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Dec 1984

Volume 27, Issue 12, pp. 2785-2975

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The moving contact line with a 180° advancing contact angle

C. G. Ngan and E. B. Dussan V

Phys. Fluids 27, 2785 (1984); http://dx.doi.org/10.1063/1.864591 (3 pages) | Cited 3 times

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A liquid spreading over a dry solid surface with a contact angle of 180° has always been regarded as a special case. It is commonly thought that this represents a unique situation in which a singularity does not arise in an analysis of the dynamics of the liquid when the usual hydrodynamic assumptions are made, i.e., when the liquid is Newtonian and incompressible and obeys the no‐slip boundary condition at the solid. In fact, there are strong indications that it is not a special case.
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81.15.Lm Liquid phase epitaxy; deposition from liquid phases (melts, solutions, and surface layers on liquids)
68.08.-p Liquid-solid interfaces
68.43.-h Chemisorption/physisorption: adsorbates on surfaces
47.90.+a Other topics in fluid dynamics (restricted to new topics in section 47)

A simple model for gas bubble drag reduction

Hartmut H. Legner

Phys. Fluids 27, 2788 (1984); http://dx.doi.org/10.1063/1.864592 (3 pages) | Cited 25 times

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A simple stress model has been developed to explain the observations of reduced drag when small gas bubbles are introduced into a turbulent boundary layer. The drag reduction is caused by a combination of density reduction and turbulence modification. The maximum reduction is obtained when the gas volume fraction approaches the bubble packing limit; the medium viscosity also increases markedly in this limit and becomes the important factor in restricting further reduction in drag. The derived analytical expression represents experimental data well.
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47.27.nb Boundary layer turbulence
47.55.Kf Particle-laden flows
46.35.+z Viscoelasticity, plasticity, viscoplasticity
83.60.Bc Linear viscoelasticity
83.60.Df Nonlinear viscoelasticity

Stabilization of the spheromak tilt instability

C. Litwin, R. N. Sudan, and A. D. Turnbull

Phys. Fluids 27, 2791 (1984); http://dx.doi.org/10.1063/1.864593 (3 pages) | Cited 11 times

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A stability criterion for the tilt mode of a spheromak‐ion ring hybrid configuration has been developed for the case where the ring current is small compared to the spheromak azimuthal current. It is shown that the stability is related to the distortion of the spheromak separatrix.
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52.55.Jd Magnetic mirrors, gas dynamic traps
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)

Onset of oscillations in Rayleigh–Bénard convection: Horizontally unbounded slab

Boyd F. Edwards and Alexander L. Fetter

Phys. Fluids 27, 2795 (1984); http://dx.doi.org/10.1063/1.864594 (8 pages) | Cited 6 times

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Rayleigh–Bénard convection in a laterally unbounded classical fluid layer with low Prandtl number P (ratio of kinematic viscosity to thermal diffusivity) is reexamined. An amplitude expansion with only a few normal modes yields lateral oscillations of the convective rolls, which are therefore only weakly nonlinear. For free boundary conditions, additional modes (absent for rigid boundaries) lead to long wavelength (‘‘hydrodynamic’’) oscillations, with explicit nonlinear distortions in the velocity and temperature fields. For oscillations with rigid boundaries, the finite critical wavenumbers are approximately independent of P for small P, and the calculated Rayleigh number, frequency, and wavenumber at onset agree well with observations in air. Discrepancies with experiments in dilute superfluid 3He–4He systems with small aspect ratios (ratio of horizontal to vertical dimensions) suggest that lateral boundaries or two‐fluid effects play an important role in these systems.
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47.20.-k Flow instabilities
47.27.T- Turbulent transport processes
67.60.Fp Bose-Fermi mixtures

On the excitation of nonlinear water waves by a moving pressure distribution oscillating at resonant frequency

T. R. Akylas

Phys. Fluids 27, 2803 (1984); http://dx.doi.org/10.1063/1.864595 (5 pages) | Cited 7 times

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A theoretical study is made of the free‐surface flow induced by a traveling oscillatory pressure distribution acting at the surface of water of finite depth. Depending on the relative values of the water depth and the frequency and speed of the applied pressure, the solution of the linearized water‐wave problem may be singular, owing to a resonance phenomenon. Through an asymptotic analysis, it is shown that, close to resonant conditions, the finite‐amplitude response is bounded, and it is governed by a forced nonlinear Schrödinger equation. It is deduced that, under certain circumstances, the generated wave disturbance may not reach a steady state; in particular, for deep water, a steady state is never attained.
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47.35.-i Hydrodynamic waves
47.20.-k Flow instabilities

An analysis of the stability of the compressible Ekman boundary layer

John R. Spall and Houston G. Wood

Phys. Fluids 27, 2808 (1984); http://dx.doi.org/10.1063/1.864596 (6 pages)

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The linear stability problem for the compressible Ekman boundary layer common to rotating fluids is formulated and the stability properties determined numerically. Three classes of unstable waves are identified (called class A, B, and C), their properties are described. The class C waves have only recently been reported in the literature and are present only in compressible Ekman boundary layers. Most of the calculations presented here are for uranium hexafluoride gas; however, critical Reynolds numbers are also computed for air and ammonia gas. Compressibility is generally found to decrease the critical Reynolds number for each class of wave. A comparison of results for the three different gases shows the stability to be largely unaffected by changes in the gas properties. Maximum growth rate calculations for each wave show the class A and B waves to be the dominant instabilities. OFF
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47.32.Ef Rotating and swirling flows
47.20.-k Flow instabilities
47.35.-i Hydrodynamic waves
51.90.+r Other topics in the physics of gases (restricted to new topics in section 51)

Approximate analysis for resonance of an incompressible shear layer plus edges

P. A. Durbin

Phys. Fluids 27, 2814 (1984); http://dx.doi.org/10.1063/1.864597 (5 pages) | Cited 1 time

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A method for approximately analyzing the feedback between downstream and upstream edges in incompressible shear flow is described. The shear flow is modeled by a vortex sheet. Equations for resonance eigenvalues are derived. After the reduction of growth rate by finite shear layer thickness is allowed for, agreement is found between calculated resonances and those that have been observed experimentally.
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47.27.nb Boundary layer turbulence
47.90.+a Other topics in fluid dynamics (restricted to new topics in section 47)

Lognormality of gradients of diffusive scalars in homogeneous, two‐dimensional mixing systems

Alan R. Kerstein and William T. Ashurst

Phys. Fluids 27, 2819 (1984); http://dx.doi.org/10.1063/1.864598 (9 pages) | Cited 16 times

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Kolmogorov’s third hypothesis, as extended by Gurvich and Yaglom, is found to be obeyed by a diffusive scalar for a class of homogeneous, two‐dimensional mixing models. The mixing models all involve the advection of fluid by discrete vortices distributed in a square region with periodic boundary conditions. By computer simulation, it is found that the squared gradient of a diffusive scalar so advected is lognormally distributed, obeys the predicted scaling when a spatial smoothing is applied, and exhibits a power‐law range in the spatial autocorrelation. In addition, it is found that the scaling property cuts off at the Batchelor length, as predicted by Gibson. Since the mixing models employed do not incorporate the dynamical features of high‐Reynolds‐number turbulence, these results suggest that scalar lognormality and associated scaling behavior may be more robust or persistent than the scaling laws of the flow field.
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47.27.T- Turbulent transport processes
47.10.-g General theory in fluid dynamics
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

Electrostatic structure of the rotational discontinuity II: Shock pair solutions

Dong‐Jian Wang and B. U. Ö. Sonnerup

Phys. Fluids 27, 2828 (1984); http://dx.doi.org/10.1063/1.864586 (7 pages) | Cited 4 times

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The structure of one‐dimensional rotational discontinuities in a collision‐free plasma is analyzed. The plasma consists of cold streaming ions, isothermal streaming electrons, and electrostatically trapped warm electrons or ions. Allowances for large deviations from charge neutrality are made. By properly adjusting the trapped particle population, the rotational discontinuity can acquire a width comparable to or greater than the ion inertial length. Its structure then consists of an approximately charge neutral region of helical magnetic field sandwiched between a reversible electrostatic shock pair in which large deviations from charge neutrality occur. The discontinuity has left‐hand (ion) polarization for positive potentials, ϕ>0, and right‐hand (electron) polarization for ϕ<0. The magnetic field magnitude is constant throughout the discontinuity and the plasma state is identical on its two sides.
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52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.30.-q Plasma dynamics and flow

Propagation and absorption of electromagnetic waves in fully relativistic plasmas

D. B. Batchelor, R. C. Goldfinger, and Harold Weitzner

Phys. Fluids 27, 2835 (1984); http://dx.doi.org/10.1063/1.864587 (12 pages) | Cited 44 times

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The propagation and absorption of electromagnetic waves in a relativistic Maxwellian plasma are investigated by solving the uniform plasma dispersion relation. Both the Hermitian and the anti‐Hermitian parts of the plasma conductivity tensor σ are calculated relativistically. The Bessel functions occurring in σ are not expanded, and many cyclotron harmonic terms are included at high temperatures. The dispersion relation is solved numerically for perpendicular propagation, k∥ =0, where the relativistic effects are maximum and are not masked by Doppler broadening, which has been more thoroughly investigated. It is found that relativistic broadening has a substantial effect on wave dispersion, shifting the extraordinary mode right‐hand cutoff and the upper‐hybrid resonance to higher magnetic field with increasing temperature. Above a critical temperature, the cutoff disappears entirely. There is a broad range of temperatures, 20 keV≤Te ≤500 keV, for which the wavenumber k⊥ differs significantly from both the cold‐plasma value and the vacuum value. This has important implications for ray tracing in relativistic plasmas. Wave damping rates are calculated and compared to results from a previous formulation using the Poynting theorem, in which only the Hermitian part of σ is calculated relativistically.
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52.25.Os Emission, absorption, and scattering of electromagnetic radiation
52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma

Transport theory: Microscopic reversibility and symmetry

K. Molvig and K. Hizanidis

Phys. Fluids 27, 2847 (1984); http://dx.doi.org/10.1063/1.864588 (12 pages) | Cited 12 times

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The general theory of Fokker–Planck equation symmetries and their relation to derived transport theory symmetries is developed. The property of microscopic reversibility implies a symmetry in the Fokker–Planck equation for processes obeying detailed balance. It is shown that this symmetry is not sufficient to guarantee Onsager reciprocity for the full matrix of transport coefficients. The general transport matrix has broken symmetry. A partial symmetry can be identified. The theory is compared to the different formulation given by Onsager.
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52.25.Fi Transport properties
52.25.Kn Thermodynamics of plasmas
52.55.Fa Tokamaks, spherical tokamaks
52.55.Hc Stellarators, torsatrons, heliacs, bumpy tori, and other toroidal confinement devices

Conductivity of weakly and highly ionized gases in quasistatic electric fields

Joseph A. Kunc

Phys. Fluids 27, 2859 (1984); http://dx.doi.org/10.1063/1.864589 (3 pages) | Cited 4 times

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Simple and accurate expressions for electric conductivity in steady‐state weakly and highly ionized plasmas are presented. These expressions give good agreement with exact ‘‘4×4 matrix formulation’’ numerical calculations. The plasmas are assumed to be isotropic, i.e., the applied magnetic field is neglected. The applied electric field is either static (dc) or of low frequency.
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52.25.Fi Transport properties
51.50.+v Electrical properties (ionization, breakdown, electron and ion mobility, etc.)

Analytical expressions for H+, H+2, and H+3 ion densities in a hydrogen glow discharge

Joseph A. Kunc and Martin A. Gundersen

Phys. Fluids 27, 2862 (1984); http://dx.doi.org/10.1063/1.864590 (6 pages) | Cited 3 times

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Simple analytical formulas for positive ion densities in high‐current, medium‐pressure (of order 1 mm Hg) steady‐state hydrogen discharges have been obtained. These plasmas have a medium to high degree of ionization (>10−4), electron temperature on the order of 1 eV, and are typical of those that occur in hydrogen thyratrons and glow discharge switches. It is found that the role of charge exchange (H++H2→H+2 +H) may be significant, and limits for the effect of this process in ion production are estimated.
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52.80.Hc Glow; corona
52.25.Kn Thermodynamics of plasmas

Parametric instabilities in the fast‐wave heating of tokamaks

V. K. Tripathi

Phys. Fluids 27, 2868 (1984); http://dx.doi.org/10.1063/1.864599 (6 pages) | Cited 7 times

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A high‐power whistler wave launched into a tokomak is susceptible to resonant decay into ion‐cyclotron and lower‐hybrid waves when the lower‐hybrid resonance layer ωlh=ω0 exists in the outer region of the plasma x2/a2≳0.6, where ω0 is the frequency of the whistler, ωlh is the lower‐hybrid frequency, x is the distance away from the center of the plasma, and a is the minor radius. For Princeton Large Torus parameters, this requires a line average density n≳6×1013 cm−3 when the whistler frequency ω0≂800 MHz and the threshold pump power for the onset of the instability is 100 kW. The threshold power is determined by the convection losses and it increases nonlinearly with the temperature and very rapidly with decreasing density. The parametric instability would tend to deposit the momentum and energy of the pump wave in the outer region of the plasma.
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52.55.Fa Tokamaks, spherical tokamaks
52.55.Hc Stellarators, torsatrons, heliacs, bumpy tori, and other toroidal confinement devices
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.50.Gj Plasma heating by particle beams
52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma

Limiter stabilization of high‐beta external kink‐tearing modes

J. K. Lee and N. Ohyabu

Phys. Fluids 27, 2874 (1984); http://dx.doi.org/10.1063/1.864600 (3 pages) | Cited 3 times

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The stabilizing effects of finite‐width poloidal limiters, toroidal limiters, and general mushroom limiters are examined for high‐beta finite resistivity tokamak plamas in free boundary. When the plasma pressure and resistivity are small, a poloidal limiter is effective in reducing the growth rate even with a small limiter size, while a toroidal limiter requires a large size for a comparable effect. As the plasma pressure or resistivity increases, a toroidal limiter becomes more effective in reducing the growth rate than a poloidal limiter of the same size. A small optimized mushroom limiter might have a stabilizing effect similar to a conducting shell.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.55.Fa Tokamaks, spherical tokamaks
52.55.Hc Stellarators, torsatrons, heliacs, bumpy tori, and other toroidal confinement devices
52.35.Bj Magnetohydrodynamic waves (e.g., Alfven waves)
52.65.-y Plasma simulation

Collisional tearing in field‐reversed configurations

A. B. Hassam

Phys. Fluids 27, 2877 (1984); http://dx.doi.org/10.1063/1.864601 (4 pages) | Cited 13 times

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It is shown by employing a more complete Ohm’s law that field‐reversed plasma configurations may magnetically tear at a rate proportional to η1/2, where η is the resistivity. Such a growth rate obtains if the current layer width is small enough and the plasma is not too collisional, the rate reverting to the usual η3/5 scaling otherwise. The present theory, however, assumes cold ions, an assumption that would have to be relaxed for most applications.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.55.Jd Magnetic mirrors, gas dynamic traps
52.35.Bj Magnetohydrodynamic waves (e.g., Alfven waves)

Current drive and helicity injection

T. H. Jensen and M. S. Chu

Phys. Fluids 27, 2881 (1984); http://dx.doi.org/10.1063/1.864602 (5 pages) | Cited 102 times

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Magnetic configurations with currents parallel to the magnetic field need means for current drive. The concepts of transport of helicity are found useful for considering methods for current drive. The paper describes a formalism for considering transport of helicity, methods of injection of helicity, and specific examples of arrangements for current drive.
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52.55.Dy General theory and basic studies of plasma lifetime, particle and heat loss, energy balance, field structure, etc.

A study of the stability of the Z pinch under fusion conditions using the Hall fluid model

M. Coppins, D. J. Bond, and M. G. Haines

Phys. Fluids 27, 2886 (1984); http://dx.doi.org/10.1063/1.864603 (4 pages) | Cited 25 times

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The Hall fluid model (a quasineutral two‐fluid model with Te=0) is used to investigate the effect of the Hall term on the m=0 instability in a pure Z pinch. The problem is treated numerically by a linearized initial value code. Two different equilibria are investigated. The growth rate of the fastest growing magnetohydrodynamic mode is increased for one equilibrium and reduced for the other by the inclusion of the Hall term, and in the second case new modes with high growth rates are found. The possibility of Hall term destabilization of MHD stable equilibria is suggested.
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52.55.Ez Theta pinch
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.35.Bj Magnetohydrodynamic waves (e.g., Alfven waves)

Ion end losses from an electrostatically plugged cusp

P. B. Parks and A. M. Sleeper

Phys. Fluids 27, 2890 (1984); http://dx.doi.org/10.1063/1.864604 (9 pages) | Cited 1 time

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A general expression for the particle end‐loss rate from a low‐beta cusp with confining electrostatic potentials is derived. The derived loss rate is a function of flux surface, reflecting the breakdown in adiabaticity and hence magnetic containment in the region near the separatrix. In the fully nonadiabatic region, the result reduces to the previously derived expression of Yushmanov. Moving away from the separatrix into the adiabatic region, the loss rate decreases monotonically to a level of about one third the rate of the nonadiabatic region. Our result for the loss rate in the adiabatic region is enhanced over magnetic square‐well estimates by a factor of three to four, which we attribute to geometrical effects owing to the curved magnetic field lines, in agreement with other calculations.
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52.55.Jd Magnetic mirrors, gas dynamic traps
52.58.-c Other confinement methods

Electron‐cyclotron heating in a pulsed mirror experiment

M. E. Mauel

Phys. Fluids 27, 2899 (1984); http://dx.doi.org/10.1063/1.864605 (13 pages) | Cited 30 times

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Experimental measurements of electron‐cyclotron resonance heating (ECRH) of a highly ionized plasma in mirror geometry is compared to a two‐dimensional, time‐dependent, Fokker–Planck simulation. Measurements of the absorption strength of the electrons and of the energy confinement of the ions helped to specify the parameters of the code. The electron energy distribution is measured with an end‐loss analyzer and a target x‐ray detector. These characterize a non‐Maxwellian distribution consisting of ‘‘passing’’ (10 eV<Te,p<30 eV), ‘‘warm’’ (50 eV<Te,w<300 eV), and ‘‘hot’’ (1.2 keV<Te,h<4.0 keV) electron populations. The temperature and fractional densities of the warm and hot populations depend on the absorbed power and total density. A similar distribution is calculated with the simulation program that reproduces the end‐loss and x‐ray signals. Both the experimental measurments and the simulation are described.
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52.50.Gj Plasma heating by particle beams
52.55.Jd Magnetic mirrors, gas dynamic traps
52.70.-m Plasma diagnostic techniques and instrumentation
52.65.-y Plasma simulation

Numerical study of the precessional instabilities in a symmetric tandem mirror with hot‐electron end cells

Kang Tsang, X. S. Lee, B. Hafizi, and T. M. Antonsen

Phys. Fluids 27, 2912 (1984); http://dx.doi.org/10.1063/1.864606 (6 pages) | Cited 1 time

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The axial eigenmode equation for a symmetric tandem mirror with hot electron end cells is solved numerically in a high‐beta long‐thin equilibrium. Stability of the precessional ballooning modes is studied in detail. It is found that stable regions in parameter space are severely restricted even for moderately long and dense center cell. OFF
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52.35.Bj Magnetohydrodynamic waves (e.g., Alfven waves)
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.55.Jd Magnetic mirrors, gas dynamic traps

Decay instability of an extraordinary em wave into electron Bernstein and electron‐acoustic waves in mirror plasmas

R. P. Sharma and A. Kumar

Phys. Fluids 27, 2918 (1984); http://dx.doi.org/10.1063/1.864607 (3 pages) | Cited 3 times

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The parametric decay instability of an extraordinary electromagnetic wave into electron Bernstein and electron‐acoustic waves in a plasma having ion temperature greater than electron temperature, is considered. Application of the present investigation to mirror devices has also been pointed out. For typical sets of parameters of the TMX‐U (tandem‐mirror) machine, the growth time of the instability comes out to be ≂0.07 μsec at a pump power flux of ≂10 W/cm2, and the threshold power at a few mW/cm2.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.55.Jd Magnetic mirrors, gas dynamic traps
52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma

Plasma current and conductivity effects on hose instability

Martin Lampe, William M. Sharp, Richard F. Hubbard, Edward P. Lee, and Richard J. Briggs

Phys. Fluids 27, 2921 (1984); http://dx.doi.org/10.1063/1.864608 (16 pages) | Cited 39 times

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Hose instability dispersion relations, which include a self‐consistent treatment of the spatial and temporal evolution of plasma conductivity and plasma current, are derived for a relativistic beam propagating in weakly ionized gas. A simplified conductivity model is used which neglects temperature dependence of the electron mobility. In some regimes the results are dramatically different from those found previously for a beam propagating in a fixed conductivity channel. For example, the hose growth rate is found to decrease with increasing current Ib for a beam propagating in initially neutral gas, even though the plasma return current fraction increases rapidly with Ib. As another example, it is found that an externally driven discharge current can completely eliminate hose instability in a fixed conductivity channel, but causes only a weak decrease in growth rate when the plasma conductivity is modeled self‐consistently. OFF
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.40.Mj Particle beam interactions in plasmas

Theory of the rippled field magnetron

C. L. Chang, Edward Ott, Thomas M. Antonsen, and Adam T. Drobot

Phys. Fluids 27, 2937 (1984); http://dx.doi.org/10.1063/1.864609 (11 pages) | Cited 14 times

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The rippled field magnetron, a device for the generation of high‐power, short‐wavelength electromagnetic radiation, is studied theoretically. This device features smooth conducting coaxial anode and cathode electrodes, an axial insulating magnetic field, and a periodic azimuthal transverse wiggler magnetic field. The analysis treats the equilibrium in the fluid limit, including self‐fields, and is fully self‐consistent. Unstable coupling and growth of the positive energy (transverse electric TE) and negative energy (transverse magnetic TM) waves is demonstrated.
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84.40.Fe Microwave tubes (e.g., klystrons, magnetrons, traveling-wave, backward-wave tubes, etc.)

Observation of the two‐dimensional structure of a stationary and transient double layer in current‐carrying magnetized plasma

H. Fujita, Shinya Yagura, and Keiji Matsuo

Phys. Fluids 27, 2948 (1984); http://dx.doi.org/10.1063/1.864610 (8 pages) | Cited 11 times

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Observation is made of the two‐dimensional structure of a stationary and transient double layer which was formed by a locally applied additional discharge in a magnetized plasma. The two‐dimensional double layer is V‐shaped. A very large negative potential dip of approximately 16 V [≂(3–5)Te/e] on the low potential tail of the layer is transiently created. The formation process of the layer and the dependence of the dip depth on the limiting current passing through the plasma are also discussed. The observed steady state is confirmed by an analysis. OFF OFF
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52.40.Kh Plasma sheaths
52.25.Mq Dielectric properties
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