is the three-dimensional one which propagates at angle cos−1(0·52/M) to the direction of the basic flow.

Three-dimensional MHD flows in rectangular ducts with internal obstacles

2000 ◽  
Vol 418 ◽  
pp. 265-295 ◽  
Author(s):  
B. MÜCK ◽  
C. GÜNTHER ◽  
U. MÜLLER ◽  
L. BÜHLER
Keyword(s):  
Magnetic Field ◽  
Numerical Simulation ◽  
Reynolds Number ◽  
Magnetic Fields ◽  
Interaction Parameter ◽  
Hartmann Number ◽  
Three Dimensional ◽  
Side Length ◽  
Two Dimensional ◽  
The Magnetic Field

This paper presents a numerical simulation of the magnetohydrodynamic (MHD) liquid metal flow around a square cylinder placed in a rectangular duct. In the hydrodynamic case, for a certain parameter range the well-known Kármán vortex street with three-dimensional flow patterns is observed, similar to the flow around a circular cylinder. In this study a uniform magnetic field aligned with the cylinder is applied and its influence on the formation and downstream transport of vortices is investigated. The relevant key parameters for the MHD flow are the Hartmann number M, the interaction parameter N and the hydrodynamic Reynolds number, all based on the side length of the cylinder. The Hartmann number M was varied in the range 0 [les ] M [les ] 85 and the interaction parameter N in the range 0 [les ] N [les ] 36. Results are presented for two fixed Reynolds numbers Re = 200 and Re = 250. The magnetic Reynolds number is assumed to be very small. The results of the numerical simulation are compared with known experimental and theoretical results. The hydrodynamic simulation shows characteristic intermittent pulsations of the drag and lift force on the cylinder. At Re = 200 a mix of secondary spanwise three-dimensional instabilities (A and B mode, rib vortices) could be observed. The spanwise wavelength of the rib vortices was found to be about 2–3 cylinder side lengths in the near wake. At Re = 250 the flow appears more organized showing a regular B mode pattern and a spanwise wavelength of about 1 cylinder side length. With an applied magnetic field a quasi-two-dimensional flow can be obtained at low N ≈ 1 due to the strong non-isotropic character of the electromagnetic forces. The remaining vortices have their axes aligned with the magnetic field. With increasing magnetic fields these vortices are further damped due to Hartmann braking. The result that the ‘quasi-two-dimensional’ vortices have a curvature in the direction of the magnetic field can be explained by means of an asymptotic analysis of the governing equations. With very high magnetic fields the time-dependent vortex shedding can be almost completely suppressed. By three-dimensional visualization it was possible to show characteristic paths of the electric current for this kind of flow, explaining the action of the Lorentz forces.

scholarly journals INCREASING THE EFFICIENCY OF MULTY-VARIANT CALCULATIONS OF ELECTROMAGNETIC FIELD DISTRIBUTION IN MATRIX OF A POLYGRADIENT SEPARATOR

2021 ◽  
Author(s):  
Jasim Mohmed Jasim Jasim ◽  
Iryna Shvedchykova ◽  
Igor Panasiuk ◽  
Julia Romanchenko ◽  
Inna Melkonova
Keyword(s):  
Magnetic Field ◽  
Field Distribution ◽  
Three Dimensional ◽  
Magnetic Potential ◽  
Geometric Parameters ◽  
Two Dimensional ◽  
Air Gaps ◽  
Vector Magnetic Potential ◽  
Electromagnetic Separator ◽  
The Magnetic Field

An approach is proposed to carry out multivariate calculations of the magnetic field distribution in the working gaps of a plate polygradient matrix of an electromagnetic separator, based on a combination of the advantages of two- and three-dimensional computer modeling. Two-dimensional geometric models of computational domains are developed, which differ in the geometric dimensions of the plate matrix elements and working air gaps. To determine the vector magnetic potential at the boundaries of two-dimensional computational domains, a computational 3D experiment is carried out. For this, three variants of the electromagnetic separator are selected, which differ in the size of the working air gaps of the polygradient matrices. For them, three-dimensional computer models are built, the spatial distribution of the magnetic field in the working intervals of the electromagnetic separator matrix and the obtained numerical values of the vector magnetic potential at the boundaries of the computational domains are investigated. The determination of the values of the vector magnetic potential for all other models is carried out by interpolation. The obtained values of the vector magnetic potential are used to set the boundary conditions in a computational 2D experiment. An approach to the choice of a rational version of a lamellar matrix is substantiated, which provides a solution to the problem according to the criterion of the effective area of the working area. Using the method of simple enumeration, a variant of the structure of a polygradient matrix with rational geometric parameters is selected. The productivity of the electromagnetic separator with rational geometric parameters of the matrix increased by 3–5 % with the same efficiency of extraction of ferromagnetic inclusions in comparison with the basic version of the device

scholarly journals 2D and 3D turbulent magnetic reconnection

2009 ◽  
Vol 5 (H15) ◽  
pp. 434-435
Author(s):  
A. Lazarian ◽  
G. Kowal ◽  
E. Vishniac ◽  
K. Kulpa-Dubel ◽  
K. Otmianowska-Mazur
Keyword(s):  
Magnetic Field ◽  
Magnetic Reconnection ◽  
Large Scale ◽  
Gamma Ray ◽  
Three Dimensional ◽  
Turnover Time ◽  
Turbulent Fluid ◽  
Astrophysical Objects ◽  
Field Lines ◽  
The Magnetic Field

AbstractA magnetic field embedded in a perfectly conducting fluid preserves its topology for all times. Although ionized astrophysical objects, like stars and galactic disks, are almost perfectly conducting, they show indications of changes in topology, magnetic reconnection, on dynamical time scales. Reconnection can be observed directly in the solar corona, but can also be inferred from the existence of large scale dynamo activity inside stellar interiors. Solar flares and gamma ray busts are usually associated with magnetic reconnection. Previous work has concentrated on showing how reconnection can be rapid in plasmas with very small collision rates. Here we present numerical evidence, based on three dimensional simulations, that reconnection in a turbulent fluid occurs at a speed comparable to the rms velocity of the turbulence, regardless of the value of the resistivity. In particular, this is true for turbulent pressures much weaker than the magnetic field pressure so that the magnetic field lines are only slightly bent by the turbulence. These results are consistent with the proposal by Lazarian & Vishniac (1999) that reconnection is controlled by the stochastic diffusion of magnetic field lines, which produces a broad outflow of plasma from the reconnection zone. This work implies that reconnection in a turbulent fluid typically takes place in approximately a single eddy turnover time, with broad implications for dynamo activity and particle acceleration throughout the universe. In contrast, the reconnection in 2D configurations in the presence of turbulence depends on resistivity, i.e. is slow.

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.

FERMION THRESHOLD ENERGY STATES

1992 ◽  
Vol 06 (24) ◽  
pp. 1531-1534
Author(s):  
CHANGHONG ZHU
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Three Dimensional ◽  
Threshold Energy ◽  
Index Theorem ◽  
Equation Of Motion ◽  
Field Configuration ◽  
Two Dimensional ◽  
Magnetic Field Configuration ◽  
The Magnetic Field

We show that for a three-dimensional non-relativistic spinor confined on a plane, the spin-up component obeys the same equation of motion as a two-dimensional spinor. Threshold energy solution is investigated when the electron is moving in the vortex field. It can be proved from the index theorem that the existence of the threshold states depends on the magnetic flux only, not on the magnetic field configuration.

On the stability of parallel flows with parallel magnetic fields

1966 ◽  
Vol 293 (1434) ◽  
pp. 342-358 ◽  
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Parallel Magnetic Field ◽  
Parallel Flows ◽  
The Mean ◽  
The Stability ◽  
The Magnetic Field ◽  
Parallel Magnetic Fields

The first part of the paper is a physical discussion of the way in which a magnetic field affects the stability of a fluid in motion. Particular emphasis is given to how the magnetic field affects the interaction of the disturbance with the mean motion. The second part is an analysis of the stability of plane parallel flows of fluids with finite viscosity and conductivity under the action of uniform parallel magnetic fields. We show that, in general, three-dimensional disturbances are the most unstable, thus disagreeing with the conclusion of Michael (1953) and Stuart (1954). We show how results obtained for two-dimensional disturbances can be used to calculate the most unstable three-dimensional disturbances and thence we prove that a parallel magnetic field can never completely stabilize a parallel flow.

scholarly journals Magnetohydrodynamic evolution of magnetic skeletons

2007 ◽  
Vol 463 (2080) ◽  
pp. 1097-1115 ◽  
Author(s):  
Andrew L Haynes ◽  
Clare E Parnell ◽  
Klaus Galsgaard ◽  
Eric R Priest
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Three Dimensional ◽  
Heating Process ◽  
Initial State ◽  
Fundamental Building Block ◽  
New Type ◽  
Field Lines ◽  
First Time ◽  
The Magnetic Field

The heating of the solar corona is probably due to reconnection of the highly complex magnetic field that threads throughout its volume. We have run a numerical experiment of an elementary interaction between the magnetic field of two photospheric sources in an overlying field that represents a fundamental building block of the coronal heating process. The key to explaining where, how and how much energy is released during such an interaction is to calculate the resulting evolution of the magnetic skeleton. A skeleton is essentially the web of magnetic flux surfaces (called separatrix surfaces) that separate the coronal volume into topologically distinct parts. For the first time, the skeleton of the magnetic field in a three-dimensional numerical magnetohydrodynamic experiment is calculated and carefully analysed, as are the ways in which it bifurcates into different topologies. A change in topology normally changes the number of magnetic reconnection sites. In our experiment, the magnetic field evolves through a total of six distinct topologies. Initially, no magnetic flux joins the two sources. Then, a new type of bifurcation, called a global double-separator bifurcation , takes place. This bifurcation is probably one of the main ways in which new separators are created in the corona (separators are field lines at which three-dimensional reconnection takes place). This is the first of five bifurcations in which the skeleton becomes progressively more complex before simplifying. Surprisingly, for such a simple initial state, at the peak of complexity there are five separators and eight flux domains present.

Proton acceleration in three-dimensional non-null magnetic reconnection

2016 ◽  
Vol 82 (5) ◽  
Author(s):  
Z. Akbari ◽  
M. Hosseinpour ◽  
M. A. Mohammadi
Keyword(s):  
Magnetic Field ◽  
Energy Distribution ◽  
Magnetic Reconnection ◽  
Electric Fields ◽  
Three Dimensional ◽  
Null Point ◽  
Proton Acceleration ◽  
Electric And Magnetic Fields ◽  
Field Lines ◽  
The Magnetic Field

In a three-dimensional non-null magnetic reconnection, the process of magnetic reconnection takes place in the absence of a null point where the magnetic field vanishes. By randomly injecting a population of 10 000 protons, the trajectory and energy distribution of accelerated protons are investigated in the presence of magnetic and electric fields of a particular model of non-null magnetic reconnection with the typical parameters for the solar corona. The results show that protons are accelerated along the magnetic field lines away from the non-null point only at azimuthal angles where the magnitude of the electric field is strongest and therefore particles obtain kinetic energies of the order of thousands of MeV and even higher. Moreover, the energy distribution of the population depends strongly on the amplitude of the electric and magnetic fields. Comparison shows that a non-null magnetic reconnection is more efficient in accelerating protons to very high GeV energies than a null-point reconnection.

A physical description of magnetic helicity evolution in the presence of reconnection lines

1991 ◽  
Vol 46 (1) ◽  
pp. 179-199 ◽  
Author(s):  
Andrew N. Wright ◽  
Mitchell A. Berger
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Magnetic Reynolds Number ◽  
Magnetic Helicity ◽  
Two Dimensional ◽  
Flux Tubes ◽  
Physical Description ◽  
Reconnection Region ◽  
Field Geometry ◽  
Field Lines

The dissipation of relative magnetic helicity due to the presence of a resistive reconnection region is considered. We show that when the reconnection region has a vanishing cross-section, helicity is conserved, in agreement with previous studies. It is also shown that in two-dimensional systems reconnection can produce highly twisted reconnected flux tubes. Reconnection at a high magnetic Reynolds number generally conserves helicity to a good approximation. However, reconnection with a small Reynolds number can produce significant dissipation of helicity. We prove that helicity dissipation in two-dimensional configurations is associated with the retention of some of the inflowing magnetic flux by the reconnection region, vr. When the reconnection site is a simple Ohmic conductor, all of the magnetic field parallel to the reconnection line that is swept into vr is retained. (In contrast, the inflowing magnetic field perpendicular to the line is annihilated.) We are able to relate the amount of helicity dissipation to the retained flux. A physical interpretation of helicity dissipation is developed by considering the diffusion of magnetic field lines through vr. When compared with helicity-conserving reconnection, the two halves of a reconnected flux sheet appear to have slipped relative to each other parallel to the reconnection line. This provides a useful method by which the reconnected field geometry can be constructed: the incoming flux sheets are ‘cut’ where they encounter vr, allowed to slip relative to each other, and then ‘pasted’ together to form the reconnected flux sheets. This simple model yields estimates for helicity dissipation and the flux retained by vr in terms of the amount of slippage. These estimates are in agreement with those expected from the governing laws.

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