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May 1988

Volume 31, Issue 5, pp. 955-1305

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Deformation of a free surface as a result of vortical flows

Grétar Tryggvason

Phys. Fluids 31, 955 (1988); http://dx.doi.org/10.1063/1.866713 (3 pages) | Cited 13 times

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The deformation of a free surface caused by the roll up of a vortex sheet below the surface is studied. The large amplitude motion depends on both the strength and depth of the vortex sheet. A distinction is made between three different scenarios of the free‐surface motion: a breaking wave, entrainment of air, and the generation of relatively short surface waves.
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47.15.ki Inviscid flows with vorticity
47.35.-i Hydrodynamic waves

Streak‐line motion during steady and unsteady axisymmetric vortex breakdown

G. P. Neitzel

Phys. Fluids 31, 958 (1988); http://dx.doi.org/10.1063/1.866714 (3 pages) | Cited 15 times

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Numerical calculations of vortex breakdown generated within a closed circular cylinder by rotation of one of the end walls have been performed. The solutions are used to compute steady streak‐line patterns for dye introduced both symmetrically and asymmetrically about the symmetry axis upstream of the breakdown bubble. Beginning from such a steady state, the end‐wall angular speed is impulsively increased and the asymmetric streak‐line pattern is observed during a portion of the subsequent period of unsteady flow.
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47.32.Ef Rotating and swirling flows

The nonlinear counterstreaming‐beam wakefield accelerator

Yiton T. Yan

Phys. Fluids 31, 960 (1988); http://dx.doi.org/10.1063/1.866715 (4 pages) | Cited 4 times

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Using a counterstreaming electron beam to support a nonlinear wakefield for particle acceleration is investigated theoretically. This scheme has the following advantages over the plasma wakefield accelerator (PWFA): (1) easier beam loading; (2) higher transformer ratio; and (3) easier beam‐pulse shaping. Additionally, the achievable accelerating gradient (GeV/m) is as large as that which can be obtained with a PWFA. A numerical comparison between this scheme and the PWFA is given.
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52.75.Di Ion and plasma propulsion
52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
52.27.Ny Relativistic plasmas

Anomalous diffusion in heterogeneous porous media

Donald L. Koch and John F. Brady

Phys. Fluids 31, 965 (1988); http://dx.doi.org/10.1063/1.866716 (9 pages) | Cited 75 times

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The dispersion of a passive tracer resulting from flow through heterogeneous porous media is studied. When the correlation length for the permeability fluctuations is finite, a normal diffusive process, with the mean‐square displacement of the tracer growing linearly with time, is obtained at long times. However, it is shown that, when the correlation length diverges, anomalous diffusion occurs in which the mean‐square displacement grows faster than linearly with time. The space–time evolution of the tracer’s concentration is calculated and shown to be universal—uniquely related to the covariance of the permeability field—in the anomalous regime.
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47.56.+r Flows through porous media
05.60.-k Transport processes
66.10.C- Diffusion and thermal diffusion

Joukovskii’s model for a rising bubble

Jean‐Marc Vanden‐Broeck

Phys. Fluids 31, 974 (1988); http://dx.doi.org/10.1063/1.866717 (4 pages) | Cited 4 times

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Joukovskii’s model [J. Russian Physico. Chem. Soc. 22, 19 (1891)] for a two‐dimensional bubble rising in an unbounded fluid is considered. This model approximates the wake behind the bubble by a region bounded by vertical walls. By using an inverse method, Joukovskii obtained an exact solution characterized by a Froude number F=U/(gL)1/2= (2π)−1/2. Here U is the velocity at which the bubble rises, g is the acceleration of gravity, and L is the distance between the vertical walls. It is shown numerically that Joukovskii’s solution is not unique. When surface tension is neglected there is a solution for each value of 0<F<Fc, where Fc ∼0.66. In addition there are solutions with a cusp at the apex of the bubble for F>Fc, and an isolated solution with a 120° at the apex for F=Fc. When surface tension is taken into account there is a discrete set of solutions. Each of these solutions corresponds to a different value of F. As the surface tension tends to zero, all these solutions approach a unique solution. The numerical results indicate that this limiting solution is Joukovskii’s exact solution.
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47.55.dp Cavitation and boiling
47.55.Kf Particle-laden flows

The calculation of some Batchelor flows: The Sadovskii vortex and rotational corner flow

D. W. Moore, P. G. Saffman, and S. Tanveer

Phys. Fluids 31, 978 (1988); http://dx.doi.org/10.1063/1.866718 (13 pages) | Cited 20 times

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Steady, inviscid, incompressible, two‐dimensional flows with vortex patches bounded by vortex sheets (Batchelor flows) are calculated numerically. Two particular cases are considered: the vortex on a plane wall (Sadovskii vortex) and the vortex in a right‐angled corner. Nonlinear integral equations are derived for the shape of the bounding vortex sheet which are solved numerically. Two different formulations are employed to check the results. Previous results by Sadovskii [Appl. Math. Mech. 35, 773 (1971)] and Chernyshenko (Royal Aircraft Establishment library translations Report No. 2133, 1983) for specific values of the parameters are confirmed. Only symmetrical solutions are found to exist.
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47.15.ki Inviscid flows with vorticity
47.32.Ef Rotating and swirling flows

Nonlinear vortex trail dynamics

Chjan C. Lim and Lawrence Sirovich

Phys. Fluids 31, 991 (1988); http://dx.doi.org/10.1063/1.866719 (8 pages) | Cited 1 time

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The nonlinear evolution of periodic disturbances on vortex trails is considered. In addition to following small initial perturbations, large amplitude initial disturbances of the vortex trails are also studied. It is shown that the equations support a rich variety of essentially nonlinear solutions including unbounded and quasisteady ones. These solutions are found to correspond to various modes of vortex clustering in the physical plane. At the close of the paper, comparisons of these results with recent numerical and experimental findings on the wakes behind stationary cylinders, and also transversely oscillating bluff objects, are made.
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47.32.Ef Rotating and swirling flows
47.35.-i Hydrodynamic waves

The absolute and convective nature of instability in two‐dimensional wakes at low Reynolds numbers

Peter A. Monkewitz

Phys. Fluids 31, 999 (1988); http://dx.doi.org/10.1063/1.866720 (8 pages) | Cited 93 times

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The linear parallel and incompressible stability of a family of bluff‐body wake profiles is studied at Reynolds numbers close to the onset of Kármán vortex shedding. The family of mean flow profiles allows for the variation of the wake depth as well as for a variable ratio of wake width to mixing layer thickness. The absolute or convective nature of the sinuous instability is determined as a function of the profile parameters and Reynolds number. A comparison of this survey with experimental data shows that in bluff‐body near wakes a region of local absolute instability begins to form at a Reynolds number of approximately one‐half the critical value for Kármán vortex shedding. Hence, at the onset of the global response (Kármán vortex shedding), a substantial region of local absolute instability already exists in the wake. This confirms the qualitative model prediction of Chomaz, Huerre, and Redekopp [submitted to Phys. Rev. Lett.] and also shows that the prediction of vortex shedding frequencies, when based on local stability properties alone, is somewhat arbitrary even at the critical Reynolds number.
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47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.27.W- Boundary-free shear flow turbulence
47.15.G- Low-Reynolds-number (creeping) flows

The Rayleigh–Taylor instability in ablatively accelerated targets with 1, 1/2 , and 1/4 μm laser light

Mark H. Emery, Jill P. Dahlburg, and John H. Gardner

Phys. Fluids 31, 1007 (1988); http://dx.doi.org/10.1063/1.866782 (10 pages) | Cited 23 times

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The results of a series of detailed numerical simulations of the Rayleigh–Taylor instability in laser ablatively accelerated targets are presented for a fairly wide range of initial conditions. It is shown that the Rayleigh–Taylor growth rate in an ablative environment is a strong function of the laser wavelength. For perturbation wavelengths about three times the in‐flight target thickness, the ratios of the numerical growth rates to the classical growth rates are of the order of 1/1.5, 1/2.5, and 1/3.5 for 1, 1/2 , and 1/4 μm laser light, respectively. The numerical results are in good agreement with the theoretical model presented here based on the ablative convection of vorticity away from the unstable ablation front. These results provide strong evidence for the viability of high‐aspect‐ratio shells in direct‐drive laser fusion.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.50.Jm Plasma production and heating by laser beams (laser-foil, laser-cluster, etc.)
52.65.-y Plasma simulation

Experimental and numerical study of a turbulent free square jet

W. R. Quinn and J. Militzer

Phys. Fluids 31, 1017 (1988); http://dx.doi.org/10.1063/1.867007 (9 pages) | Cited 39 times

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Results of an experimental and numerical study of a turbulent free jet of air from a sharp‐edged square slot are presented. The jet was treated as elliptic in the numerical study that predicted mean streamwise velocity, mean static pressure, and turbulence kinetic energy distributions. The experimental results include the mean velocity, the turbulent normal and shearing stresses obtained with hot‐wire anemometry, and the mean static pressure acquired with a pitot‐static tube in conjunction with a pressure transducer. The experimental results reveal the existence of pronounced mean streamwise velocity off‐center peaks in the very near field, where positive mean static pressures were also found. Furthermore, the square jet is found to spread significantly faster in the near flow field than a jet from a round slot that has the same exit area as the square slot under identical test conditions. The general agreement between experimental results and numerical predictions is relatively good.
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47.27.W- Boundary-free shear flow turbulence

The fluctuating wall‐shear stress and the velocity field in the viscous sublayer

P. Henrik Alfredsson, Arne V. Johansson, Joseph H. Haritonidis, and Helmut Eckelmann

Phys. Fluids 31, 1026 (1988); http://dx.doi.org/10.1063/1.866783 (8 pages) | Cited 99 times

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The fluctuating wall‐shear stress was measured with various types of hot‐wire and hot‐film sensors in turbulent boundary‐layer and channel flows. The rms level of the streamwise wall‐shear stress fluctuations was found to be 40% of the mean value, which was substantiated by measurements of the streamwise velocity fluctuations in the viscous sublayer. Heat transfer to the fluid via the probe substrate was found to give significant differences between the static and dynamic response for standard flush‐mounted hot‐film probes with air or oil as the flow medium, whereas measurements in water were shown to be essentially unaffected by this problem.
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47.27.N- Wall-bounded shear flow turbulence
47.80.-v Instrumentation and measurement methods in fluid dynamics

A direct interaction approximation treatment of turbulence in a compressible fluid. I. Formalism

Gregory J. Hartke, V. M. Canuto, and Carol T. Alonso

Phys. Fluids 31, 1034 (1988); http://dx.doi.org/10.1063/1.866784 (17 pages) | Cited 9 times

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The direct interaction approximation (DIA) is used to treat turbulence in a compressible medium with constant mean gradients. The set of coupled nonlinear integrodifferential equations is derived that is satisfied by the transverse and longitudinal energy spectral functions, QT and QL, and by the transverse and longitudinal response functions, GT and GL. Finally, expressions for the average of the product of pairs of physically relevant fluctuating quantities (velocity, temperature, density) are derived in terms of QT and QL. The numerical solution of this set of equations will be presented in part II of this work.
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47.27.-i Turbulent flows
47.40.-x Compressible flows; shock waves
02.60.Nm Integral and integrodifferential equations

The thermophoretic force in the Knudsen regime near a wall

M. M. R. Williams

Phys. Fluids 31, 1051 (1988); http://dx.doi.org/10.1063/1.866785 (7 pages) | Cited 2 times

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The thermophoretic forces acting on a Small Knudsen particle in the neighborhood of a boundary have been investigated. The applied temperature gradient is constant, but it is not normal to the wall, thereby leading to thermophoretic forces both normal to and parallel with the wall. Using the velocity distribution of the gas atoms for this problem it has been possible to obtain the variation of the thermophoretic force as a function of distance from the boundary. It is noted, that for equal temperature gradients, the force is greater in the direction normal to the wall than along it. In addition, it is observed that the velocity dependence of the mean free path has a significant effect on the force in the neighborhood of the wall. In contrast to the normal force, which is in the direction of decreasing temperature, the mass flow induced by thermal creep along the wall leads to a parallel wall force that moves the particle in the direction of increasing temperature. When these two forces are compounded they indicate that particles can move in curved paths en route to the wall surface. As a by‐product of the calculation, an exact expression for the thermal creep velocity as a function of distance from the wall for the case of constant collision cross‐section is presented.
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47.55.Kf Particle-laden flows
42.68.Ge Effects of clouds and water; ice crystal phenomena
42.68.Kh Effects of air pollution
05.60.-k Transport processes
47.45.-n Rarefied gas dynamics

Compressible rotational flows generated by the substitution principle

J. L. Rodriguez Azara and George Emanuel

Phys. Fluids 31, 1058 (1988); http://dx.doi.org/10.1063/1.866786 (6 pages) | Cited 3 times

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A theory is developed for compressible rotational flow that is based on the substitution principle. The theory encompasses a formula for the transformation of the vorticity under the principle. Solutions are found for four rotational flows. These are the rotational counterparts of a parallel flow, flow behind a planar oblique shock wave, Prandtl–Meyer flow, and Taylor–Maccoll flow. A surprising variation of the vorticity is found for the planar oblique shock wave and the Prandtl–Meyer flow. Irrotational flow behind a curved shock wave, where the upstream flow is rotational, is examined and shown not to be possible.
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47.40.Nm Shock wave interactions and shock effects
47.32.Ef Rotating and swirling flows

Structure of shock waves in relativistic simple gases

C. Cercignani and A. Majorana

Phys. Fluids 31, 1064 (1988); http://dx.doi.org/10.1063/1.866787 (5 pages) | Cited 4 times

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The method proposed by Mott‐Smith [Phys. Rev. 82, 885 (1951)] to compute the structure of shock waves according to classical kinetic theory is extended to relativistic shocks. The results for the shock thickness are in remarkably good agreement with the results obtained from Eckart’s continuum theory.
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47.40.Nm Shock wave interactions and shock effects
47.75.+f Relativistic fluid dynamics
47.45.-n Rarefied gas dynamics

Nonlinear focusing and the Kelvin–Helmholtz instability in ferrofluid/nonmagnetic fluid systems

S. K. Malik and M. Singh

Phys. Fluids 31, 1069 (1988); http://dx.doi.org/10.1063/1.867018 (5 pages) | Cited 6 times

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The nonlinear focusing or collapse is considered for the superposed magnetic fluids in motion at uniform speeds. The magnetic field is applied along the direction of streaming. It is shown that the evolution of the amplitude is governed by a two‐dimensional Schrödinger equation with cubic nonlinearity. This equation gives rise to a self‐focusing singularity when the velocity difference is in the subcritical regime. It is shown that such a self‐focusing effect is direction dependent, and predominant at shorter wavelengths.
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47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
47.35.-i Hydrodynamic waves
47.65.-d Magnetohydrodynamics and electrohydrodynamics

The dynamic sheath: Objects coupling to plasmas on electron‐plasma‐frequency time scales

Joseph E. Borovsky

Phys. Fluids 31, 1074 (1988); http://dx.doi.org/10.1063/1.866788 (27 pages) | Cited 22 times

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The time‐dependent interaction between solid objects and the unmagnetized plasmas in which they are immersed is investigated. To this end over 1900 high‐resolution, one‐dimensional particle‐in‐cell simulations of the plasmas surrounding cylindrical and planar objects are statistically analyzed. Numerical shot noise produces an electron‐plasma‐frequency ringing in the simulations, the amplitude of which is related to the plasma temperature and to the numerical system temperature. Whenever the potential of an object is rapidly biased, the surrounding plasma rings with a large amplitude at the electron‐plasma frequency. During this ringing, a depletion layer forms around the object on ion‐acoustic time scales. Positively charged objects discharge via plasma currents in about τpe /4 and negatively charged objects discharge in about τpi . Owing to charge separations in the plasmas, for the first few ion‐plasma periods after a perturbation, the potential of an object is not directly related to the charge on it. The electron‐plasma‐frequency ringing drives large‐amplitude Langmuir waves, which energize electrons and drive cavitation in the plasma. The fluxes of electrons reaching the objects are bursty at ωpe, and the energies of the ions striking the object slowly and systematically vary with time.
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52.40.Hf Plasma-material interactions; boundary layer effects
52.65.-y Plasma simulation

Simulations of electrically polarized gravitational condensations in a grain plasma

G. R. Gisler and E. R. Wollman

Phys. Fluids 31, 1101 (1988); http://dx.doi.org/10.1063/1.866789 (4 pages) | Cited 3 times

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The two long‐range forces in nature, gravitation and electromagnetism, are generally not jointly important in determining the dynamics of physical systems. There is, however, a case in which equilibrium large‐scale electrostatic and gravitational forces can be similar in magnitude. In a two‐component plasma, in which the massive species is a charged grain with charge‐to‐mass ratio of order (G)1/2, self‐gravitation and thermalization result in strong electrical polarization since the oppositely charged low‐mass component has a scale height much greater than that of the grains. Preliminary results of a computer simulation of this behavior are presented here. Properties of steady‐state gravitational condensations in grain plasmas have been studied with a one‐dimensional particle‐in‐cell code, and an investigation of the ratio of electrostatic to gravitational energy for various values of the grain charge‐to‐mass ratio has been performed. As expected, this ratio is maximized when the grain charge‐to‐mass ratio is approximately (G)1/2.
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52.25.Dg Plasma kinetic equations
52.65.-y Plasma simulation
95.30.Qd Magnetohydrodynamics and plasmas
98.54.Aj Quasars

Dependence of heat pulse propagation on transport mechanisms: Consequences of nonconstant transport coefficients

K. W. Gentle

Phys. Fluids 31, 1105 (1988); http://dx.doi.org/10.1063/1.866790 (6 pages) | Cited 65 times

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The transport coefficients for particles and heat will certainly depend upon plasma parameters. Besides making the equilibrium equations nonlinear, this introduces a multitude of new terms in the set of linearized equations, which can be used to describe the effects of perturbations to the system. A general set of such equations is obtained that includes most physical dependences of the transport coefficients. If transport is driven by gradients in density or temperature, as would be expected from most turbulence theories, significant quantitative effects result. Perturbations no longer evolve at the equilibrium transport rates, and the density and temperature perturbations can be strongly coupled. Results are presented for several specific cases.
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52.25.Fi Transport properties
52.55.Dy General theory and basic studies of plasma lifetime, particle and heat loss, energy balance, field structure, etc.

Saturation induction and radiation in wave‐driven plasmas

Jean M. Rax

Phys. Fluids 31, 1111 (1988); http://dx.doi.org/10.1063/1.866739 (12 pages) | Cited 8 times

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A study of some problems associated with noninductive current drive is presented. Both slow and fast waves, weak and strong power, and transient and steady‐state responses are considered. The wave‐induced deformation of the electron distribution function is expressed as a linear functional of the absorbed power. This expression is then used to study three important phenomena: saturation of the absorption, coupling with an inductive field, and wave‐induced electron cyclotron emission.
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52.25.Fi Transport properties
52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma

Dispersion relations for the lower hybrid frequency range

Suwon Cho and D. G. Swanson

Phys. Fluids 31, 1123 (1988); http://dx.doi.org/10.1063/1.866740 (7 pages) | Cited 7 times

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The hot plasma electrostatic dispersion relation for the lower hybrid frequency range has been cast into a form without any sums using the method of steepest descents. This new form of the dispersion relation with the exact resonance term, which is valid for general complex wavenumber and each term of which is identified according to its role of representing physical waves, is shown to be accurate and to be reducible to an expression obtained by Brambilla [Plasma Phys. 18, 699 (1976)] when some approximations are taken. A very simple dispersion relation is also obtained without singular terms near the high ion cyclotron harmonics that are encountered by lower hybrid waves propagating in inhomogeneous magnetic fields. Finally, the damping rate in space is numerically calculated using the equation derived and compared with the result from the unmagnetized ion dispersion relation.
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52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma
52.50.Gj Plasma heating by particle beams
52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)

Linear mode conversion of an electrostatic wave at the upper‐hybrid frequency

O. Randriamboarison, F. Braun, and G. Leclert

Phys. Fluids 31, 1130 (1988); http://dx.doi.org/10.1063/1.866741 (3 pages) | Cited 4 times

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An analysis of the mode conversion of an electrostatic Bernstein wave in a plasma near the upper‐hybrid resonance is developed. The conversion coefficients for the reflected extraordinary and electrostatic waves and for the transmitted electromagnetic wave are derived and calculated for various values of the inhomogeneity length and wave frequency.
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52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
52.35.Hr Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)

Resistive evolution of plasmas with imperfect magnetic surfaces

Guthrie Miller

Phys. Fluids 31, 1133 (1988); http://dx.doi.org/10.1063/1.866742 (9 pages) | Cited 8 times

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The theory of resistive evolution of plasmas is extended to include plasmas with imperfect magnetic surfaces, that is, plasmas having magnetic field lines that wander stochastically. In resistive evolution theory the plasma is assumed to be always in mechanical equilibrium and the evolution occurs by allowing the magnetic flux constraints determining the equilibrium to change, which happens on a resistive time scale. In this paper a formalism is created to describe magnetic field line structure in a general way in order to evaluate the field line integrals that are the magnetic flux constraints. The equations expressing evolution of these flux constraints, along with the plasma mechanical equilibrium equations, are a mathematical model that can be solved to determine the evolution of the plasma. An immediate result of this model is that, for plasmas with stochastic magnetic field lines, the current density has a filamentary structure, giving a self‐consistent source of the stochasticity. A simple two‐field‐line model of the reversed field pinch is discussed.
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52.55.Dy General theory and basic studies of plasma lifetime, particle and heat loss, energy balance, field structure, etc.
52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)
52.55.Ez Theta pinch

Self‐organization in three‐dimensional compressible magnetohydrodynamic flow

Ritoku Horiuchi and Tetsuya Sato

Phys. Fluids 31, 1142 (1988); http://dx.doi.org/10.1063/1.866743 (11 pages) | Cited 24 times

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A three‐dimensional self‐organization process of a compressible dissipative plasma with a velocity‐magnetic field correlation is investigated in detail by means of a variational method and a magnetohydrodynamic simulation. There are two types of relaxation, i.e., fast relaxation in which the cross helicity is not conserved and slow relaxation in which the cross helicity is conserved approximately. In the slow relaxation case the cross helicity consists of two components with opposite sign that have almost the same amplitude in the large wavenumber region. In both cases the system approaches a high correlation state, dependent on the initial condition. These results are consistent with observational data of the solar wind. Selective dissipation of magnetic energy, normal cascade of magnetic energy spectrum, and inverse cascade of magnetic helicity spectrum are observed for the sub‐Alfvénic flow case, as was observed previously for the zero‐flow case. When the flow velocity is super‐Alfvénic, the relaxation process is altered significantly from the zero‐flow case.
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52.30.-q Plasma dynamics and flow
52.55.Dy General theory and basic studies of plasma lifetime, particle and heat loss, energy balance, field structure, etc.
52.65.-y Plasma simulation

Energy confinement in turbulent fluid plasmas

A. Bhattacharjee and Eliezer Hameiri

Phys. Fluids 31, 1153 (1988); http://dx.doi.org/10.1063/1.866744 (8 pages) | Cited 5 times

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Scaling laws for energy confinement in a turbulent plasma dominated by resistive pressure‐driven modes are revisited. New scaling laws are obtained under a consistent low‐beta approximation, and differ from earlier theories primarily in their dependence on the plasma pressure.
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52.25.Fi Transport properties
52.35.Ra Plasma turbulence
52.55.Ez Theta pinch
52.55.Fa Tokamaks, spherical tokamaks
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