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Nov 1959

Volume 2, Issue 6, pp. 585-721


Nonlinear Alfvén Waves in a Cold Ionized Gas

David Montgomery

Phys. Fluids 2, 585 (1959); http://dx.doi.org/10.1063/1.1705958 (4 pages) | Cited 16 times

Online Publication Date: 22 November 2004

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Nonlinear constant‐profile Alfvén waves are studied in an ionized gas in which thermal motions are negligible. The system of differential equations possesses numerous integrals, and can be solved up to a single quadrature. Many properties of the waves can be inferred without performing any numerical integrations. The waves necessarily involve nonzero magnetic field components in both directions perpendicular to the direction of propagation, and plane polarized waves are impossible except in the special case of equal mass particles. Circularly polarized modes are also a special case, and, unlike the more general solutions, involve neither longitudinal electric fields nor compression of the gas.

High‐Speed Shock Waves in a Magnetic Annular Shock Tube

Richard M. Patrick

Phys. Fluids 2, 589 (1959); http://dx.doi.org/10.1063/1.1705959 (10 pages) | Cited 57 times

Online Publication Date: 22 November 2004

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Experiments were carried out with two magnetic field configurations ahead of the shock front, the first with a magnetic field ahead of the shock front in the direction of motion of the shock. In the second configuration the magnetic field ahead of the shock had its principal component in the plane of the shock front and a small component in the direction of the shock motion. The continuum radiation emitted by the shock‐heated plasma was measured with photomultipliers. Use of probes to measure the change in the local magnetic field in the shock front was investigated. With the second configuration, shock velocities in excess of 4 × 107 cm∕sec were measured in hydrogen. For these high‐speed shock waves, shock thicknesses, obtained from measured rise times of the emitted visible radiation, are thinner than the mean free path in the shock‐heated plasma, an observation which agrees with a theoretical prediction.

Theory of the Flow in the Magnetic Annular Shock Tube

Nelson H. Kemp and Harry E. Petschek

Phys. Fluids 2, 599 (1959); http://dx.doi.org/10.1063/1.1705960 (10 pages) | Cited 43 times

Online Publication Date: 22 November 2004

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The magnetic annular shock tube uses a magnetic field to drive a shock wave through an annular region, producing a very high‐temperature plasma [cf. R. M. Patrick, Phys. Fluids 2, 589 (1959)]. It is shown that this particular configuration allows a fairly precise calculation of the flow parameters. Numerical calculations of the significant flow properties for a complete range of the initial field strength and orientation have been made and are presented graphically.

Moving Magnetic Field behind a Strong Deuterium Shock

F. R. Scott and R. F. Wenzel

Phys. Fluids 2, 609 (1959); http://dx.doi.org/10.1063/1.1705961 (5 pages) | Cited 13 times

Online Publication Date: 22 November 2004

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By introducing a spiral in the return conductor of a conical discharge tube with a hollow electrode, a magnetic multipole has been observed propagating down a cylinder extending out from the hollow electrode. This magnetic field appears to have an extremely complicated internal structure when observed with small magnetic probes; when observed by an external loop, the net axial leakage flux shows a structure consistent with the characteristics of a shock produced deuterium plasma.
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Thermal and Electrical Properties of an Argon Plasma

H. N. Olsen

Phys. Fluids 2, 614 (1959); http://dx.doi.org/10.1063/1.1705962 (10 pages) | Cited 97 times

Online Publication Date: 22 November 2004

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Temperatures ranging from 10 000 to 25 000°K have been measured spectroscopically in thermal plasmas of atmospheric pressure argon arcs at currents in the range of 200 to 800 amp. Electrical properties of the plasmas have been derived from measured radial temperature distributions using Spitzer's theory for the temperature dependence of electrical conductivity of a completely ionized gas. Existence of local thermal equilibrium has been demonstrated by the agreement between excitation temperatures determined from both atomic and ionic spectral line intensities. Agreement between values of electrical quantities obtained by direct measurement and those derived from measured temperatures based on the assumption of thermal equilibrium demonstrates the internal consistency of the experimental and analytical methods.

Some Interior Problems of Hydromagnetics

J. D. Cole and J. H. Huth

Phys. Fluids 2, 624 (1959); http://dx.doi.org/10.1063/1.1705963 (3 pages) | Cited 9 times

Online Publication Date: 22 November 2004

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The static boundary problems of line currents and dipoles immersed in a perfectly conducting static fluid are considered first. The perturbing effect of moving fluid on the magnetostatic boundary about an isolated line current is then investigated. In this case, the initial circular boundary is distorted into an ellipse with major axis transverse to the direction of flow.

Flow of an Incompressible Fluid in a Hydromagnetic Capacitor

C. C. Chang and T. S. Lundgren

Phys. Fluids 2, 627 (1959); http://dx.doi.org/10.1063/1.1705964 (6 pages) | Cited 12 times

Online Publication Date: 22 November 2004

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An incompressible electrically conducting fluid is contained in a torus of rectangular cross section. A uniform magnetic field is maintained along the polar axis of the tube. A radial electric field is suddenly applied, causing the fluid to flow through the tube. Over‐all properties such as the time required to reach steady state, resistance and capacitance are calculated, and an equivalent electrical circuit is given.

Magnetohydrodynamic Waves in Wave Guides

Ryszard Gajewski

Phys. Fluids 2, 633 (1959); http://dx.doi.org/10.1063/1.1705965 (9 pages) | Cited 14 times

Online Publication Date: 22 November 2004

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Propagation of magnetohydrodynamic waves is investigated in a fluid bounded by a cylindrical surface of constant, but not necessarily circular, cross section. The fluid is assumed to be nonviscous and perfectly conducting with a constant magnetic field applied parallel to the walls of the cylinder. It is shown that the following types of waves can propagate in such a wave guide: (1) transverse waves propagating without dispersion with the velocity of Alfvén waves; (2) a longitudinal wave, identical with the wave of the principal mode for an acoustic wave guide; (3) waves having both longitudinal and transverse components propagating with a dispersion, their group and phase velocity being close to the respective velocities for an acoustic wave guide; (4) waves having both longitudinal and transverse components propagating with a small dispersion, their group and phase velocity being close to the velocity of Alfvén waves. When the applied frequency is too low, damping of certain modes appears for waves of type (3), only; the cut‐off frequencies turn out to be slightly higher than the corresponding cut‐off frequencies for an acoustic wave guide.

Instability of Certain Electrohydrodynamic Systems

Otmar M. Stuetzer

Phys. Fluids 2, 642 (1959); http://dx.doi.org/10.1063/1.1705966 (7 pages) | Cited 13 times

Online Publication Date: 22 November 2004

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The production of ion drag pressure under dynamic conditions, i.e., with the carrier medium in motion, is theoretically investigated. It is shown that for constant applied voltage the pressure increases with increasing velocity of the carrier fluid. This can lead to instability of the system which is theoretically discussed and experimentally demonstrated.

Electrostatic Field About an Ion Moving Slowly in a Plasma

S. Rand

Phys. Fluids 2, 649 (1959); http://dx.doi.org/10.1063/1.1705967 (4 pages) | Cited 5 times

Online Publication Date: 22 November 2004

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A particle treatment is used to determine the potential distribution about an ion moving subsonicly through a plasma. A fore‐aft asymmetry is obtained which has the effect of producing a drag on the ion. This asymmetry is the most important difference between the results of this treatment and those obtained for the subsonic case by the linearized treatment of the electrohydrodynamic equations.

Distribution of Density in a Planetary Exosphere

E. J. Öpik and S. F. Singer

Phys. Fluids 2, 653 (1959); http://dx.doi.org/10.1063/1.1705968 (3 pages) | Cited 9 times

Online Publication Date: 22 November 2004

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A theory has been developed which gives the distribution of density with altitude for a planetary exosphere in the absence of local thermodynamic equilibrium. It gives values considerably lower than those conventionally calculated on the basis of the hydrostatic equation. Our results apply to the case where the field of force is gravitational; hence in the case of the earth, they give the density variation of only the neutral component of the exosphere.

Dynamic Instability of Accelerated Fluids

C. T. Chang

Phys. Fluids 2, 656 (1959); http://dx.doi.org/10.1063/1.1705969 (8 pages) | Cited 6 times

Online Publication Date: 22 November 2004

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See Also: Erratum

Show Abstract
The asymmetrical growth of an interface separating two fluids of different densities, under the influence of an imposed acceleration (Rayleigh‐Taylor instability), is shown to be mainly a nonlinear phenomenon. When the initial disturbance is a simple sinusoidal wave and is started from rest, it is found that the growth of the interface depends explicitly on two dimensionless parameters of the initial disturbance, namely, the dimensionless amplitude (i.e., the amplitude‐to‐wave‐length ratio) and the dimensionless wave number (i.e., the wave number of the initial disturbance to the ``cutoff'' wave number of the medium under the prevailing experimental condition). Results of the analysis show that the asymmetrical development of the interface occurs much earlier for disturbances of larger amplitudes and lower wave numbers than those of smaller amplitudes and higher wave numbers, i.e., those with wave numbers near the ``cutoff.'' Surface tension shows a definite stabilizing effect. Because of the nonlinear effect, for a sinusoidal initial disturbance, a generation of higher harmonics as well as a feed‐back to the fundamental is noted. Contrary to the prediction of the linearized theory, the present analysis, based on higher order approximations, reveals an ``over‐stable'' phenomenon for disturbances having initial wave numbers beyond the ``cutoff.''

Some Transition Patterns in Axisymmetric Boundary Layers

Francis R. Hama

Phys. Fluids 2, 664 (1959); http://dx.doi.org/10.1063/1.1705970 (4 pages) | Cited 9 times

Online Publication Date: 22 November 2004

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Direct observation of the vortex pattern caused by a ring‐shaped trip is made on 1‐in. and ☒‐in. circular cylinders and on a 30° cone in a water tank. Over the cylinders the boundary‐layer thickness is approximately equal to the radius of the cylinders. Ring‐shaped vortices are shed and deformed into vortex loops in the same manner as on a flat plate. On the cone the ring‐shaped vortices are stretched and then inevitably deformed into vortex loops, indicating that a mere stretching is not a sufficient mechanism for the creation of a turbulence spot. A mechanism of the final breakdown from the vortex loop is tentatively proposed.

Turbulent Boundary Layer Measurements at Mach Numbers from 8 to 10

F. K. Hill

Phys. Fluids 2, 668 (1959); http://dx.doi.org/10.1063/1.1705971 (13 pages) | Cited 10 times

Online Publication Date: 22 November 2004

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Data are presented showing the properties of hypersonic boundary layers at Mach numbers from 8 to 10. The measurements extend experimental data on skin friction and heat transfer previously reported in the literature, and provide a basis for comparison with theory. Significant results of the investigation include the relatively rapid growth of the laminar sublayer at high Mach numbers, the increase in the momentum thickness with heat transfer, the decrease in the heat transfer coefficient, and the skin friction dependence on heat transfer and pressure gradient at high Mach numbers. The velocity profiles in the turbulent portion of the boundary layer are found to extend the trend evidenced at lower Mach numbers of a fit to a power profile, but with a somewhat lower velocity index (n = 5 as compared to 7 and 9 at lower supersonic Mach numbers). On the other hand an exponential fit to the experimental points provides equally good agreement, and satisfies better the physical conditions at the edge of the boundary layer.

Simple Wave Flow in Ducts

Roy Gundersen

Phys. Fluids 2, 680 (1959); http://dx.doi.org/10.1063/1.1705972 (8 pages) | Cited 1 time

Online Publication Date: 22 November 2004

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A centered simple wave is generated by the impulsive retraction of a piston. The sound speed perturbation and particle velocity perturbation are determined when the wave passes into a slowly diverging (or converging) section or a section which presents a throat. When the section of varying area terminates in a channel of constant cross section, the result of passage through the transition section of varying area is the superposition of a perturbation which tends to decrease the flow velocity by a term which varies inversely with the time for a point moving with the wave, but increases linearly with the time at a fixed point in the channel, in agreement with results first presented by Chester with the use of a two‐dimensional analysis. The flow of an arbitrary simple wave in the section of varying area is solved.

Transport Properties of High‐Temperature Multicomponent Gas Mixtures

Edward A. Mason, Joseph T. Vanderslice, and Jerrold M. Yos

Phys. Fluids 2, 688 (1959); http://dx.doi.org/10.1063/1.1705973 (7 pages) | Cited 69 times

Online Publication Date: 22 November 2004

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An investigation is made of some modifications in the kinetic theory of gaseous transport properties which are necessary to take account of effects encountered at high temperatures. In particular, complications arise because of the existence of a multiplicity of different interaction energy curves governing collisions, and because of the possibility of resonant excitation and charge exchange during collisions. It is shown that the results of classical kinetic theory can be kept in the same form, but the cross sections or collision integrals have to be computed differently. It is pointed out that the present modifications are valid to all orders of Chapman‐Enskog approximation. It is also shown that excitation exchange is important in determining the transport properties of mixtures at high temperatures, and the method of calculation of the excitation exchange probability is extended to cases for which multiple interaction curves are involved.

Collision Integrals for the Exponential Repulsive Potential

Louis Monchick

Phys. Fluids 2, 695 (1959); http://dx.doi.org/10.1063/1.1705974 (6 pages) | Cited 101 times

Online Publication Date: 22 November 2004

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The exponential potential function, Ae−r∕ρ long has been regarded as the true qualitative form of the repulsive intermolecular potential at moderately small internuclear distances (or equivalently, high temperatures). Because of the increasing interest in gases at high temperatures it has become desirable to be able to evaluate the transport properties under these conditions. The calculation of integrals related to the usual collision integrals Ω(l,s) and cross sections Q(l) have been carried out for the exponential repulsive potential. Some high‐temperature viscosities have been calculated and compared to the calculated results of Amdur and Mason which are based on an experimental scattering potential.

Heat Flow Between Parallel Plates

E. P. Gross and S. Ziering

Phys. Fluids 2, 701 (1959); http://dx.doi.org/10.1063/1.1705975 (12 pages) | Cited 35 times

Online Publication Date: 22 November 2004

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A study is made of the flow of heat between parallel plates of slightly different temperatures. The problem is described by the linearized Boltzmann equation which is subject to microscopic boundary conditions. We approximate the distribution function by half‐range polynomials in velocity space and determine the space‐dependent coefficients by forming half‐range moment equations. An approximation involving four pairs of space functions suffices to give an accurate treatment of the heat flow and of the density and temperature profiles for the entire range of conditions from free molecule to hydrodynamic. Detailed numerical results for the temperature slip and molecular boundary structure are obtained for hard‐sphere molecules. The accuracy of cruder half‐range approximations and other methods of fixing the coefficients is established.
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Oscillations in the B‐1 Stellarator

W. Bernstein, A. Z. Kranz, and F. Tenney

Phys. Fluids 2, 713 (1959); http://dx.doi.org/10.1063/1.1705976 (2 pages) | Cited 5 times

Online Publication Date: 22 November 2004

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Abstract Unavailable

On the ``Escape Speed'' of a Conducting Fluid in a Transverse Magnetic Field

William J. Guman

Phys. Fluids 2, 714 (1959); http://dx.doi.org/10.1063/1.1705977 (1 page) | Cited 2 times

Online Publication Date: 22 November 2004

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Abstract Unavailable

Stagnation Point Fluctuations on a Body of Revolution

Arnold M. Kuethe, William W. Willmarth, and Gage H. Crocker

Phys. Fluids 2, 714 (1959); http://dx.doi.org/10.1063/1.1705978 (3 pages) | Cited 4 times

Online Publication Date: 22 November 2004

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Abstract Unavailable

Streamlines in Bénard Convection Cells

W. H. Reid and D. L. Harris

Phys. Fluids 2, 716 (1959); http://dx.doi.org/10.1063/1.1705979 (2 pages) | Cited 5 times

Online Publication Date: 22 November 2004

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Abstract Unavailable

Heat Loss from Very Thin Heated Wires in Rarefied Gases

Herbert J. Bomelburg

Phys. Fluids 2, 717 (1959); http://dx.doi.org/10.1063/1.1705980 (2 pages) | Cited 6 times

Online Publication Date: 22 November 2004

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Abstract Unavailable

Patterns in Turbulent Flow in the Wall‐Adjacent Region

F. M. Richardson and K. O. Beatty

Phys. Fluids 2, 718 (1959); http://dx.doi.org/10.1063/1.1705981 (2 pages) | Cited 3 times

Online Publication Date: 22 November 2004

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Abstract Unavailable

Thin‐Film Thermometer Measurements In Partially Ionized Shock‐Tube Flows

P. V. Marrone and R. A. Hartunian

Phys. Fluids 2, 719 (1959); http://dx.doi.org/10.1063/1.1705982 (3 pages) | Cited 7 times

Online Publication Date: 22 November 2004

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Abstract Unavailable
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