scholarly journals Ray Paths in Inhomogeneous Anisotropic Media

1962 ◽  
Vol 15 (1) ◽  
pp. 96 ◽  
Author(s):  
RF Mullaly
Keyword(s):  
Magnetic Field ◽  
Refractive Index ◽  
Uniform Magnetic Field ◽  
Anisotropic Media ◽  
The Media ◽  
Axis Of Symmetry ◽  
Ray Path ◽  
Inhomogeneous Anisotropic Media ◽  
Moving Fluid ◽  
Ray Paths

The paths of rays in inhomogeneous anisotropic media are studied, starting from Fermat's Principle of Stationary Time. The media considered have a refractive index which depends on the angle between the direction of propagation and an axis of symmetry in the medium, and on several scalar parameters; both these and the direction of the axis are functions of position. Expressions are developed for the curvature of a ray path and are applied to (a) radio rays in an ionized medium pervaded by a non-uniform magnetic field and (b) acoustical rays in a moving fluid.

Torsional oscillations of a fluid sphere with a rigid boundary in a uniform magnetic field

1966 ◽  
Vol 24 (2) ◽  
pp. 275-284
Author(s):  
R. A. Wentzell
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Uniform Magnetic Field ◽  
Perfect Conductor ◽  
Rigid Boundary ◽  
Torsional Oscillations ◽  
Magnetic Viscosity ◽  
Eigen Values ◽  
Infinite Conductivity ◽  
Axis Of Symmetry

Plumpton & Ferraro (1955) considered the torsional oscillations of an infinitely conducting sphere in a uniform magnetic field. They showed that if the fluid and magnetic viscosity were assumed to be zero in the governing differential equations, then a continuous spectrum of eigenvalues could be obtained. This novel feature was clarified by Stewartson (1957) when he obtained the exact solution and showed that in the correct limit of a perfect conductor the eigen-values are discrete. Furthermore, in the limit of infinite conductivity the oscillations occur only on the axis of symmetry (figure 1).

Fluid flow in a hemispherical container induced by a distributed source of current and a superimposed uniform magnetic field

1980 ◽  
Vol 99 (1) ◽  
pp. 1-11 ◽  
Author(s):  
R. E. Craine ◽  
N. P. Weatherill
Keyword(s):  
Magnetic Field ◽  
Fluid Flow ◽  
Uniform Magnetic Field ◽  
Current Source ◽  
Welding Process ◽  
Nonlinear Flow ◽  
Axial Section ◽  
Axis Of Symmetry ◽  
Source Sink ◽  
Applied Fields

In arc welding electromagnetic forces are thought to be the major cause of motion in the weldpool, and it has recently been found by experimentalists that the application to the workpiece of a uniform magnetic field normal to the weldpool surface appears to stabilize the welding process. In this paper we investigate motion in a hemisphere due to a stationary distributed current source with a superimposed uniform magnetic field applied parallel to the axis of symmetry. When inertial effects are ignored and a simple source-sink model of the current source is introduced, we obtain an analytic solution for the fluid flow valid for low currents and low applied fields. A numerical scheme is then developed to solve the full nonlinear-flow problem and results are obtained for the source-sink model of the current source and for a more realistic numerically constructed distributed current source. For values of the externally applied magnetic field and the current flowing through the hemisphere typical of those occurring in practical welding situations we discover that the flow in an axial section through the pool is radially outwards on the free surface. This is in the opposite direction to that generally predicted by the theory when there is no superimposed magnetic field.

Exact solutions for vertically polarized electromaǵnetic waves in a horizontally stratified maǵneto-plasma

1970 ◽  
Vol 67 (2) ◽  
pp. 491-501 ◽  
Author(s):  
B. S. Westcott
Keyword(s):  
Magnetic Field ◽  
Refractive Index ◽  
Wave Propagation ◽  
Exact Solutions ◽  
Radio Wave ◽  
Static Magnetic Field ◽  
Electromagnetic Waves ◽  
Anisotropic Media ◽  
Radio Wave Propagation ◽  
Isotropic Media

AbstractIn a previous paper (11) refractive index profiles capable of yielding exact solutions for vertically polarized electromagnetic waves propagating in horizontally stratified isotropic media were derived systematically. The present work extends the method to deal with anisotropic media in which propagation is transverse to a horizontally applied static magnetic field. The relevance to ELF radio wave propagation in the terrestrial ionosphere is noted.

On the decay of Saffman turbulence subject to rotation, stratification or an imposed magnetic field

2010 ◽  
Vol 663 ◽  
pp. 268-292 ◽  
Author(s):  
P. A. DAVIDSON
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Temporal Evolution ◽  
Data Sets ◽  
Limited Data ◽  
Magnetohydrodynamic Turbulence ◽  
Integral Scales ◽  
Self Similar ◽  
Axis Of Symmetry

We consider freely decaying, statistically axisymmetric turbulence evolving in the presence of a background rotation, an imposed stratification or a uniform magnetic field. We focus on the case of Saffman turbulence in which E(k → 0) ~ k2 and show that, if the large scales evolve in a self-similar manner, then u⊥2 ℓ⊥2 ℓ∥ = constant in rotating, stratified and magnetohydrodynamic turbulence. This may be contrasted with E(k → 0) ~ k4 turbulence, in which u⊥2 ℓ⊥4 ℓ∥ ≈ constant. (Here the subscripts ⊥ and ∥ indicate directions perpendicular and parallel to the axis of symmetry, and ℓ⊥, ℓ∥ and u⊥ are suitably defined integral scales.) This constraint on the integral scales allows us to make simple, testable predictions for the temporal evolution of ℓ⊥, ℓ∥ and u⊥ in all three systems. There are only limited data sets against which to compare these predictions, but they are consistent with those data which are currently available.

scholarly journals The Ray Paths of Whistling Atmospherics: Differential Geometry

1962 ◽  
Vol 15 (1) ◽  
pp. 106 ◽  
Author(s):  
F Mullaly
Keyword(s):  
Magnetic Field ◽  
Differential Geometry ◽  
Field Strength ◽  
Electron Density ◽  
Magnetic Field Strength ◽  
Geometrical Optics ◽  
Plane Curves ◽  
Ray Path ◽  
Wave Normal ◽  
Ray Paths

Expressions are developed on the basis of geometrical optics for the curvature of a whistler ray path in terms of the gradients of electron density, magnetic field strength, and field direction, the analysis being restricted for simplicity to paths which are plane curves. It is shown that there is in general no tendency for the rays to follow the lines of force closely unless the wave-normal is very nearly at right angles to the direction of the ray.

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