Plane Magnetofluiddynamic Flows with Constantly Inclined Magnetic and Velocity Fields

1974 ◽  
Vol 52 (9) ◽  
pp. 753-758 ◽  
Author(s):  
H. Toews ◽  
O. P. Chandna
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Incompressible Flows ◽  
Fluid Flows ◽  
Velocity Fields ◽  
Parallel Flows ◽  
Definite Manner ◽  
Flow Variables ◽  
Compressible Fluid Flows ◽  
The Magnetic Field

Plane steady state nondissipative compressible fluid flows, in which the conductivity is infinite and in which the magnetic field and the velocity field are constantly inclined to one another, are considered. Sonic flows, and flows for which the velocity is constant along each streamline, are studied and the related results are applied to flows in poly-tropic gases. It is shown that if two distinct incompressible flows have the same streamline pattern, then the flow variables are related in a definite manner. Finally, solutions are obtained for vortex flows and also for parallel flows.

Plane MHD Steady Flows with Constantly Inclined Magnetic and Velocity Fields

1975 ◽  
Vol 53 (23) ◽  
pp. 2613-2616 ◽  
Author(s):  
O. P. Chandna ◽  
H. Toews ◽  
V. I. Nath
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Velocity Field ◽  
Fluid Flows ◽  
Velocity Fields ◽  
Steady Flows ◽  
Physical Conditions ◽  
Zero Current ◽  
Necessary And Sufficient ◽  
The Magnetic Field

Plane steady state viscous fluid flows, in which the magnetic field and velocity field are constantly inclined to one another, are considered. Necessary and sufficient physical conditions have been derived for flows with zero current density and the general solutions for these flows are obtained. Irrotational flows and flows with straight streamlines are also studied.

scholarly journals Mapping of steady-state electric fields and convective drifts in geomagnetic fields – Part 1: Elementary models

2016 ◽  
Vol 34 (1) ◽  
pp. 55-65 ◽  
Author(s):  
A. D. M. Walker ◽  
G. J. Sofko
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Electric Field ◽  
Electric Fields ◽  
Magnetic Field Line ◽  
Geomagnetic Field ◽  
Geomagnetic Field Models ◽  
Spatial Derivatives ◽  
Field Lines ◽  
The Magnetic Field

Abstract. When studying magnetospheric convection, it is often necessary to map the steady-state electric field, measured at some point on a magnetic field line, to a magnetically conjugate point in the other hemisphere, or the equatorial plane, or at the position of a satellite. Such mapping is relatively easy in a dipole field although the appropriate formulae are not easily accessible. They are derived and reviewed here with some examples. It is not possible to derive such formulae in more realistic geomagnetic field models. A new method is described in this paper for accurate mapping of electric fields along field lines, which can be used for any field model in which the magnetic field and its spatial derivatives can be computed. From the spatial derivatives of the magnetic field three first order differential equations are derived for the components of the normalized element of separation of two closely spaced field lines. These can be integrated along with the magnetic field tracing equations and Faraday's law used to obtain the electric field as a function of distance measured along the magnetic field line. The method is tested in a simple model consisting of a dipole field plus a magnetotail model. The method is shown to be accurate, convenient, and suitable for use with more realistic geomagnetic field models.

scholarly journals Propagation of Blast waves in a Non-Ideal Magnetogasdynamics

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 458 ◽  
Author(s):  
Astha Chauhan ◽  
Rajan Arora ◽  
Mohd Siddiqui
Keyword(s):  
Magnetic Field ◽  
Gas Dynamics ◽  
Approximate Analytical Solution ◽  
Ideal Gas ◽  
Specific Conductance ◽  
Blast Waves ◽  
Highly Nonlinear ◽  
Vast Literature ◽  
Flow Variables ◽  
The Magnetic Field

Blast waves are generated when an area grows abruptly with a supersonic speed, as in explosions. This problem is quite interesting, as a large amount of energy is released in the process. In contrast to the situation of imploding shocks in ideal gas, where a vast literature is available on the effect of magnetic fields, very little is known about blast waves propagating in a magnetic field. As this problem is highly nonlinear, there are very few techniques that may provide even an approximate analytical solution. We have considered a problem on planar and radially symmetric blast waves to find an approximate solution analytically using Sakurai’s technique. A magnetic field has been taken in the transverse direction. Gas particles are supposed to be propagating orthogonally to the magnetic field in a non-deal medium. We have further assumed that specific conductance of the medium is infinite. Using Sakurai’s approach, we have constructed the solution in a power series of ( C / U ) 2 , where C is the velocity of sound in an ideal gas and U is the velocity of shock front. A comparison of obtained results in the absence of a magnetic field within the published work of Sakurai has been made to generate the confidence in our results. Our results match well with the results reported by Sakurai for gas dynamics. The flow variables are computed behind the leading shock and are shown graphically. It is very interesting that the solution of the problem is obtained in closed form.

scholarly journals Ideal magnetohydrodynamic equilibria with helical symmetry and incompressible flows

1999 ◽  
Vol 62 (4) ◽  
pp. 449-459 ◽  
Author(s):  
G. N. THROUMOULOPOULOS ◽  
H. TASSO
Keyword(s):  
Electric Fields ◽  
Incompressible Flows ◽  
Elliptic Partial Differential Equation ◽  
Equilibrium Equations ◽  
Flux Function ◽  
Parallel Flows ◽  
Magnetic Surfaces ◽  
Ideal Magnetohydrodynamic ◽  
The Magnetic Field ◽  
Constant Mach Number

A recent study on axisymmetric ideal magnetohydrodynamic equilibria with incompressible flows [H. Tasso and G. N. Throumoulopoulos, Phys. Plasmas5, 2378 (1998)] is extended to the generic case of helically symmetric equilibria with incompressible flows. It is shown that the equilibrium states of the system under consideration are governed by an elliptic partial differential equation for the helical magnetic flux function containing five surface quantities along with a relation for the pressure. The above-mentioned equation can be transformed to one possessing a differential part identical in form to the corresponding static equilibrium equation, which is amenable to several classes of analytical solutions. In particular, equilibria with electric fields perpendicular to the magnetic surfaces and non-constant-Mach-number flows are constructed. Unlike the case in axisymmetric equilibria with isothermal magnetic surfaces, helically symmetric T = T(ψ) equilibria are overdetermined, i.e. in this case the equilibrium equations reduce to a set of eight ordinary differential equations with seven surface quantities. In addition, the non-existence is proved of incompressible helically symmetric equilibria with (a) purely helical flows and (b) non-parallel flows with isothermal magnetic surfaces and with the magnetic field modulus a surface quantity (omnigenous equilibria).

scholarly journals Deformation of a magnetic liquid drop in an applied non-stationary uniform magnetic field

2018 ◽  
Vol 185 ◽  
pp. 09006
Author(s):  
Alexander Tyatyushkin
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Steady State ◽  
Uniform Magnetic Field ◽  
Liquid Drop ◽  
Magnetic Liquid ◽  
Stationary Approximation ◽  
The Magnetic Field

Small steady-state deformational oscillations of a drop of magnetic liquid in a nonstationary uniform magnetic field are theoretically investigated. The drop is suspended in another magnetic liquid immiscible with the former. The Reynolds number is so small that the inertia can be neglected. The variation of the magnetic field is so slow that the quasi-stationary approximation for the magnetic field and the quasi-steady approximation for the flow may be used.

A Discussion on solar studies with special reference to space observations - The manifold structure of the chromosphere and corona

1971 ◽  
Vol 270 (1202) ◽  
pp. 77-80 ◽  
Keyword(s):  
Magnetic Field ◽  
Fine Structure ◽  
High Resolution ◽  
Field Strength ◽  
Special Reference ◽  
Velocity Fields ◽  
Field Patterns ◽  
Uniform Region ◽  
Determining Factor ◽  
The Magnetic Field

Although the photosphere is a uniform region for scales greater than the granulation, the fact that the magnetic field strength falls off less sharply than the gas pressure leads to strong magnetic influence at greater heights in the solar atmosphere. This magnetic influence leads to non-uniformity and fine structure in the chromosphere and corona. The existence of such structure has been deduced mostly from measurements of photospheric phenomena; in particular, from measurements of photospheric velocity fields (Leighton, Noyes & Simon 1962) and of photospheric magnetic fields (Bumba & Howard 1965). The determining factor would thus appear to be in the photosphere; but visible effects only are produced in the chromosphere and corona. In recent years, high resolution filter photography has enabled us to recognize different regions of the chromosphere, where qualitatively different structure is associated with distinct magnetic field patterns. This progress has been possible because of better Lyot filters, better films and better observing sites; the spectroheliograph has always been limited for high resolution work by the finite slit width and the difficulty of accurate guiding during the long exposures.

Rayleigh–Bénard convection and pattern formation in magnetohydrodynamics

1998 ◽  
Vol 60 (3) ◽  
pp. 529-539 ◽  
Author(s):  
RENU BAJAJ ◽  
S. K. MALIK
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Thermal Instability ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Steady State Bifurcation ◽  
The Stability ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
The Magnetic Field

A nonlinear thermal instability in a layer of electrically conducting fluid in the presence of a magnetic field is discussed. Steady-state bifurcation results in the formation of patterns: rolls, squares and hexagons. The stability of various patterns is also investigated. It is found that in the absence of a magnetic field only rolls are stable, but when the magnetic field strength exceeds a certain finite value, squares and hexagons also become stable.

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 Side-conditioned axisymmetric equilibria with incompressible flows

2008 ◽  
Vol 74 (3) ◽  
pp. 327-344 ◽  
Author(s):  
G. N. THROUMOULOPOULOS ◽  
H. TASSO ◽  
G. POULIPOULIS
Keyword(s):  
Magnetic Field ◽  
Incompressible Flows ◽  
Plasma Temperature ◽  
Magnetic Axis ◽  
Toroidal Shell ◽  
Initial Value ◽  
Magnetic Field Topology ◽  
Equilibrium Configurations ◽  
Magnetic Surfaces ◽  
The Magnetic Field

AbstractAxisymmetric equilibria with incompressible flows of arbitrary direction are studied in the framework of magnetohydrodynamics under a variety of physically relevant side conditions consisting, for example, in that the plasma temperature or the magnetic field modulus are uniform on magnetic surfaces. To this end a set of pertinent nonlinear ordinary differential equations (ODEs) are transformed to quasilinear ODEs and the respective initial value problem is solved numerically with appropriately determined initial values near the magnetic axis. Several equilibrium configurations are then constructed surface by surface. It turns out that in addition to the usual configurations with a magnetic axis, the non-field aligned flow results to novel toroidal shell equilibria in which the plasma is confined within a couple of magnetic surfaces. In addition, the flow affects the elongation and triangularity of the magnetic surfaces and opens up the possibility of changing the magnetic field topology by creating double toroidal shell-like configurations.

scholarly journals 5. The axisymmetric case in hydromagnetics

1958 ◽  
Vol 6 ◽  
pp. 46-49
Author(s):  
S. Chandrasekhar ◽  
Kevin H. Prendergast
Keyword(s):  
Magnetic Field ◽  
Recent Work ◽  
Hydrodynamic Equation ◽  
Azimuthal Angle ◽  
Unit Vector ◽  
Velocity Fields ◽  
Laplacian Operator ◽  
Axis Of Symmetry ◽  
Image Position ◽  
The Magnetic Field

Recent work at the Yerkes Observatory has been concerned with the study of configurations in which the magnetic and velocity fields possess a common axis of symmetry. In those cases where the density ρ may be assumed constant, it has proved advantageous to employ a representation suggested by Lüst and Schlüter[1]: in cylindrical co-ordinates (ω, ϕ, z) let and where is a unit vector and T, P, V, and U are independent of the azimuthal angle Φ. The hydrodynamic equation may then be replaced by the pair of equations (cf. Ghandrasekhar [2]) and where Δ5 is the Laplacian operator in 5 dimensions. The equation for the magnetic field, may similarly be replaced by the pair of equations and

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