On magnetohydrodynamic flows with aligned magnetic fields

1964 ◽  
Vol 19 (1) ◽  
pp. 49-59 ◽  
Author(s):  
M. B. Glauert

The boundary layers due to finite viscosity and magnetic diffusivity are studied in relation to two models of the flow of a conducting fluid past a body in an aligned magnetic field. In each case it is deduced that the growth of the boundary layer may have substantial effects, such as to raise doubts about the validity of the assumed basic flow patterns.

2005 ◽  
Vol 23 (4) ◽  
pp. 1481-1497 ◽  
Author(s):  
G. Paschmann ◽  
S. Haaland ◽  
B. U. Ö. Sonnerup ◽  
H. Hasegawa ◽  
E. Georgescu ◽  
...  

Abstract. The paper discusses properties of the near-tail dawnside and boundary layer, as obtained from Cluster plasma and magnetic field measurements during a single skimming orbit on 4 and 5 July 2001 that included 24 well-defined crossings by all four spacecraft. As a result of variations of the interplanetary magnetic field, the magnetic shear across the local varied between ~0° and ~180°. Using an improved method, which takes into account acceleration and thickness variation, we have determined the orientation, speed, thickness and current for the 96 individual crossings. The orientations show clear evidence of surface waves. Magnetopause thicknesses range from ~100 to ~2500km, with an average of 753km. The speeds range from less than 10up to more than 300, with an average of 48. Both results are consistent with earlier ISEE and AMPTE results obtained for the dayside magnetopause. Importantly, scaling the thicknesses to the ion gyro radius or the ion inertial length did not reduce the large dynamic range. There is also no significant dependence of thickness on magnetic shear. Current densities range from ~0.01 up to ~0.3uA, with an average value of 0.05 . By including some extra crossings that did not involve all four spacecraft, we were able to apply the Walén test to a total of 60 by Cluster 1 and 3, and have classified 19 cases as rotational discontinuities (RDs), of which 12 and 7 were sunward and tailward of an X-line, respectively. Of these 60 crossings, 26 show no trace of a boundary layer. The only with substantial boundary layers are into the plasma mantle. Of the 26 without a boundary layer, 8 were identified as RDs. Since reconnection produces wedge-shaped boundary layers emanating from the X-line, RDs without may be considered close to the X-line, in which case the observed magnetic shear and Alfvén Mach number should be representative of the conditions at the X-line itself. It is therefore important that four of the eight cases had shear angles ≤100, i.e. the reconnecting fields were far from being anti-parallel, and that all eight cases had Alfvén Mach numbers MA>1 in the adjoining magnetosheath. Another important conclusion can be drawn from the without a that were tangential discontinuities (TDs). To observe TDs with no at such large distances from the subsolar point appears to rule out diffusion over large portions of the as an effective means for plasma transport across the magnetopause.


1993 ◽  
Vol 157 ◽  
pp. 395-401 ◽  
Author(s):  
Harald Lesch

Stimulated by recent high frequency radio polarization measurements of M83 and M51, we consider the influence of non-axisymmetric features (bars, spiral arms, etc…) on galactic magnetic fields. The time scale for the field amplification due to the non-axisymmetric velocity field is related to the time scale of angular momentum transport in the disk by the non-axisymmetric features. Due to its dissipational character (cooling and angular momentum transport) the gas plays a major role for the excitation of non-axisymmetric instabilities. Since it is the gaseous component of the interstellar gas in which magnetic field amplification takes place we consider the interplay of gasdynamical processes triggered by gravitational instabilities and magnetic fields. A comparison with the time scale for dynamo action in a disk from numerical models for disk dynamos gives the result that field amplification by non-axisymmetric features is faster in galaxies like M83 (strong bar) and M51 (compagnion and very distinct spiral structure), than amplification by an axisymmetric dynamo. Furthermore, we propose that axisymmetric gravitational instabilities may provide the turbulent magnetic diffusivity ηT. Based on standard galaxy models we obtain a radially dependent diffusivity whose numerical value rises from 1025cm2s−1 to 1027cm2s−1, declining for large radii.


1981 ◽  
Vol 34 (3) ◽  
pp. 317 ◽  
Author(s):  
RR Burman

Where the number density of a species becomes very small, inertial development of vorticity occurs; so a magnetospheric zone in which a species is contained must be enclosed by a vortical boundary layer. Where zones of corotating electrons and ions abut, there exists a large local non-corotational electric field, directed so as to force a merging of the electron and ion boundary layers. The poloidalaccelerations and azimuthal drift velocities generated in these layers are estimated here. Ions are accelerated to nonrelativistic or mildly relativistic poloidal speeds, then penetrate into the electron corotation zones where they are centrifugally decelerated as they travel approximately along magnetic field lines. They mirror between points above the stellar surface and the boundary layer, resumably moving to lower magnetic field lines until they reach the star. Electrons are accelerated to poloidal speeds that are relativistic for istances from the axis of rotation exceeding about 1/30 of the radius of the light cylinder. They enter the ion corotation zone where they are further accelerated as they travel approximately along outgoing portions of the closed magnetic field lines, and are then decelerated on ingoing portions. They mirror between the northern and southern boundary layers, presumably moving to lower magnetic field lines until they reach the star. The electrons in the outer parts of the ion.zone are very highly relativistic and emit gamma radiation which, in the case of the Crab pulsar, might create electron-positron pairs.


1984 ◽  
Vol 51 (1) ◽  
pp. 13-18 ◽  
Author(s):  
P. R. Hays ◽  
J. S. Walker

Many metallurgical applications of magnetohydrodynamics (MHD) involve open-channel liquid-metal flows with magnetic fields. This paper treats the three-dimensional, variable-depth flow in a rectangular open channel having an electrically insulating bottom and perfectly conducting sides. A steady, uniform magnetic field is applied perpendicular to the channel bottom. Induced magnetic fields and surface tension effects are neglected, while the applied magnetic field is sufficiently strong that inertial effects are negligible everywhere. Viscous effects are confined to boundary layers adjacent to the bottom, sides, and free surface. Solutions are presented for the inviscid core and the boundary layers. The locations of the free surface above the core and above the boundary layers adjacent to the sides are obtained. The side-layer variables are rescaled into universal profile functions which depend on the coordinates in the channel’s cross section and on a parameter related to the local slopes of the bottom and the free surface. The solutions for the side layers in open channels are compared to the side-layer solutions for certain rectangular closed ducts in order to reveal the effects of the free surface. This comparison leads to a qualitative correspondence principle between open-channel and closed-duct side-layer solutions. The similarities and differences between corresponding open-channel and closed-duct side layers are discussed.


1971 ◽  
Vol 11 (03) ◽  
pp. 223-228 ◽  
Author(s):  
C.I. Pierce ◽  
L.C. Headley ◽  
W.K. Sawyer

Abstract Simplified models, consisting of single, circular channels and channels of different length and diameter in series and parallel combinations, are used in conjunction with the equations of Poiseuille and Hartmann to demonstrate the dependence of the rate of flow of mercury in the models on channel dimensions when the models are subjected to transverse magnetic fields. Experimental tests conducted on mercury-saturated, glass-bead packs and a natural rock sample show that a magnetic field applied transversely to the direction of flow retards flow rate. The magnitude of the magnetic effect increased with increasing bead size and field intensity. Results of this work suggest that magnetic fields have potential in the study of the internal geometry of flow channels in porous media. Introduction The purpose of this work is to determine qualitatively by theoretical and experimental considerations whether or not a magnetic method has potential in the study of the basic properties of rock. The nature of the solid surface and the geometry of the pore network in petroleum-bearing rock plays an important role in the flow behavior of fluids in a petroleum reservoir. Hence, any technique of study that would provide new and additional information on the rock matrix would contribute to a better understanding of petroleum reservoir performance. One such technique appearing to offer performance. One such technique appearing to offer promise is in the area of magnetohydrodynamics. promise is in the area of magnetohydrodynamics. While much research, both theoretical and experimental, has been devoted to the problems concerned with the flow of conducting fluids in transverse magnetic fields in single channels, very little information has been published regarding the behavior of conducting liquids in porous media under the influence of a transverse magnetic field. Perhaps this dearth of information can be attributed Perhaps this dearth of information can be attributed to two main causes:the pores and pore connections are generally so small that intense magnetic fields are required to produce Hartmann numbers of sufficient magnitude to exert appreciable influence on flow rate, andthe extreme complexity of the channel systems in porous media render them intractable to theoretical analysis unless numerous assumptions are made to simplify network geometry. When a conducting fluid moves in a channel in a transverse magnetic field, a force is exerted on the fluid which retards its flow. The magnitude of flow-rate retardation increases with increasing field intensity, channel dimensions and channel-wall conductivity. These magnetohydrodynamic phenomena and theory have been described and developed by various investigators. Since a petroleum reservoir rock is an interconnected network of pores and channels within a rock framework, one would anticipate that the geometry of the network would exert some influence on the magnitude of the effect of a transverse magnetic field on the rate of flow of a conducting fluid therein. The purpose of this work is to demonstrate through the use of simple models and experimental data that the magnetic field effect on flow rate has potential for use in determining size and size potential for use in determining size and size distribution of pores in porous materials. THEORY Electromagnetic induction in liquids is not completely defined, and the complexities involved in many cases appear to defy true analytical expression. However, by applying some simplifying assumptions, these cases may be made tractable to solution to provide qualitative indication of system behavior. The following analysis was conducted in conjunction with laboratory tests to determine if magnet ohydrodynamics has possible potential as a tool for studying the internal geometry of porous systems. When a conducting liquid moves in a channel in a transverse magnetic field, an emf is developed in the channel normal to both the channel axis and the magnetic field. This emf causes circulating currents to flow in the liquid as shown in Fig. 1. SPEJ P. 223


RSC Advances ◽  
2016 ◽  
Vol 6 (113) ◽  
pp. 112641-112645 ◽  
Author(s):  
R. Shirsavar ◽  
M. Nasiri ◽  
A. Amjadi ◽  
A. Nejati ◽  
S. O. Sobhani ◽  
...  

External magnetic field induces controllable rotation in a conducting fluid carrying an electric current.


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