Magnetofluid Dynamics Research Articles

Relativistic magneto-acoustic simple wave solutions for a Synge gas

Simple wave solutions for test-relativistic magneto-fluid dynamics in a flat space-time are considered for one-dimensional flow. A numerical integration of the equations has been performed and a discussion of the qualitative behaviour of the solution is also given.

Magnetoacoustic shock waves in a relativistic gas

Fast and slow magnetoacoustic shocks are studied in the framework of relativistic magneto-fluid dynamics with the Synge equation of state. An approximate analytical solution is presented in a particular case. The general case is treated by numerical methods.

О цирку Ляции, сохраяющей плоские магнитно-гидродинамические течения

A theoretical analysis based on the equations of magnetofluid dynamics is undertaken in order to completely classify the flow geometries admitted by these equations. It is shown that the only possible flows with steady vorticity are i) motions having constant vorticity magnitude, ii) motions whose stream lines are concentric circles. Conditions are derived for which the results hold also for the unsteady case.

A Lagrangian formulation in magnetofluid dynamics

By using Clebsch representations for all necessary vector fields, an action principle for a compressible, inviscid, one-component magneto-fluid, undergoing isentropic motion in an electromagnetic field, is given.

A variational principle in relativistic magnetofluid dynamics

The definition of the generalized antipotential four-vector makes it possible to give a relativistically covariant variational formulation in the dynamics of ideal charged fluids. A special relativistically covariant form of Maxwell's equation is given. The antipotential four-vector does not explicitly appear in the Lagrangian density. The derivation of the equation of motion of a single charged particle is given, to illustrate the theory.

Alcune soluzioni esatte delle equazioni della magnetofluidodinamica per il moto stazionario di un fluido viscoso, incomprimibile e a conducibilità elettrica finita

With regard to the non-linear equations of Magneto-Fluid Dynamics in this paper we examine the steady, axially symmetric motion of an incompressible, homogeneous, viscous and electrically conducting fluid when such a fluid moves also around the axis of symmetry. We give some classes of exact solutions and then we generalize the problem taking also in account the Hall effect.

Source of the solar flare energy

Recent Skylab and magnetograph observations indicate that strong photospheric electric currents underlie small flare events such as X-ray loops and surges. What is not yet certain, because of the non-local dynamics of a fluid with embedded magnetic field, is whether flare emission derives from the energy of on-site electric currents or from energy which is propagated to the flare site through an intermediary, such as a stream of fast electrons or a group of waves. Nevertheless, occurrences of: (1) strong photospheric electric currents beneath small flares; (2) similar magnetic fine structure inside and outside active regions; (3) eruptive prominences and coronal white light transients in association with big flares; and, (4) active boundaries of large unipolar regions suggest the possibility that all phenomena of solar activity are manifestations of the rapid ejection and/or gradual removal of electric currents of various sizes from the photosphere. The challenge is to trace the precise magnetofluid dynamics of each active phenomenon, particularly the role of electric current build-up and dissipation in the low corona.

Spherical harmonic analysis of the Navier-Stokes equation in magnetofluid dynamics

The equation of motion (Navier-Stokes equation) for a uniformly rotating, compressible, magnetic, viscous fluid is analyzed in terms of infinite series of spherical surface harmonics. Differential equations are obtained for the radial functions of the poloidal and toroidal harmonics of the velocity, corresponding to those obtained by Bullard and Gellman for the magnetic field from the electromagnetic induction equation. This new analysis opens the way for the dynamical problem of electromagnetic induction in the earth's core to be considered by the spherical harmonic method.

New from mcgraw‐hill magnetofluid dynamics for engineers and applied physicists

New from mcgraw‐hill magnetofluid dynamics for engineers and applied physicists

Experimental studies in magneto-fluid dynamics: flow over a sphere with a cylindrical afterbody

The measured pressure distributions over the front hemisphere of a hemispherecylinder combination placed in an aligned fields magneto-fluid dynamic flow are presented. Integration of the pressure profiles show that the form or pressure drag of the composite body first increases as the magnetic field strength increases, at a fixed flow velocity, but then decreases as the magnetic field becomes still stronger.

Experimental studies in magneto-fluid dynamics: pressure distribution measurements around a sphere

Measurements of the pressure distribution around a sphere placed in aligned magnetic and velocity fields show that an increase in drag is mainly due to a decrease in the pressure on the base of the body. When magnetic forces are large compared to inertia forces, this decrease is due to a loss in total pressure along streamlines just outside the surface boundary layer and an acceleration of the flow to a velocity much larger than the reference velocity. Separation of a viscous boundary layer takes place behind the equator and still, to a large extent, controls the magnitude of the base pressure and the drag experienced by the sphere. A model consistent with these findings is presented.

Some intrinsic properties of steady parallel flows in magneto-fluid dynamics

Some intrinsic properties of steady parallel flows in magneto-fluid dynamics

Anisotropic waves in elastoplastic soils

The Prandtl-Reuss theory extended to consider a medium which is compressible in the plastic region is utilized to study waves in elastoplastic soils. The von Mises yield condition is applied with the yield stress a function of the pressure, which is typical of soils. An arbitrary pressure-density relationship with noncoincident loading and unloading paths is also allowed. The full nonlinear three-dimensional unsteady partial differential equations are analyzed by determining their characteristic or discontinuity surfaces. The characteristic analysis results in equations for the wave speed of infinitesimal disturbances in the medium as a function of the orientation of the wave normal vector, the stress, the shear modulus, the bulk modulus and the density. These equations have been coded for digital computer solution and automatic plotting of the three-dimensional normal wave speed diagrams and their corresponding wave surfaces or fronts. Results in the form of normal wave speed diagrams and wave surfaces reveal the nature of the anisotropic waves which are found in soils in the nonlinear elastic and plastic regimes. The variation of the waves with variation in the parameters is also found. Most of the phenomena of cusped wave surfaces and intersecting normal wave speed diagrams found in anisotropic elastic waves, magnetofluid dynamics and crystal optics are also observed in the present results. In addition, it is found that certain waves do not propagate (their wave speeds become imaginary) in directions normal to the axis of the principal deviatoric stress whose absolute value is maximum.

The method of characteristics for the three-dimensional unsteady magnetofluid dynamics of a multi-component medium

A general numerical method of characteristics applicable to problems in magneto-fluid dynamics as well as ordinary fluid dynamics is described. The method can be applied to unsteady three-dimensional flows of chemically reacting, non-equilibrium, multi-component media. Dissipative phenomena must be neglected in order to make the governing equations of change hyperbolic, because the method can be applied only to quasi-linear, hyperbolic, partial differential equations. Practical restrictions on computation time usually require unsteady problems to be limited to cases with short transient times although theoretically the method applies to all unsteady flows. In steady flow the local velocity must be greater than the largest local wave speed. The characteristic and compatibility equations are derived for the most general case of magnetofluid dynamics. A new finite-difference network and its corresponding equations are developed similarly. Specialization of the general method to consider simpler problems is outlined. Preliminary numerical results of calculations using the method are presented. The practicality and feasibility of utilizing the general numerical method of characteristics on presently available, electronic digital computers is evaluated in the light of recent experience in calculating multi-dimensional flows with the method.

Magneto-fluid dynamics of bodies in alined fields

The motion of a perfectly conducting fluid past a fixed body in the presence of an alined magnetic field can be regarded as the limit of a number of problems, namely (i) when the fluid is a finite conductor, (ii) an unsteady problem, (iii) when themagnetic and velocity fields are not parallel at infinity. The limits of these m ore general problems agree in predicting a force on the body and on the existence of upstream and downstream wakes. However, if the magnetic field is fairly strong (i) does not predict a downstream wake while (ii) and (iii) do. An attempt to reconcile these limit results is made here. In the first part we show that the unsteady problem associated with a finitely conducting fluid and an alined field is nonunique but that by making an appeal to the theory of real fluids the conclusion of (i) and (ii) can be obtained as special cases of the general solution. In the second part the steady problem, assuming that the conductivity is finite and the magnetic field is nearly alined, is considered and it is shown that the flow fields predicted in (i) and (ii) are limiting cases of this more general problem. The manner of the changeover from the solution for (i) to that for (iii) is elucidated.

Covariant Treatment of Linearized Magneto-Fluid Dynamics

A perfectly conducting, nonviscous fluid is assumed to be permeated by an inhomogeneous, time independent magnetic field satisfying the magnetohydrostatic equation. This fluid shall be perturbed by hydromagnetic waves of small amplitude. The wave equation is expressed in a completely covariant form. This formulation allows to search for simplifying coordinate systems intrinsically adapted to the undisturbed field configuration. Hydromagnetic waves with the velocity vector satisfying the equation div v=0, which are the natural generalization of ALFVÉN waves have been investigated especially. It is shown that there are simplifying coordinate systems for the hydromagnetic wave equation. Especially it is shown that the solution of the ALFVÉN wave equation can always be reduced to the solution of an ordinary differential equation if in the equilibrium configuration the current is either perpendicular on the magnetic field line or zero.

REFRACTION ANGLES FOR LUMINOUS SOURCES WITHIN THE ATMOSPHERE

1 Sears, W. R. and Resler, E. L., Theory of thin airfoils in fluids of high electrical conductivity, J. Fluid Mech. 5, 257 (1959); also McCune, J. E. and Resler, E. L., Compressibility effects in magnetoaerodynamic flows past thin bodies, J. Aerospace Sci. 27, 493 (1960). 2 Grad, H., Reducible problems in magneto-fluid dynamic steady flows, Revs. Mod. Phys. 32, 830 (1960). 3 Cumberbatch, E., Sarason, L., and Weitzner, H., A magnetofluid-dynamic Kutta-Joukowsky condition, J. Aerospace Sci. 29, 244 (1962). 4 Mikhlin, S. G., Integral Equations (Pergamon Press, New York, 1957), p. 126. Stewartson, K., Magneto-fluid dynamics of thin bodies in oblique fields, Z. Angew. Math. Phys. 12, 261 (1961).

Magnetically Driven Cylindrical Shock Waves

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Experiments in magneto-fluid dynamics

Magneto-fluid dynamics deals with the motion of electrically conducting gases and liquids in the presence of magnetic fields. The macroscopic description of such motions involves the coupling of the equations of hydrodynamics and Maxwell's equations. For velocities small compared to that of light, and if one neglects displacement and charge convection currents, the coupling in the equations of motion occurs through a Lorentz body force term—a term involving the current density j and the magnetic induction, B, viz., j×B/c. The requirement of Lorentz invariance effects the introduction of the coupling into Maxwell's equations, so that one calculates j from the generalized Ohm's law j = σ(E+V×B/c), where σ is the fluid conductivity, E the electric field intensity and V the fluid velocity. Both j×B and V×B are basically nonlinear terms, whence the already uncomfortable situation with nonlinearities in hydrodynamics is quite considerably aggravated. Linearization on the one hand and “simple” experiments on the other must be invoked to convey a physical feeling for the phenomena to be expected from this coupling.

Two-Dimensional Boundary Layers and Jets in Magneto-Fluid Dynamics

The main assumptions and results are given for an investigation of two- dimensional incompressible laminar boundary layers in flows of electrically conducting fluids under the influence of a magnetic field having a direction coincident with the plane of flow. These assumptions and results are extended to the case of similar solutions for laminar jets. It is shown that the equation derived by Pai for jet flow into a fluid at rest has no solution. A generalization of Pai's transformation leads to a class of solutions which can be shown to contain all the possible similar solutions for that case. Two classes of solutions are given for jet flow into a moving fluid with pressure gradient. (B.O.G.) the limits of the theory of a perfect fluid. The main features