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Nov 1958

Volume 1, Issue 6, pp. 457-548


Surface Wake of a Submerged Sphere

Carl Eckart

Phys. Fluids 1, 457 (1958); http://dx.doi.org/10.1063/1.1724367 (5 pages)

Online Publication Date: 22 November 2004

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The problem of a sphere moving in an infinite homogeneous incompressible liquid has been discussed by many writers. The corresponding problem for a semi‐infinite liquid with a free surface has not been treated earlier.
It is shown that the surface wake of such a submerged sphere is approximately the same as that which would be caused by a traveling pressure disturbance in the atmosphere above the free surface. This is, essentially, a consequence of the Bernoulli theorem.
If the motion is sufficiently slow, the surface reacts to this equivalent pressure as a barometer (equilibrium theory). For more rapid motions, dynamic effects reduce the response of the surface, but leave a wake in the region already traversed by the sphere. The calculation of this wake involves the usual distinction between incoming and outgoing waves, which is introduced in the Fourier transform of the solution. The resulting integrals are evaluated by Kelvin's approximate method of stationary phase.

Space‐Time Correlations in Stationary Isotropic Turbulence

G. Münch and Albert D. Wheelon

Phys. Fluids 1, 462 (1958); http://dx.doi.org/10.1063/1.1724368 (7 pages) | Cited 7 times

Online Publication Date: 22 November 2004

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The correlation between Fourier velocity components at the same wave number k and two instants separated by a time τ is investigated for a homogeneous, isotropic, and stationary turbulent field. Ensemble averages of four velocity components are related to second‐order averages as in a normal distribution. A power series in τ for the time‐displaced kinetic energy spectrum E(k, τ) is derived and the coefficient of τ2 evaluated explicitly using the Heisenberg spectrum for τ = 0. The asymptotic behavior of this term for an infinite Reynolds number R shows that the relaxation time associated with eddies of wave number k varies as k−1. These results were verified by numerical integrations for finite large R. The resulting discrepancy with the dimensional result τkαk−2∕3 is ascribed to the nonuniversality of the method of analysis followed. A general integrodifferential equation for E(k, τ) is then derived and shown to admit solutions in similarity variables of the form ξ = k τ1∕β. The case β = 2∕3 corresponds to the Kolmogoroff spectral law. Recent objections to the quasi‐normal approximation are criticized briefly in an appendix.

The Free Molecule Probe and Its Use for the Study of Leading Edge Flows

J. A. Laurmann

Phys. Fluids 1, 469 (1958); http://dx.doi.org/10.1063/1.1724369 (9 pages) | Cited 11 times

Online Publication Date: 22 November 2004

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The development of a free molecule probe for use as an instrument in the investigation of two dimensional rarefied gas flow fields is described. The probe consists of a cross‐stream cylindrical wire of diameter small compared with the mean free path of the gas. Measurement of the probe temperature and heat transfer characteristics yields information that can be related theoretically to the state of the flowing gas. This paper describes the use of such information in the study of the qualitative nature of supersonic flow about sharp leading edges in regions where rarefaction, slip, and boundary layer‐shock wave interaction effects are important. The results showed clearly the effect of increasing density. Thus, at the lowest densities and Mach numbers, a clearly defined shock wave and boundary layer emerged from a region of mixed compressive and viscous action at the leading edge, while at the higher densities and Mach numbers there was a large region of strong boundary layer‐shock wave interaction and a considerable delay in the formation of clearly defined shock wave.

Comparison of High‐Altitude Rocket and Satellite Density Measurements

H. E. LaGow and R. Horowitz

Phys. Fluids 1, 478 (1958); http://dx.doi.org/10.1063/1.1724370 (2 pages) | Cited 1 time

Online Publication Date: 22 November 2004

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Atmospheric density measurements obtained with rocket‐borne ionization gauges are compared with U. S. A. and U. S. S. R. satellite‐drag density measurements. There is no significant disagreement between the results obtained by the two methods once atmospheric variations are taken into account.

Plasma Motions Induced by Satellites in the Ionosphere

Lester Kraus and Kenneth M. Watson

Phys. Fluids 1, 480 (1958); http://dx.doi.org/10.1063/1.1724371 (9 pages) | Cited 33 times

Online Publication Date: 22 November 2004

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The electrohydrodynamic phenomena associated with the high‐velocity motion of a charged body in a plasma are investigated with a view to applications to satellite motion in the ionosphere. It is shown that the effect of the electric field due to the charge on the body in inducing collective motion leads to similar results both for high‐ and low‐density gases. By using a linearized theory, formulas are obtained for the electrohydrodynamic drag and for the increased ionization in the Mach cone behind the body.

Inverse Pinch Effect

O. A. Anderson, H. P. Furth, J. M. Stone, and R. E. Wright

Phys. Fluids 1, 489 (1958); http://dx.doi.org/10.1063/1.1724372 (6 pages) | Cited 21 times

Online Publication Date: 22 November 2004

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In the conventional pinch effect an ionized gas is enclosed by a conducting cylinder, and a sufficiently large current passing through the gas and returning along the inner wall of the cylinder produces a magnetic field which compresses the gas into an axial filament. A device is described which produces an inverse pinch effect. Here the above conducting cylinder is replaced by an axial rod surrounded by the ionized gas. When a current passes through the gas and returns along the rod the magnetic field pushes the plasma outward, leaving a cylindrical vacuum region behind. The velocity and thickness of the expanding plasma front have been studied optically and by means of magnetic probes. Except at the highest gas densities, the velocity is in good agreement with the ``snow plow'' theory of Rosenbluth, and the thickness of the front is reasonably consistent with the ``snow plow'' model. At the higher densities it appears that diffusion of magnetic field into the plasma is significant. The advantages of the inverse pinch effect in studying plasma behavior and the idea of a magnetically stabilized inverse pinch are discussed.

Ignition of a Thermonuclear Plasma by High‐Energy Injection

Albert Simon

Phys. Fluids 1, 495 (1958); http://dx.doi.org/10.1063/1.1724373 (6 pages) | Cited 4 times

Online Publication Date: 22 November 2004

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The effect of the neutral gas background on the formation of a thermonuclear plasma by highenergy injection is discussed. There ways of overcoming this barrier are detailed. The first is by sufficiently reducing the initial gas pressure; the second by injecting sufficient current so that plasma self‐shielding or ``burnout'' occurs; and the third by use of the ion pumping or ``gettering'' action of the trapped plasma. Numerical examples are given. In particular the requirements for ``burnout'' do not seem excessively difficult to attain.

Collective Oscillations in a Cold Plasma

P. L. Auer, H. Hurwitz, and R. D. Miller

Phys. Fluids 1, 501 (1958); http://dx.doi.org/10.1063/1.1724374 (14 pages) | Cited 36 times

Online Publication Date: 22 November 2004

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The collective motions of a fully ionized cold plasma in a uniform external magnetic field are treated by standard small amplitude theory. Finite temperature and collision effects are neglected. Specializing the analysis to a neutral plasma of uniform unperturbed density containing electrons and ions of one species, one obtains a dielectric tensor and dispersion relation which is a special example of results previously given by Aström. A detailed discussion of the exact dispersion relation is given for the entire frequency spectrum, and completeness theorems are presented with the aid of scalar potentials representing the electromagnetic field quantities. It is found that when the Alfvén dielectric constant α = 4πn(m + M)c2∕B02 becomes comparable in magnitude to the ion‐to‐electron mass ratio, the plasma space charge may play an important role in determining the nature of collective oscillations. In particular, if the axial wavelength of the perturbation is sufficiently large, the singularities of the effective dielectric constant become displaced from the neighborhood of the particle cyclotron frequencies to hybrid frequencies, which, in the limit of high plasma density, become equal to the geometric mean of the cyclotron frequencies and the plasma frequency, respectively. The last two sections discuss particle orbits in idealized oscillatory modes and simplified boundary value problems associated with plasma resonance.

Energy Partition in the Exploding Wire Phenomena

F. D. Bennett

Phys. Fluids 1, 515 (1958); http://dx.doi.org/10.1063/1.1724375 (8 pages) | Cited 11 times

Online Publication Date: 22 November 2004

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Streak camera and oscillographic circuit‐damping data are presented for exploded copper wires varying in diameter from 3 to 8 mils. A maximum of specific shock‐wave energy in the induced flow is found at a wire diameter different from that of a minimum in the total damping time of the circuit. This displacement is shown to be caused by the presence of residual circuit resistance. The proof is based on a critical analysis of optimum damping conditions in the exploding wire circuit. A maximum of apparent energy within the contact surface appears at about the same wire diameter as the minimum of total damping time. Discussion of the implications of the Taylor‐Lin similarity theory indicates that lack of similarity of the flow is probably connected with the displacement of the maximum energies associated with shock‐wave and contact surface.

Measurement of the Reflected Shock Hugoniot and Isentrope for Explosive Reaction Products

W. E. Deal

Phys. Fluids 1, 523 (1958); http://dx.doi.org/10.1063/1.1724376 (5 pages) | Cited 22 times

Online Publication Date: 22 November 2004

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Measurement of the hydrodynamic state in an inert material adjacent to an interface with a detonating explosive yields a data point on the reflected shock Hugoniot of the explosive reaction products centered at the Chapman‐Jouguet state or on the isentrope below this state. Such measurements have been made, using various inert materials, for a range of shock impedances which yields pressures in the explosive reaction products from 515 000 bars down to 571 bars. The data fit a polytropic equation of state (P∕ργ = const. for the isentrope) with γ = 2.77.

A Detonation‐Product Equation of State Obtained from Hydrodynamic Data

W. Fickett and W. W. Wood

Phys. Fluids 1, 528 (1958); http://dx.doi.org/10.1063/1.1724377 (7 pages) | Cited 11 times

Online Publication Date: 22 November 2004

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A recent experimental measurement of the Chapman‐Jouguet isentrope of the solid explosive Composition B, together with the experimental detonation velocity vs initial density curve, give considerable information about the equation of state of the detonation products. With the aid of some thermodynamic assumptions, a simple explicit form is obtained for the energy as a function of pressure and volume.

Explosively Induced Nonuniform Oblique Shocks

John O. Erkman

Phys. Fluids 1, 535 (1958); http://dx.doi.org/10.1063/1.1724378 (6 pages) | Cited 7 times

Online Publication Date: 22 November 2004

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At the high pressures induced by explosive attack, metals are assumed to behave like nonviscous, non‐heat‐conducting fluids. Within these assumptions, intensity and duration of explosively induced nonuniform oblique shocks are calculated by the method of characteristics for aluminum and copper in those cases involving supersonic flow both in the metal and in the explosive gas. Flow in both metal and explosive product gas is assumed to be isentropic even in the presence of shock waves. When a three‐parameter equation of state is used for the gas, an arbitrary assumption must be made concerning the magnitude of one of these parameters, since pressure, density, and sound speed are known only for the Chapman‐Jouguet point for the explosive gas. Reasonableness of this assumption is tested by comparing the results of the calculation with experiment. Results for oblique shocks confirm the results obtained previously for plane shocks in regard to the equation of state of the gas.

Spray Combustion and Atomization

F. A. Williams

Phys. Fluids 1, 541 (1958); http://dx.doi.org/10.1063/1.1724379 (5 pages) | Cited 57 times

Online Publication Date: 22 November 2004

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A statistical formalism for describing the behavior of sprays is presented, which includes the effects of droplet growth, the formation of new droplets, collisions, and aerodynamic forces. Criteria for the efficiency of impinging jet atomization are developed. It is shown that if the incident jets have a size distribution of a generalized Rosin‐Rammler type, then the resulting spray belongs to the same class of distributions. The size history of evaporating sprays is also obtained from the theory. A spray combustion analysis given by Probert is extended to include more general size distributions and the effects of droplet interactions and the relative motion of the droplets and the fluid. It is shown that the over‐all spray evaporation rate is largest for uniform sprays.
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On the Existence of Recombination Shocks

Saul Feldman

Phys. Fluids 1, 546 (1958); http://dx.doi.org/10.1063/1.1724380 (1 page) | Cited 5 times

Online Publication Date: 22 November 2004

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Abstract Unavailable

Laminar Boundary Layer Development behind Shock Waves in Argon

Russell E. Duff

Phys. Fluids 1, 546 (1958); http://dx.doi.org/10.1063/1.1724381 (2 pages)

Online Publication Date: 22 November 2004

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Abstract Unavailable

Electron Acceleration against an Opposing Field in a Vacuum Electromagnetic Discharge

Joseph Slepian

Phys. Fluids 1, 547 (1958); http://dx.doi.org/10.1063/1.1724382 (2 pages) | Cited 1 time

Online Publication Date: 22 November 2004

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Abstract Unavailable
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Errata: High‐Altitude Atmospheric Density

Theodore E. Sterne

Phys. Fluids 1, 548 (1958); http://dx.doi.org/10.1063/1.1724383 (1 page)

Online Publication Date: 22 November 2004

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Abstract Unavailable
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