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Jan 1985

Volume 28, Issue 1, pp. 1-438

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The 1984 François Naftali Frenkiel Award for Fluid Mechanics

Phys. Fluids 28, 1 (1985); http://dx.doi.org/10.1063/1.3480118 (1 page)

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Abstract Unavailable

The rewetting of an inclined solid surface by a liquid

N. Silvi and E. B. Dussan V

Phys. Fluids 28, 5 (1985); http://dx.doi.org/10.1063/1.865410 (3 pages) | Cited 62 times

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When a thin layer of liquid flowing down an inclined solid surface becomes unstable, a dry region may appear. It is of general engineering interest to identify the parameters which control the ability of the liquid to rewet the solid so that a uniform film of liquid can be reestablished. The role played by the contact angle in the rewetting process is investigated by performing a specific set of experiments of the type introduced by Huppert [(Nature 300, 427 (1982)]. It is found that a small static advancing contact angle promotes rewetting, while a large value of the angle does not.
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68.03.Cd Surface tension and related phenomena
81.15.Lm Liquid phase epitaxy; deposition from liquid phases (melts, solutions, and surface layers on liquids)
68.15.+e Liquid thin films
47.15.-x Laminar flows

Vortex pair annihilation in Taylor wavy‐vortex flow

Gerald L. Crawford, Kwangjai Park, and Russell J. Donnelly

Phys. Fluids 28, 7 (1985); http://dx.doi.org/10.1063/1.865129 (3 pages) | Cited 5 times

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We have made precision measurements of the vortex pair size and wavy mode amplitude of vortices in wavy Taylor–Couette vortex flow. These results are compared to a model advanced by Park and Crawford to account for expulsion of vortex pairs as the Reynolds number is increased in the wavy‐vortex regime.
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47.20.-k Flow instabilities

Intermittency and attractor size in isotropic turbulence

Robert H. Kraichnan

Phys. Fluids 28, 10 (1985); http://dx.doi.org/10.1063/1.865189 (2 pages) | Cited 8 times

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Qualitative arguments suggest that the Kolmogorov 1941 (K41) inertial range for space dimensionality D3 corresponds to a maximum attractor size if compared with alternative inertial ranges in which intermittency increases as a power of wavenumber. Therefore upper bounds on attractor size consistent with K41 do not either rule out or imply intermittency corrections to the −5/3 law. In contrast, the K41 inertial range corresponds to minimum attractor size if D>4.
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47.27.Gs Isotropic turbulence; homogeneous turbulence
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

The production of highly unidirectional lower‐hybrid waves

R. McWilliams, M. Okubo, R. C. Platt, and D. P. Sheehan

Phys. Fluids 28, 11 (1985); http://dx.doi.org/10.1063/1.865413 (3 pages) | Cited 2 times

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The development of a highly unidirectional lower‐hybrid wave source would improve the electron current drive efficiency in tokamaks. Lower‐hybrid waves launched from a phased wave array are shown to be reflected from a grid placed in a cold, low‐density plasma. The antenna–grid combination results in highly unidirectional lower‐hybrid waves.
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52.40.Fd Plasma interactions with antennas; plasma-filled waveguides
52.35.Hr Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)
52.50.Gj Plasma heating by particle beams

Anomalous losses from relativistic electron rings in decreasing toroidal fields

R. A. Meger, M. R. Parker, and H. H. Fleischmann

Phys. Fluids 28, 13 (1985); http://dx.doi.org/10.1063/1.865174 (4 pages)

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Anomalously enhanced fast‐electron losses are observed on relativistic E layers in the RECE‐Christa device when the applied toroidal magnetic field decreases to zero in times shorter than ring lifetime. These losses consistently occur in a certain region of the field‐reversal parameter and the ratio of applied toroidal to axial magnetic fields at the ring position. The critical parameter range is independent of the radial gradient of the applied mirror field, the background gas pressure, and the rate‐of‐decay of Bθ; however, it depends on the axial length of the rings, and there may be a threshold in dBθ/dt. The observed parameter dependence as well as the absence of any kink or tilt motions point to new orbital resonances as the cause of these losses.
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52.20.Dq Particle orbits
28.52.Av Theory, design, and computerized simulation
52.55.-s Magnetic confinement and equilibrium
52.75.Di Ion and plasma propulsion
52.27.Ny Relativistic plasmas

Inverse resonance absorption in an inhomogeneous magnetized plasma

H. C. Barr, T. J. M. Boyd, G. A. Gardner, and R. Rankin

Phys. Fluids 28, 16 (1985); http://dx.doi.org/10.1063/1.865177 (3 pages) | Cited 4 times

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The linear mode conversion of a plasma wave to a light wave in a magnetized plasma has been examined theoretically and by computer simulation. This conversion is the inverse of resonance absorption exhibiting an identical dependence on magnetic field and density scale length with an optimum conversion efficiency of approximately 60%. Radiation from this source may contribute to the harmonic spectra observed from laser‐irradiated plasmas.
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52.25.Os Emission, absorption, and scattering of electromagnetic radiation
52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
52.50.Jm Plasma production and heating by laser beams (laser-foil, laser-cluster, etc.)

Two‐dimensional ray‐trace calculations of thermal whole beam self‐focusing

Kent Estabrook, W. L. Kruer, and D. S. Bailey

Phys. Fluids 28, 19 (1985); http://dx.doi.org/10.1063/1.865180 (3 pages) | Cited 38 times

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Thermal self‐focusing of laser light may be significant when a plasma is irradiated with short‐wavelength laser light. Self‐focusing magnifies the light intensity which can increase absorption by plasma waves (producing hot electrons which may cause preheat), could increase scattering, and could be a perturbation source for the Rayleigh–Taylor instability. We use two‐dimensional hydrodynamic simulations to characterize thermal self‐focusing for parameters of interest to laser fusion applications, and present a simple model. A diverging beam is shown to reduce the self‐focusing.
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52.50.Jm Plasma production and heating by laser beams (laser-foil, laser-cluster, etc.)
52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma
52.65.-y Plasma simulation

The separation of viscous jets

R. I. Tanner, H. Lam, and M. B. Bush

Phys. Fluids 28, 23 (1985); http://dx.doi.org/10.1063/1.865185 (3 pages) | Cited 3 times

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A viscous jet is not usually observed to separate from a sharp edge in the manner expected theoretically. In the present paper the separation of a creeping jet emerging from a tube with a rounded exit is considered. As a separation criterion, in the absence of surface tension, we propose that the traction normal to the nozzle surface drops to zero at the separation point. Boundary‐element calculations then show a behavior that agrees with experimental data and with previous finite‐element computations. They also permit the Michael condition to be observed at separation, so that the discrepancy between finite‐element calculations and theory is removed.
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47.27.wg Turbulent jets

Fingering with miscible fluids in a Hele Shaw cell

Lincoln Paterson

Phys. Fluids 28, 26 (1985); http://dx.doi.org/10.1063/1.865195 (5 pages) | Cited 49 times

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Unstable, two‐fluid miscible displacements in a Hele Shaw cell of plate spacing b are analyzed by considering viscous dissipation of energy. A perturbation theory is presented that predicts the wavelength of fingers, λ, as λ≊4b. Experiments with a circular Hele Shaw cell are shown to support this result. In a porous medium, the analogous fingers are demonstrated to be the size of a pore, which is much larger than the corresponding fingers in the analogous Hele Shaw cell. These results provide the lower limits of finger wavelength for the theories of Saffman and Taylor, and Chuoke, van Meurs, and van der Poel.
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47.55.Kf Particle-laden flows
47.56.+r Flows through porous media

The stability of buoyancy‐driven rolls aligned with a shear flow when the temperature gradient is nonlinear

A. D. W. Jones

Phys. Fluids 28, 31 (1985); http://dx.doi.org/10.1063/1.865150 (6 pages) | Cited 4 times

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The buoyancy driven instability of rolls aligned with a shear flow of a Boussinesq fluid is considered. It is supposed that the temperature varies not only with height but also in the direction of the flow thus allowing the vertical temperature profile to be nonlinear. Conditions are derived for the neglect of the horizontal temperature gradient in the perturbation equations. These are (i) that the vertical temperature gradient varies sufficiently slowly in the direction of the flow and (ii) that Pr h/d≫1, where Pr is the Prandtl number and h and d are the length scales for the vertical variation of velocity and temperature, respectively. Under these conditions, stability is governed by the equation for Bénard convection. The principle of exchange of stabilities is proved for an arbitrary temperature gradient profile, with isothermal, free‐surface boundary conditions, and the equation is solved numerically and by an asymptotic method for a model thermal boundary layer. The analysis is then applied to an experimental study of spoke patterns, observed in the growth of electronic materials. This work also indicates that a previous investigation of the stability of stratified shear flow has a restricted range of validity.
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47.20.-k Flow instabilities

Nonlinear instability at the interface between two viscous fluids

A. P. Hooper and R. Grimshaw

Phys. Fluids 28, 37 (1985); http://dx.doi.org/10.1063/1.865160 (9 pages) | Cited 71 times

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Co‐current flow of two viscous fluids in a channel is linearly unstable to long wavelength disturbances. The weakly nonlinear evolution of this instability is examined. It is shown that, because of surface tension and nonlinear effects, the interface can either return to its original undisturbed state or evolve to some finite amplitude steady state.
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47.20.-k Flow instabilities
47.55.Hd Stratified flows

Capillary‐gravity waves generated in a viscous fluid

A. K. Pramanik and S. R. Majumdar

Phys. Fluids 28, 46 (1985); http://dx.doi.org/10.1063/1.865124 (6 pages)

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The linearized initial‐value problem of capillary‐gravity waves generated by a moving oscillatory surface pressure distribution in a viscous incompressible fluid of infinite depth is solved. It is found that viscosity apart from introducing a damping factor into the amplitude of each wave plays an important role in the critical case. While the solution in the inviscid fluid becomes singular for certain values of the parameters of the problem, the solution in viscous fluid remains valid for all values of the parameters, though the amplitudes are relatively large in the critical case.
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47.32.Ef Rotating and swirling flows

Turbulence structures associated with the bursting event

John Kim

Phys. Fluids 28, 52 (1985); http://dx.doi.org/10.1063/1.865401 (7 pages) | Cited 25 times

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Turbulence structures in a wall‐bounded shear layer during the bursting event detected by a conditional sampling technique are investigated using data obtained from large‐eddy simulation of turbulent channel flow. Streamlines are constructed from the ensemble‐averaged velocity field to illustrate the flow patterns associated with the bursting event. They exhibit the ‘‘splatting’’ motions during the sweep event and the existence of a pair of counterrotating streamwise vortices during the ejection process.
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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)

A statistically derived system of equations for turbulent shear flows

Akira Yoshizawa

Phys. Fluids 28, 59 (1985); http://dx.doi.org/10.1063/1.865125 (5 pages) | Cited 21 times

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A system of equations governing turbulent shear flows is discussed. In this system the mean velocity, the mean pressure, and four statistical quantities related to the fluctuating field constitute the fundamental quantities for shear flows. A closed system of equations for these quantities is derived statistically with the aid of the two‐scale direct‐interaction approximation, where the Reynolds stress is expressed in the form of the eddy‐viscosity representation. On this basis, some turbulence models are discussed from the statistical viewpoint.
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47.27.nb Boundary layer turbulence

A consistency condition for Reynolds stress closures

Sanjiva K. Lele

Phys. Fluids 28, 64 (1985); http://dx.doi.org/10.1063/1.865126 (5 pages) | Cited 4 times

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A new consistency condition is derived for the Reynolds stress turbulent closures. Recommended values of model constants used with the k‐ϵ model and with various Reynolds stress closures do not satisfy this condition exactly. It is shown that a slight adjustment of certain computer‐optimized constants would make some of these models internally consistent.
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47.27.T- Turbulent transport processes
47.27.Gs Isotropic turbulence; homogeneous turbulence

Modeling the pressure gradient–velocity correlation of turbulence

Charles G. Speziale

Phys. Fluids 28, 69 (1985); http://dx.doi.org/10.1063/1.865127 (3 pages) | Cited 11 times

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The modeling of the pressure gradient–velocity correlation of turbulence is considered. Two distinctly different approaches have been proposed in the turbulence literature: one in which the pressure gradient–velocity correlation is decomposed into a pressure‐strain correlation and a pressure‐diffusion correlation, and another in which the pressure gradient–velocity correlation is split into its deviatoric and isotropic parts. By examining the limit of two‐dimensional turbulence, it is demonstrated that the models obtained from the former approach are inconsistent with the Navier–Stokes equations in a fundamental way, whereas the models obtained from the latter approach are not. Consequently, it appears that the direct modeling of the pressure gradient–velocity correlation in its deviatoric and isotropic parts should be favored. The implications that this result has on turbulence modeling are discussed briefly.
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47.27.Gs Isotropic turbulence; homogeneous turbulence

A model for the spectrum of passive scalars in an isotropic turbulence field

Richard J. Driscoll and Lawrence A. Kennedy

Phys. Fluids 28, 72 (1985); http://dx.doi.org/10.1063/1.865128 (9 pages) | Cited 9 times

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A simple model is developed for the wavenumber spectrum of the variance of a passive scalar quantity in an isotropic turbulence field. The model can define the spectral distributions at all wavenumbers as an arbitrary function of a scalar Reynolds number Reθ=R Reλ and the Schmidt number Sc=ν/D (where R=τθ/τe is the scalar/kinetic energy time scale ratio and Reλ=u′λ/ν is the turbulence Reynolds number). The model is compared with one‐dimensional spectral data over a range of Reynolds numbers and for Sc=0.7, 7, and 700; model and data are shown to be in reasonable agreement.
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47.27.Gs Isotropic turbulence; homogeneous turbulence

Effect of intake flow on ambient turbulence

Mahinder S. Uberoi and Randall T. Nishiyama

Phys. Fluids 28, 81 (1985); http://dx.doi.org/10.1063/1.865130 (9 pages)

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A small streamlined axisymmetric intake is placed at various locations on the axis of a large axisymmetric turbulent jet. The ratio of the mean velocity in the intake to that of the ambient fluid is varied from zero to thirteen. The effective diameter d∗ of the intake is determined by its physical size and the range of influence of the intake flow on the ambient jet fluid. Intensities of the components of turbulent velocity are measured in the ambient fluid and in and around the intake. In most cases the intake faced the jet. The ambient turbulence may be idealized as three mutually orthogonal linear vortex filaments of circular cross section and diameter S which is indicative of the scale of energy containing eddies. The vortex filaments deform as the flow is drawn into the intake. In the case d∗<S, only parts of vortex filaments of size d∗ enter the intake. The two effects are used to calculate the intensities of the components of turbulent velocity as a function of d∗/S and ratios of mean velocity and density in the intake to their respective values in the ambient fluid. The results agree with experiments within wide ranges of the parameters.
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47.27.nb Boundary layer turbulence
47.27.wg Turbulent jets

Cusp catastrophe in flow acoustics

Ingo Rehberg

Phys. Fluids 28, 90 (1985); http://dx.doi.org/10.1063/1.865131 (7 pages)

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The transonic flow in a tube following an abrupt enlargement of the cross section produces self‐induced flow oscillations which generate sound (whistler). The frequency of the oscillation is influenced by the tube length: increasing length leads to a frequency decrease, but only up to a critical length lc of the tube. If this length is further increased, the frequency will jump to higher values. This jump shows hysteresis: decreasing the tube length again leads to a jump to the lower frequency at a length lc1<lc. Having presented details of the above phenomenon, the two mathematical models are then presented, in which the transonic oscillator is represented by two simple nonlinear equations which behave harmonically, and the acoustic resonator, i.e., the tube, is represented by a term including a time lag. It is shown that the hysteresis vanishes for both the experiment and the model if the sound reflection at the end of the tube is decreased below a certain critical value. This behavior is one of the few reported examples of a cusp catastrophe in an oscillating system.
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47.40.Hg Transonic flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.20.-k Flow instabilities

Formation and damping of relativistic strong shocks in a Synge gas

A. Lanza, J. C. Miller, and S. Motta

Phys. Fluids 28, 97 (1985); http://dx.doi.org/10.1063/1.865132 (7 pages) | Cited 4 times

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Results are presented from a detailed study of the formation of strong relativistic shocks from simple waves in a fluid obeying the Synge equation of state for a relativistic particle gas. Subsequent damping is also followed, and the results are compared with those obtained previously for a model radiation‐dominated gas. In this paper, planar flow is considered and self‐gravity of the waves is neglected.
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47.75.+f Relativistic fluid dynamics
47.40.Nm Shock wave interactions and shock effects

A numerical study of nonlinear Alfvén waves and solitons

Steven R. Spangler, James P. Sheerin, and Gerald L. Payne

Phys. Fluids 28, 104 (1985); http://dx.doi.org/10.1063/1.865188 (6 pages) | Cited 25 times

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Finite‐amplitude Alfvén waves can be modeled by a nonlinear wave equation termed the derivative nonlinear Schrödinger equation. A computer program has been developed that solves the derivative nonlinear Schrödinger equation via the ‘‘split‐step’’ Fourier method. This program has been used to investigate a number of topics in the area of nonlinear Alfvén waves. When analytic envelope solitons are used as initial conditions, the wave packets propagate without distortion and with the expected speed–amplitude relation. When an arbitrary, amplitude‐modulated wave is used as an initial condition, the results depend strongly on the β of the plasma and the polarization of the wave. For a left circularly polarized wave in a β<1 plasma, or a right circularly polarized wave with β>1, a collapse instability has been observed in which the wave amplitude increases and modulation scale decreases. For other combinations of polarization and value of β, the wave packet tends to broaden, eliminating the initial modulation.
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52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
95.30.Qd Magnetohydrodynamics and plasmas

Single‐mode saturation of a linearly unstable plasma

C. Burnap, M. Miklavčič, B. L. Willis, and P. F. Zweifel

Phys. Fluids 28, 110 (1985); http://dx.doi.org/10.1063/1.865190 (6 pages) | Cited 13 times

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The nonlinear oscillations of an electron plasma described by the collisionless Vlasov equation are studied using a perturbation technique previously applied by Simon and Rosenbluth [Phys. Fluids 19, 1567 (1976)]. It is proved by a characteristic argument that the plasma is globally stable, so that Bogoliuboff’s method of ‘‘secular regularization’’ is applicable. Assuming the plasma is confined in a box, and that only the lowest mode is unstable, it is shown that the ‘‘eigenmode dominance’’ approximation of Simon and Rosenbluth fails to conserve energy, but that energy and momentum conservation can be regained by considering interaction between the discrete and continuum modes. A formula is derived for the amplitude and phase of the saturated nonlinear oscillations. In a subsidiary result, it is shown that nonlinear effects damp the steady‐state oscillations predicted by linearized theory for some stable plasmas.
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52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)

Efficiency of current drive by fast waves

Charles F. F. Karney and Nathaniel J. Fisch

Phys. Fluids 28, 116 (1985); http://dx.doi.org/10.1063/1.865191 (11 pages) | Cited 86 times

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The Rosenbluth form for the collision operator for a weakly relativistic plasma is derived. The formalism adopted by Antonsen and Chu can then be used to calculate the efficiency of current drive by fast waves in a relativistic plasma. Accurate numerical results and analytic asymptotic limits for the efficiencies are given.
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52.50.Gj Plasma heating by particle beams
52.20.Fs Electron collisions
52.27.Ny Relativistic plasmas

Electron‐cyclotron heating in the presence of a dc electric field in tokamak plasmas

R. L. Meyer, I. Fidone, G. Giruzzi, and G. Granata

Phys. Fluids 28, 127 (1985); http://dx.doi.org/10.1063/1.865192 (6 pages) | Cited 5 times

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The combined effects of the dc electric field and electron‐cyclotron wave absorption in tokamak plasmas are investigated. The case of the ordinary mode for nearly normal propagation from the low magnetic field side is studied by a two‐dimensional Fokker–Planck code. It is found that the small fraction of the wave energy that goes into the superthermal electrons enhances the effect of the continuous pushing of the tokamak electric field.
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52.50.Gj Plasma heating by particle beams
52.55.Fa Tokamaks, spherical tokamaks
52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma
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