Two-dimensional incompressible magneto-hydrodynamic flow across an elliptical solenoid

1958 ◽  
Vol 4 (6) ◽  
pp. 553-584 ◽  
Author(s):  
Nelson H. Kemp ◽  
Harry E. Petschek
Keyword(s):  
Magnetic Field ◽  
Flow Field ◽  
Hall Current ◽  
Dynamic Pressure ◽  
Magnetic Reynolds Number ◽  
Two Dimensional ◽  
Zeroth Order ◽  
First Order ◽  
Ion Slip ◽  
The Magnetic Field

An analysis has been made of the two-dimensional flow of an incompressible constant-conductivity fluid through an elliptically shaped solenoid containing a constant magnetic field directed normal to the flow plane. The effect of both Hall current and ion slip has been included in the generalized Ohm's law used for the fluid. The analysis is based on a perturbation procedure in two parameters, one being the magnetic Reynolds number Rm and the other the ratio S of magnetic force per unit area to dynamic pressure. Calculations have been carried to the first order in each parameter, and closed-form analytic expressions have been obtained for the force and moment on the solenoid, the current density, stream function, magnetic field and other pertinent physical quantities.It was found that, to the zeroth order, there is a force but no moment on the solenoid. To the first order in S, where the flow field is modified but the magnetic field is not, there is a moment and a force, the latter being anti-parallel to the zeroth order force. To the first order in Rm, where the magnetic field is modified but the flow field is not, there is a moment but no force. Thus, to the first order the lift to drag ratio is the same as in the zeroth order. Graphs which illustrate some of the effects of angle of attack, fineness ratio of the ellipse, Hall current and ion slip, on the forces and moments are presented.

scholarly journals Why, how and when MHD turbulence at low becomes three-dimensional

2014 ◽  
Vol 761 ◽  
pp. 168-205 ◽  
Author(s):  
Alban Pothérat ◽  
Rico Klein
Keyword(s):  
Magnetic Field ◽  
Metal Flow ◽  
Three Dimensional ◽  
Magnetic Reynolds Number ◽  
Two Dimensional ◽  
Mhd Turbulence ◽  
Opposite Wall ◽  
Liquid Metal Flow ◽  
Dc Current ◽  
The Magnetic Field

AbstractMagnetohydrodynamic (MHD) turbulence at low magnetic Reynolds number is experimentally investigated by studying a liquid metal flow in a cubic domain. We focus on the mechanisms that determine whether the flow is quasi-two-dimensional, three-dimensional or in any intermediate state. To this end, forcing is applied by injecting a DC current $I$ through one wall of the cube only, to drive vortices spinning along the magnetic field. Depending on the intensity of the externally applied magnetic field, these vortices extend part or all of the way through the cube. Driving the flow in this way allows us to precisely control not only the forcing intensity but also its dimensionality. A comparison with the theoretical analysis of this configuration singles out the influences of the walls and of the forcing on the flow dimensionality. Flow dimensionality is characterised in several ways. First, we show that when inertia drives three-dimensionality, the velocity near the wall where current is injected scales as $U_{b}\sim I^{2/3}$. Second, we show that when the distance $l_{z}$ over which momentum diffuses under the action of the Lorentz force (Sommeria & Moreau, J. Fluid Mech., vol. 118, 1982, pp. 507–518) reaches the channel width $h$, the velocity near the opposite wall $U_{t}$ follows a similar law with a correction factor $(1-h/l_{z})$ that measures three-dimensionality. When $l_{z}<h$, by contrast, the opposite wall has less influence on the flow and $U_{t}\sim I^{1/2}$. The central role played by the ratio $l_{z}/h$ is confirmed by experimentally verifying the scaling $l_{z}\sim N^{1/2}$ put forward by Sommeria & Moreau ($N$ is the interaction parameter) and, finally, the nature of the three-dimensionality involved is further clarified by distinguishing weak and strong three-dimensionalities previously introduced by Klein & Pothérat (Phys. Rev. Lett., vol. 104 (3), 2010, 034502). It is found that both types vanish only asymptotically in the limit $N\rightarrow \infty$. This provides evidence that because of the no-slip walls, (i) the transition between quasi-two-dimensional and three-dimensional turbulence does not result from a global instability of the flow, unlike in domains with non-dissipative boundaries (Boeck et al. Phys. Rev. Lett., vol. 101, 2008, 244501), and (ii) it does not occur simultaneously at all scales.

The decay of wall-bounded MHD turbulence at low

2015 ◽  
Vol 783 ◽  
pp. 605-636 ◽  
Author(s):  
Alban Pothérat ◽  
Kacper Kornet
Keyword(s):  
Magnetic Field ◽  
Three Dimensional ◽  
Viscous Friction ◽  
Magnetic Reynolds Number ◽  
Two Dimensional ◽  
Mhd Turbulence ◽  
Velocity Gradients ◽  
Two Phases ◽  
Experimental Findings ◽  
The Magnetic Field

We present direct numerical simulations of decaying magnetohydrodynamic (MHD) turbulence at low magnetic Reynolds number. The domain considered is bounded by periodic boundary conditions in the two directions perpendicular to the magnetic field and by two plane Hartmann walls in the third direction. Regimes of high magnetic fields (Hartmann number of up to 896) are reached thanks to a new spectral method using the eigenvectors of the dissipation operator. The decay is found to proceed through two phases: first, energy and integral length scales vary rapidly during a two-dimensionalisation phase extending over approximately a Hartmann friction time. During this phase, the evolution of the former appears significantly more impeded by the presence of walls than that of the latter. Once the large scales are nearly quasi-two-dimensional, the decay results from the competition of a two-dimensional dynamics driven by dissipation in the Hartmann boundary layers and the three-dimensional dynamics of smaller scales. In the later stages of the decay, three-dimensionality subsists under the form of barrel-shaped structures. A purely quasi-two dimensional decay entirely dominated by friction in the Hartmann layers is not reached because of residual dissipation in the bulk. However, this dissipation is not generated by the three-dimensionality that subsists, but by residual viscous friction due to horizontal velocity gradients. In the process, the energy in the velocity component aligned with the magnetic field is found to be strongly suppressed, as is skewness. This result reproduces the experimental findings of Kolesnikov & Tsinober (Fluid Dyn., vol. 9, 1974, pp. 621–624), where, as in the present simulations, Hartmann walls were present.

The annihilation of a two-dimensional jet by a transverse magnetic field

1967 ◽  
Vol 30 (1) ◽  
pp. 65-82 ◽  
Author(s):  
H. K. Moffatt ◽  
J. Toomre
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Transverse Magnetic Field ◽  
Magnetic Interaction ◽  
Transverse Magnetic ◽  
Magnetic Reynolds Number ◽  
Two Dimensional ◽  
Dimensionless Numbers ◽  
Order Unity ◽  
The Magnetic Field

The effect of an applied transverse magnetic field on the development of a two-dimensional jet of incompressible fluid is examined. The jet is prescribed in terms of its mass flux ρQ0 and its lateral scale d at an initial section x = 0. The three dimensionless numbers characterizing the problem are a Reynolds number R = Q0/ν, a magnetic Reynolds number Rm = μσQ0, and a magnetic interaction parameter N = σB20d2/ρQ0, where ρ represents density, σ conductivity, μ permeability and B0 applied field strength, and it is assumed that \[ R_m \ll 1,\quad R\gg 1,\quad N\ll 1. \] It is shown that when M2 = RN [Gt ] 1, an inviscid treatment is appropriate, and that the effect of the magnetic field is then to destroy the jet momentum within a distance of order N−1 in the downstream direction. A general solution for inviscid development is obtained, and it is shown that a large class of velocity profiles (though not all of them) are self-preserving.When M2 [Lt ] 1, it is shown that the viscous similarity solution obtained by Moreau (1963a, b) is relevant. This solution is re-derived and re-interpreted; it implies that the jet momentum is destroyed within a distance of order $R^{\frac{1}{4}}N^{-\frac{3}{4}}$ in the downstream direction.Some further aspects of the jet annihilation problem are qualitatively discussed in § 4, viz. the nature of the overall flow field, the effect of the presence of distant boundaries, the effect of increasing Rm to order unity and greater, and the effect of oblique injection. Finally the development of a jet of conducting fluid into a nonconducting environment is considered; in this case the jet is not stopped by the magnetic field unless a return path outside the fluid for the induced current is available.

scholarly journals On the flow of a conducting fluid past a magnetized sphere

1960 ◽  
Vol 7 (4) ◽  
pp. 516-528 ◽  
Author(s):  
G. S. S. Ludford ◽  
J. D. Murray
Keyword(s):  
Free Stream ◽  
Dynamic Pressure ◽  
Magnetic Reynolds Number ◽  
Magnetic Pressure ◽  
Conducting Fluid ◽  
Order Effects ◽  
Magnetic Intensity ◽  
First Order ◽  
Prime 2 ◽  
The Magnetic Field

In the steady flow of an incompressible, inviscid, conducting fluid past a magnetized sphere, the first-order effects of the magnetic field and the conductivity are studied. Paraboloidal wakes of vorticity and magnetic intensity are formed, the former being half the size of the latter. The vorticity, generated by the non-conservative electromagnetic force, is logarithmically infinite on the sphere. For the case of a dipole of moment M at the centre of a sphere of radius a, the drag coefficient is $C_D = \frac {144 \mu^{\prime 2}}{5(2\mu + \mu^{\prime})^2} \beta R_M,$ where μ and μ′ are the permeabilities of the fluid and sphere, respectively, β is the ratio of the representative magnetic pressure μM2/2a6 to the free-stream dynamic pressure, and RM is the magnetic Reynolds number.

scholarly journals Cluster observations of sudden impulses in the magnetotail caused by interplanetary shocks and pressure increases

2005 ◽  
Vol 23 (2) ◽  
pp. 609-624 ◽  
Author(s):  
K. E. J. Huttunen ◽  
J. Slavin ◽  
M. Collier ◽  
H. E. J. Koskinen ◽  
A. Szabo ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Dynamic Pressure ◽  
Solar Wind Speed ◽  
Interplanetary Shock ◽  
Wind Pressure ◽  
Shock Propagation ◽  
Interplanetary Shocks ◽  
Maximum Variance ◽  
The Magnetic Field

Abstract. Sudden impulses (SI) in the tail lobe magnetic field associated with solar wind pressure enhancements are investigated using measurements from Cluster. The magnetic field components during the SIs change in a manner consistent with the assumption that an antisunward moving lateral pressure enhancement compresses the magnetotail axisymmetrically. We found that the maximum variance SI unit vectors were nearly aligned with the associated interplanetary shock normals. For two of the tail lobe SI events during which Cluster was located close to the tail boundary, Cluster observed the inward moving magnetopause. During both events, the spacecraft location changed from the lobe to the magnetospheric boundary layer. During the event on 6 November 2001 the magnetopause was compressed past Cluster. We applied the 2-D Cartesian model developed by collier98 in which a vacuum uniform tail lobe magnetic field is compressed by a step-like pressure increase. The model underestimates the compression of the magnetic field, but it fits the magnetic field maximum variance component well. For events for which we could determine the shock normal orientation, the differences between the observed and calculated shock propagation times from the location of WIND/Geotail to the location of Cluster were small. The propagation speeds of the SIs between the Cluster spacecraft were comparable to the solar wind speed. Our results suggest that the observed tail lobe SIs are due to lateral increases in solar wind dynamic pressure outside the magnetotail boundary.

Flow Visualization by Means of Contactless Inductive Flow Tomography in the Presence of a Magnetic Brake

2015 ◽  
Vol 15 (1) ◽  
pp. 41-48 ◽  
Author(s):  
Matthias Ratajczak ◽  
Thomas Wondrak ◽  
Klaus Timmel ◽  
Frank Stefani ◽  
Sven Eckert
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Magnetic Fields ◽  
Flow Field ◽  
Continuous Casting ◽  
Flow Structure ◽  
Cross Section ◽  
Two Dimensional ◽  
Slab Casting ◽  
Two Dimensional Flow

AbstractIn continuous casting DC magnetic fields perpendicular to the wide faces of the mold are used to control the flow in the mold. Especially in this case, even a rough knowledge of the flow structure in the mold would be highly desirable. The contactless inductive flow tomography (CIFT) allows to reconstruct the dominating two-dimensional flow structure in a slab casting mold by applying one external magnetic field and by measuring the flow-induced magnetic fields outside the mold. For a physical model of a mold with a cross section of 140 mm×35 mm we present preliminary measurements of the flow field in the mold in the presence of a magnetic brake. In addition, we show first reconstructions of the flow field in a mold with the cross section of 400 mm×100 mm demonstrating the upward scalability of CIFT.

scholarly journals THE ENERGY EIGENVALUES OF THE TWO DIMENSIONAL HYDROGEN ATOM IN A MAGNETIC FIELD

2006 ◽  
Vol 15 (06) ◽  
pp. 1263-1271 ◽  
Author(s):  
A. SOYLU ◽  
O. BAYRAK ◽  
I. BOZTOSUN
Keyword(s):  
Magnetic Field ◽  
Hydrogen Atom ◽  
Iteration Method ◽  
Weak Magnetic Field ◽  
The Other ◽  
Asymptotic Iteration Method ◽  
Iterative Approach ◽  
Two Dimensional ◽  
Energy Eigenvalues ◽  
The Magnetic Field

In this paper, the energy eigenvalues of the two dimensional hydrogen atom are presented for the arbitrary Larmor frequencies by using the asymptotic iteration method. We first show the energy eigenvalues for the case with no magnetic field analytically, and then we obtain the energy eigenvalues for the strong and weak magnetic field cases within an iterative approach for n=2-10 and m=0-1 states for several different arbitrary Larmor frequencies. The effect of the magnetic field on the energy eigenvalues is determined precisely. The results are in excellent agreement with the findings of the other methods and our method works for the cases where the others fail.

Doppler-Shifted Cyclotron Resonance in Thin Metal Films

1972 ◽  
Vol 50 (18) ◽  
pp. 2122-2137
Author(s):  
R. Turner ◽  
J. F. Cochran
Keyword(s):  
Magnetic Field ◽  
Metal Films ◽  
Thin Metal Film ◽  
Thin Metal ◽  
Free Electrons ◽  
Fermi Surfaces ◽  
First Order ◽  
Simple Quantum ◽  
The Magnetic Field ◽  
Good Agreement

According to Van Gelder the microwave absorption by a thin metal film in the presence of a static magnetic field normal to the film contains a series of peaks as the magnetic field is varied. In the present paper it is argued that these peaks correspond to Doppler-shifted cyclotron resonances of the carriers in the metal due to the quantization of electron momenta normal to the plane of the film. A simple quantum calculation is presented for the case of free electrons where the film is thin enough that to first order the microwave fields within are determined only by the boundary conditions and Maxwell's equations. The quantum expression is in good agreement with the absorption calculated using semiclassical arguments which can be readily extended to more complicated Fermi surfaces.

scholarly journals Reversibility of the Magnetocaloric Effect in the Bean-Rodbell Model

2021 ◽  
Vol 7 (5) ◽  
pp. 60
Author(s):  
Luis M. Moreno-Ramírez ◽  
Victorino Franco
Keyword(s):  
Magnetic Field ◽  
Thermal Hysteresis ◽  
Entropy Change ◽  
Second Order ◽  
Zero Field ◽  
First Order ◽  
Magnetic Field Change ◽  
Magnetocaloric Materials ◽  
Moderate Magnetic Field ◽  
The Magnetic Field

The applicability of magnetocaloric materials is limited by irreversibility. In this work, we evaluate the reversible magnetocaloric response associated with magnetoelastic transitions in the framework of the Bean-Rodbell model. This model allows the description of both second- and first-order magnetoelastic transitions by the modification of the η parameter (η<1 for second-order and η>1 for first-order ones). The response is quantified via the Temperature-averaged Entropy Change (TEC), which has been shown to be an easy and effective figure of merit for magnetocaloric materials. A strong magnetic field dependence of TEC is found for first-order transitions, having a significant increase when the magnetic field is large enough to overcome the thermal hysteresis of the material observed at zero field. This field value, as well as the magnetic field evolution of the transition temperature, strongly depend on the atomic magnetic moment of the material. For a moderate magnetic field change of 2 T, first-order transitions with η≈1.3−1.8 have better TEC than those corresponding to stronger first-order transitions and even second-order ones.

High magnetic field NMR investigation of the spin density wave phase of TMTSF2PF6

2002 ◽  
Vol 12 (9) ◽  
pp. 389-389
Author(s):  
W. G. Clark ◽  
F. Zamborsky ◽  
B. Alavi ◽  
P. Vonlanthen ◽  
W. Moulton ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Spin Density ◽  
Density Wave ◽  
Spin Density Wave ◽  
Proton Relaxation ◽  
High Magnetic Fields ◽  
Organic Conductor ◽  
First Order ◽  
The Magnetic Field ◽  
Very High

We report proton NMR measurements of the effect of very high magnetic fields up to 44.7 T (1.9 GHz) on the spin density wave (SDW) transition of the organic conductor TMTSF2PF6. Up to 1.8 GHz, no effect of critical slowing close to the transition is seen on the proton relaxation rate (1/T1), which is determined by the SDW fluctuations associated with the phase transition at the NMR frequency. Thus, the correlation time for such fluctuations is less than $1O^{-10}$s. A possible explanation for the absence of longer correlation times is that the transition is weakly first order, so that the full critical divergence is never achieved. The measurements also show a dependence of the transition temperature on the orientation of the magnetic field and a quadratic dependence on its magnitude that agrees with earlier transport measurements at lower fields. The UCLA part of this work was supported by NSF Grant DMR-0072524.

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