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Jul 1974

Volume 17, Issue 7, pp. 1353-1479

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Further applications of hot‐wire anemometry to turbulence measurements in helium‐air mixtures

Richard A. Stanford and Paul A. Libby

Phys. Fluids 17, 1353 (1974); http://dx.doi.org/10.1063/1.1694895 (9 pages) | Cited 19 times

Online Publication Date: 11 August 2003

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The extension of the Way‐Libby probe to permit the measurement of two velocity components u and υ in the usual notation, and the mass fraction c of helium in turbulent flows involving helium‐air mixtures is described. The accuracy of the technique, especially the sensitivity to flow deflection, is carefully assessed. Interesting results obtained in applying the new probe show, inter alia, highly skewed probability density functions of helium concentration in an internal flow.

First‐order reactant in homogeneous turbulence before the final period of decay

Prem Kumar and S. R. Patel

Phys. Fluids 17, 1362 (1974); http://dx.doi.org/10.1063/1.1694896 (7 pages) | Cited 1 time

Online Publication Date: 11 August 2003

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Following Deissler's approach the concentration fluctuation of a dilute contaminant undergoing a first‐order chemical reaction is studied. Two‐, three‐, and four‐point correlation equations have been obtained and to make the set of equations determinate, the terms containing quintuple correlations are neglected in comparison to those containing lower‐order correlation terms. The solution obtained gives the state of concentration fluctuation in a homogeneous turbulence between its initial and final periods.

Convective rolls driven by internal heat sources

R. S. Peckover and I. H. Hutchinson

Phys. Fluids 17, 1369 (1974); http://dx.doi.org/10.1063/1.1694897 (3 pages) | Cited 4 times

Online Publication Date: 11 August 2003

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Two‐dimensional convection in a layer of volumetrically heated fluid confined between free horizontal boundaries has been studied using numerical experiments. The dependence on the appropriate modified Rayleigh number of the maximum horizontally averaged temperature and of the fraction of thermal flux emerging from the upper surface has been found for RaH  ≤  80 RaHC.

Inertial oscillations and multiple boundary layers in an unsteady rotating flow

Lokenath Debnath and Sukla Mukherjee

Phys. Fluids 17, 1372 (1974); http://dx.doi.org/10.1063/1.1694898 (4 pages) | Cited 5 times

Online Publication Date: 11 August 2003

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An asymptotic analysis is made of the unsteady boundary layer flow generated impulsively in an incompressible homogeneous viscous fluid bounded by an infinite porous plate with uniform suction or blowing to describe the manner of the transient approach to the ultimate steady state. It is shown that the initial motion for small times describes the general features of the unsteady boundary‐layer flow and consists of three boundary layers on the plate which are unaffected by rotation. In subsequent large times, the effect of rotation manifests itself through inertial oscillations of frequency 2Ω and the generation of diffused waves propagating outward from the plate with velocity 2(Ων)1/2a1. It is found that the final steady boundary layers are established in a dimensional time (4/Ω) (S4/4E2 + 4)−1/2 which decreases with an increase in the suction parameter. Several limiting cases of interest are recovered from this analysis.

Thermal force on aerosol particles

C. Y. Cha and B. J. McCoy

Phys. Fluids 17, 1376 (1974); http://dx.doi.org/10.1063/1.1694899 (5 pages) | Cited 7 times

Online Publication Date: 11 August 2003

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With a method previously applied to thermal transpiration and planar radiometric force, the force on a spherical aerosol particle in a gas which sustains a temperature gradient is analyzed. Expressions for thermal force and thermal velocity span all values of the particle Knudsen number and show the effect of imperfect accommodation. The results are compared with other theories and with experimental data.

Laminar boundary layer over a body of revolution at extremely high incidence

K. C. Wang

Phys. Fluids 17, 1381 (1974); http://dx.doi.org/10.1063/1.1694900 (5 pages) | Cited 5 times

Online Publication Date: 11 August 2003

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Results of exact, full three‐dimensional solutions of the incompressible laminar boundary layer over a prolate spheroid at an extremely high incidence are presented. This extremely high incidence problem is characterized by features reflecting the predominance of the circumferential flow over the meridional flow and, more importantly, by a change of separation pattern from an open type to a closed type. These features include much larger circumferential skin friction than meridional skin friction and that the limiting streamlines are more closely oriented along the parallels.

Effects of nonadiabatic transitions on invariants of the motion

R. E. Aamodt and E. F. Jaeger

Phys. Fluids 17, 1386 (1974); http://dx.doi.org/10.1063/1.1694901 (5 pages) | Cited 9 times

Online Publication Date: 11 August 2003

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A computer study is made of the change in adiabatic invariant for a plane pendulum when a slow variation in the pendulum length forces the pendulum to change from circularly rotating motion to an oscillating state. The numerical results are shown to be in good agreement with a simply derived analytic expression which itself is generalizable to calculations of nonadiabatic transitions in other problems.

Stability of filamentary structures

Ernest Valeo

Phys. Fluids 17, 1391 (1974); http://dx.doi.org/10.1063/1.1694902 (3 pages) | Cited 32 times

Online Publication Date: 11 August 2003

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Isolated, one‐dimensional channels of electromagnetic radiation in a plasma are shown to be unstable to bending perturbations. Let l be the wave vector of the perturbation along the channel, k be that of the radiation, and C8 be the sound speed. Then, the growth rate γ  ∼  lC8 for l/k ≪ 1.

Influence of ion tail formation and ion resonance broadening on the dynamical behavior of a current‐carrying plasma

M. Z. Caponi and R. C. Davidson

Phys. Fluids 17, 1394 (1974); http://dx.doi.org/10.1063/1.1694903 (5 pages) | Cited 14 times

Online Publication Date: 11 August 2003

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The influence of ion tail formation on the dynamical behavior and anomalous resistivity of a current‐carrying plasma is studied within the context of a quasilinear model that includes ion resonance broadening as a possible quasi‐saturation mechanism for the ion acoustic instability. Although the detailed time development of macroscopic plasma parameters depends on nh/ni (the ratio of ion tail density to total ion density), the value of anomalous resistivity at quasi‐saturation is found to be relatively insensitive to the formation of a low‐density high‐energy ion tail. For example, if nh/ni  =  0.2, the anomalous resistivity is lowered by 15% relative to its value in the absence of an ion tail.
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Plasma heating by spatial resonance of Alfvén wave

Liu Chen and Akira Hasegawa

Phys. Fluids 17, 1399 (1974); http://dx.doi.org/10.1063/1.1694904 (5 pages) | Cited 194 times

Online Publication Date: 11 August 2003

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Heating of a collisionless plasma by utilizing the spatial resonance of shear Alfvén waves is proposed and application to toroidal plasmas is discussed. The resonance exists due to the nonuniform Alfvén speed. This heating scheme is analyzed in one dimension including the effects of a shear magnetic field and plasma compressibility. For plasmas with smooth nonuniformities (∣ k⊥l ∣ ≫ 1, k⊥ is the wavenumber prependicular to the ambient magnetic field and the nonuniformity direction, and l is the scale length of the nonuniformity), the energy absorbed per unit surface area per driving cycle is [b02(μ0k⊥)−1]. Here, b0 is the flux density of the driving magnetic field evaluated at the resonant point. With sharp nonuniformities (∣ k⊥l ∣ ≪ 1), absorption is large if the surface eigenmode is excited. The corresponding value is [b02(μ0k⊥)−1(k⊥l)−1]. Otherwise, it is [b02(μ0k⊥)−1(k⊥l)].

Stability test for strongly inhomogenous plasmas through Nyquist diagrams

H. W. Bloomberg

Phys. Fluids 17, 1404 (1974); http://dx.doi.org/10.1063/1.1694905 (6 pages) | Cited 3 times

Online Publication Date: 11 August 2003

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The stability of inhomogeneous plasma equilibria in the water bag approximation is discussed by means of Nyquist diagrams. A function suitable for a Nyquist diagram is constructed, and the method is applied to demonstrate the instability of the electron sheath configuration. The behavior of the Nyquist diagram shows directly that instabilities occur near multiples of the bounce frequency of the innermost sheath contour in phase space.

Microwave emissions from turbulent plasmas generated in a fast, high voltage theta pinch

C. Chin‐Fatt

Phys. Fluids 17, 1410 (1974); http://dx.doi.org/10.1063/1.1694906 (3 pages) | Cited 6 times

Online Publication Date: 11 August 2003

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Intense, and evidently nonthermal, bremsstrahlung has been observed from turbulent helium plasmas that were generated in a large, high voltage theta pinch operated in two different experimental configurations. The emissions were in the wavelength range 1 mm ≲ λ ≲ 16 mm, and are identified as collective bremsstrahlung, originating from the interaction of longitudinal modes of the turbulent plasmas by wave‐wave scattering.

Parametric instabilities induced by the coupling of high and low frequency plasma modes

Wallace M. Manheimer and Edward Ott

Phys. Fluids 17, 1413 (1974); http://dx.doi.org/10.1063/1.1694907 (9 pages) | Cited 92 times

Online Publication Date: 11 August 2003

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A general dispersion relation is derived for parametric instabilities caused by a large amplitude pump wave which couples high and low frequency modes of a magnetized plasma. The nonlinear effects coupling the high and low frequency waves are: (1) the low‐frequency pondermotive force due to the coupling of the pump with the high frequency perturbations, and (2) the high frequency nonlinear source current density produced by coupling of the pump with the low frequency perturbations. The dispersion relation contains decay instabilities, purely growing instabilities, modulational instabilities, self‐focusing and nonlinear Landau damping. As examples the dispersion relation is applied to self‐focusing, magnetosonic decay and purely growing instabilities, whistler decay and nonlinear Landau dumping of electron plasma waves and transverse electromagnetic waves.

Experimental determination of the rate of slowing of fast ions in a dense plasma in a magnetic field

R. J. Burke and R. F. Post

Phys. Fluids 17, 1422 (1974); http://dx.doi.org/10.1063/1.1694908 (6 pages) | Cited 6 times

Online Publication Date: 11 August 2003

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An experiment to measure the energy loss rate of fast ions moving in a dense magnetized plasma is described. In the experiment, proton and deuteron test particles lose energy predominantly to plasma electrons of comparable thermal speed. Interaction of the test particles with the plasma is limited to a defined path between two charge changing reactions. The time of interaction is determined from the cyclotron frequency of the test ions and the entrance and exit angles of the test particles. The observed energy losses are compared to the Spitzer formula and to more recent theoretical calculations. It is concluded that the Spitzer formula underestimates the energy loss by about a factor of 2; the disagreement with the more recent calculations amounts to about a factor of 3. It is proposed that the observed discrepancies may arise from cooperative particle‐wave energy transport effects in the magnetized plasma.

Theory and simulation of higher‐order cyclotron damping

S. J. Gitomer and D. W. Forslund

Phys. Fluids 17, 1428 (1974); http://dx.doi.org/10.1063/1.1694909 (4 pages) | Cited 1 time

Online Publication Date: 11 August 2003

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The infinity of roots for real wavenumber k and complex frequency ω of the dispersion relation for transverse electromagnetic waves propagating in a thermal plasma parallel to an applied magnetic field B are studied theoretically and observed in numerical simulations. In addition to the usual weakly damped whistler and ion cyclotron roots, there are infinitely many more heavily damped electron (ion) roots characterized by real frequency near the gyrofrequency and damping rate proportional to the wavenumber. The electron modes have been observed in a thermal electromagnetic numerical simulation plasma and their dispersion agrees well with finite temperature linear theory. These modes may be observable experimentally.

Theory of parametric instability near the lower‐hybrid frequency

Miklos Porkolab

Phys. Fluids 17, 1432 (1974); http://dx.doi.org/10.1063/1.1694910 (11 pages) | Cited 121 times

Online Publication Date: 11 August 2003

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The dispersion relation for parametric instabilities near the lower‐hybrid frequency is derived and analyzed. It is found that for propagation angles cos2θ(mi/me) math 1 resonant decay into ion acoustic (ion‐cyclotron) waves does not occur; rather, decay into nonresonant quasi‐ion modes and lower‐hybrid waves occurs. The driving mechanism for this instability is shown to be analogous to nonlinear Landau damping in perturbation theory. The large amplitude dispersion relation is analyzed numerically for a number of typical experimental regimes, and growth rates and thresholds are obtained for both the purely growing mode and the newly found quasi‐ion modes.

Experimental observations of the parametric decay instability

Edward J. Yadlowsky and Paul D. Goldan

Phys. Fluids 17, 1443 (1974); http://dx.doi.org/10.1063/1.1694911 (6 pages) | Cited 5 times

Online Publication Date: 11 August 2003

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The parametric decay instability has been excited in a low‐pressure argon plasma characterized by ne  ∼  5 × 108 cm−3, Te  ∼  2 eV, Ti  ∼  0.2 eV. An electron beam probe has been used to measure the frequency and spatial distribution of the fields associated with the pump wave and excited Langmuir and ion waves. The wavenumber matching (K0  =  Ke + Ki) and frequency matching (ω0  =  ωe + ωi) conditions are well satisfied. If particle losses in the finite geometry are taken into account, the minimum threshold pump electric field is in good quantative agreement with the theoretical prediction ϵ0Ec2/nkT  =  64math/9 × γiγe2/ωi2ωe in the limit of γe > ωi ≫ γi.

Spectra and growth rates of a generalized screw pinch

George Vahala

Phys. Fluids 17, 1449 (1974); http://dx.doi.org/10.1063/1.1694912 (12 pages) | Cited 6 times

Online Publication Date: 11 August 2003

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The theory of Weitzner for the bumpy θ pinch is extended to the case of a generalized screw pinch in which the equilibrium magnetic field is B  =  (ϵBr, ϵBθ, Bz). ϵ represents the slow periodic z variation of the axisymmetric equilibrium and the stability relative to their r variation. Perturbation expansions in ϵ and in the bumpiness of the flux surfaces are performed on the linearized equations of ideal magnetohydrodynamics. From the theory of Grad there should be four stable continua, two of which are found for modes with ω2  =  O (ϵ2), while for the transverse modes a generalized Suydam criterion for local instability is derived. The (global) growth rates of the most unstable transverse modes are computed numerically for various Bθ and the results are compared to those of the bumpy θ pinch (where Bθ  ≡  0)) as well as to the ordinary screw pinch (where Br  ≡  0).
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Bubble growth in dilute polymer solutions

R. Y. Ting and A. T. Ellis

Phys. Fluids 17, 1461 (1974); http://dx.doi.org/10.1063/1.1694913 (2 pages) | Cited 13 times

Online Publication Date: 11 August 2003

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Under a free‐fall condition, the growth of individual gas bubbles in dilute polymer solutions was observed experimentally. A retardation in the growth rate was found as compared with the case in water.

Flow due to an impulsive rotation of infinite disk

M. Katagiri

Phys. Fluids 17, 1463 (1974); http://dx.doi.org/10.1063/1.1694914 (2 pages) | Cited 2 times

Online Publication Date: 11 August 2003

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Numerical solutions for the extended von Kármán rotating disk problem to the case of impulsive rotation from rest are given and used to discuss the ultimate approach to the steady state.

Laminar flow in a rectangular duct bounded by a porous wall

E. M. Sparrow, Gordon S. Beavers, and B. A. Masha

Phys. Fluids 17, 1465 (1974); http://dx.doi.org/10.1063/1.1694915 (3 pages) | Cited 1 time

Online Publication Date: 11 August 2003

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Velocity field solutions for finite aspect ratio rectangular ducts with one prous bounding wall were obtained and employed to determine friction factors. Comparisons were made with results for the parallel plate channel in order to illuminate published interpretations of experimental data.

Stokes' paradox in second‐order fluids

R. R. Huilgol and L. N. Tao

Phys. Fluids 17, 1468 (1974); http://dx.doi.org/10.1063/1.1694916 (1 page)

Online Publication Date: 11 August 2003

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It is shown that Stokes' paradox for incompressible Newtonian fluids also arises in the two‐dimensional creeping flows of incompressible second‐order fluids. The velocity field in both fluids is again identical for the flow past two or more cylinders, provided the geometries in both flows are identical.

Drop spectrometry of laminar and turbulent jets

Pierre Lafrance, G. Aiello, R. C. Ritter, and J. S. Trefil

Phys. Fluids 17, 1469 (1974); http://dx.doi.org/10.1063/1.1694917 (2 pages) | Cited 7 times

Online Publication Date: 11 August 2003

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Drops resulting from the breakup of laminar and turbulent jets are electro‐optically measured and drop size histograms are electronically generated. Having large numbers of drops and good statistics, they permit quantitative analysis to an extent not feasible with photographic methods.

Continuous spectra of a cylindrical magnetohydrodynamic equilibrium

K. Appert, R. Gruber, and J. Vaclavik

Phys. Fluids 17, 1471 (1974); http://dx.doi.org/10.1063/1.1694918 (2 pages) | Cited 130 times

Online Publication Date: 11 August 2003

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It is shown that, for a cylindrical equilibrium of a perfectly conducting plasma, the magnetohydrodynamic spectrum contains at most two continua.

Two‐dimensional growth of a bleaching wave

Ronald G. Rehm

Phys. Fluids 17, 1473 (1974); http://dx.doi.org/10.1063/1.1694919 (3 pages) | Cited 2 times

Online Publication Date: 11 August 2003

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An analytical solution is presented which describes the axisymmetric growth of a high‐temperature region heated by laser radiation, known as a bleaching wave. Constant‐temperature profiles for the wave are shown for ruby laser radiation and for CO2 laser radiation incident upon a plasma.
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