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Nov 1986

Volume 29, Issue 11, pp. 3503-3898

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Fluid mixing (stretching) by time periodic sequences for weak flows

D. V. Khakhar and J. M. Ottino

Phys. Fluids 29, 3503 (1986); http://dx.doi.org/10.1063/1.865824 (3 pages) | Cited 16 times

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The stretching of material lines in time periodic sequences of ‘‘weak’’ flows (i.e., characterized by a linear stretching for long times) in which streamlines change at the end of each periodic unit is quantified in terms of a mixing efficiency. Two different flows and two different strain distributions give nearly identical results in terms of the mixing efficiency and indicate the existence of an optimal operating condition for maximum stretch. The results are relevant to fluid mixing in chaotic flows.
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47.27.W- Boundary-free shear flow turbulence

The helical nature of unforced turbulent flows

Richard B. Pelz, Leonid Shtilman, and Arkady Tsinober

Phys. Fluids 29, 3506 (1986); http://dx.doi.org/10.1063/1.865825 (3 pages) | Cited 19 times

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Results of direct numerical simulations of the decay of nearly isotropic turbulence exhibit clearly that much of the flow evolves in orientation to a state in which the vorticity vector is nearly aligned with the velocity vector.
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47.27.Gs Isotropic turbulence; homogeneous turbulence

Null‐collision technique in the direct‐simulation Monte Carlo method

Katsuhisa Koura

Phys. Fluids 29, 3509 (1986); http://dx.doi.org/10.1063/1.865826 (3 pages) | Cited 25 times

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The null‐collision concept is introduced into the direct‐simulation Monte Carlo method in the rarefied gas dynamics. The null‐collision technique overcomes the principle fault in the time‐counter technique and the difficulties in the collision‐frequency technique. The computation time required for the null‐collision technique is comparable to that for the time‐counter technique. Therefore, it is concluded that the null‐collision technique is superior to any other existing techniques in the direct‐simulation Monte Carlo method.
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47.45.-n Rarefied gas dynamics
02.70.-c Computational techniques; simulations

Hot‐electron instability in mirror geometry

A. J. Lichtenberg and H. Meuth

Phys. Fluids 29, 3511 (1986); http://dx.doi.org/10.1063/1.865827 (4 pages) | Cited 2 times

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Plasmas with variable ratios of hot electrons to colder background plasma, but without significant neutral gas, are investigated in the multiple mirror experiment (MMX) [Phys. Fluids 29, 1208 (1986)]. The device permits, sequentially, the injection of plasma (H2 or He) into a stable mirror cell, and electron‐cyclotron resonance heating (ECRH) to an electron temperature of several keV. A second source then provides the cold‐electron component with arbitrary nc/nh≤50. At any point in time, the field coils that provide magnetohydrodynamic (MHD) stability for the hot electrons may be pulsed off for times short in comparison to the time required for cold plasma density to change. Instantaneous destabilization, even for plasma parameters well in excess of the value of nc/nh for which a hot‐electron drift approximation would predict stability, was observed. This result suggests that a mechanism in addition to a cold plasma background is required to stabilize a hot‐electron distribution. Comparison is made with recent theoretical work.
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52.35.Bj Magnetohydrodynamic waves (e.g., Alfven waves)
28.52.Av Theory, design, and computerized simulation
52.55.-s Magnetic confinement and equilibrium

Chaotic advection in a Stokes flow

H. Aref and S. Balachandar

Phys. Fluids 29, 3515 (1986); http://dx.doi.org/10.1063/1.865828 (7 pages) | Cited 114 times

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Chaotic advection can be produced whenever the kinematic equations of motion for passively advected particles give rise to a nonintegrable dynamical system. Although this interpretation of the phenomenon immediately shows that it is possible for flows at any value of Reynolds number, the notion of stochastic particle motion within laminar flows runs counter to common intuition to such a degree that the range of applicability of early model results has been questioned. To dispel lingering doubts of this type a study of advection in a two‐dimensional Stokes flow slowly modulated in time is presented. Even for this very low Reynolds number, manifestly ‘‘laminar’’ flow chaotic particle motion is readily realizable. Standard diagnostics of chaos are computed for various methods of time modulation. Relations to the general ideas of parametric resonance and adiabatic invariance are pointed out.
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66.20.-d Viscosity of liquids; diffusive momentum transport
47.10.-g General theory in fluid dynamics

Film flow on a rotating disk

Brian G. Higgins

Phys. Fluids 29, 3522 (1986); http://dx.doi.org/10.1063/1.865829 (8 pages) | Cited 47 times

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Unsteady liquid film flow on a rotating disk is analyzed by asymptotic methods for low and high Reynolds numbers. The analysis elucidates how a film of uniform thickness thins when the disk is set in steady rotation. In the low Reynolds number analysis two time scales for the thinning film are identified. The long‐time‐scale analysis ignores the initial acceleration of the fluid layer and hence is singular at the onset of rotation. The singularity is removed by matching the long‐time‐scale expansion for the transient film thickness with a short‐time‐scale expansion that accounts for fluid acceleration during spinup. The leading order term in the long‐time‐scale solution for the transient film thickness is shown to be a lower bound for film thickness for all time. A short‐time analysis that accounts for boundary layer growth at the disk surface is also presented for arbitrary Reynolds number. The analysis becomes invalid either when the boundary layer has a thickness comparable to that of the thinning film, or when nonlinear effects become important.
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68.15.+e Liquid thin films
47.27.N- Wall-bounded shear flow turbulence

Growth of a gas bubble in a viscous fluid

Hsueh‐Chia Chang and Liang‐Heng Chen

Phys. Fluids 29, 3530 (1986); http://dx.doi.org/10.1063/1.865830 (7 pages) | Cited 12 times

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The cavitation pressure of spherical gas bubbles is correlated to the fluid viscosity in a theoretical investigation of the viscous Rayleigh–Plesset equation. The analysis is complicated by the absence of a first integral for the dissipative system. A qualitative normal form bifurcation analysis about a double‐zero codimension 2 singularity is used to guide a quantitative estimate of the cavitation pressure by numerical and Melnikov perturbation techniques.
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47.55.dp Cavitation and boiling
47.55.Kf Particle-laden flows
51.10.+y Kinetic and transport theory of gases

The effect of surface tension on the shape of a Hele–Shaw cell bubble

Saleh Tanveer

Phys. Fluids 29, 3537 (1986); http://dx.doi.org/10.1063/1.865831 (12 pages) | Cited 40 times

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Numerical and asymptotic solutions are found for the steady motion of a symmetrical bubble through a parallel‐sided channel in a Hele–Shaw cell containing a viscous liquid. The degeneracy of the Taylor–Saffman zero surface‐tension solution is shown to be removed by the effect of surface tension. An apparent contradiction between numerics and perturbation arises here as it does for the finger. This contradiction is resolved analytically for small bubbles and is shown to be the result of exponentially small terms. Numerical results suggest that this is true for bubbles of arbitrary size. The limit of infinite surface tension is also analyzed.
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47.27.T- Turbulent transport processes
47.55.Kf Particle-laden flows
68.03.Cd Surface tension and related phenomena
51.10.+y Kinetic and transport theory of gases

Stability of miscible displacements in porous media: Rectilinear flow

C. T. Tan and G. M. Homsy

Phys. Fluids 29, 3549 (1986); http://dx.doi.org/10.1063/1.865832 (8 pages) | Cited 108 times

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A theoretical treatment of the stability of miscible displacement in a porous medium is presented. For a rectilinear displacement process, since the base state of uniform velocity and a dispersive concentration profile is time dependent, we make the quasi‐steady‐state approximation that the base state evolves slowly with respect to the growth of disturbances, leading to predictions of the growth rate. Comparison of results with initial value solutions of the partial differential equations shows that, excluding short times, there is good agreement between the two theories. Comparison of the theory with several experiments in the literature indicates that the theory gives a good prediction of the most dangerous wavelength of unstable fingers. An approximate analysis for transversely anisotropic media has elucidated the role of transverse dispersion in controlling the length scale of fingers.
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47.20.-k Flow instabilities
47.56.+r Flows through porous media

Monte Carlo simulation of two‐fluid flow through porous media at finite mobility ratio—the behavior of cumulative recovery

A. J. DeGregoria

Phys. Fluids 29, 3557 (1986); http://dx.doi.org/10.1063/1.865833 (5 pages) | Cited 4 times

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Curves for cumulative recovery of driven fluid, as a function of pore volume injected of driving fluid, are computed using a previously developed Monte Carlo simulation of two‐fluid flow through porous media at finite viscosity ratio. Both the linear channel and five‐spot geometries are examined at various grid sizes. For a range of unfavorable viscosity ratios, the trend is toward greater recovery as grid size increases, in the opposite direction to the trend at infinite unfavorable viscosity ratio, which is toward zero recovery as grid size increases.
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47.55.Kf Particle-laden flows
47.56.+r Flows through porous media

Three‐dimensional numerical study of convection in a cylindrical thermal diffusion cell: Its influence on the separation of constituents

D. Henry and B. Roux

Phys. Fluids 29, 3562 (1986); http://dx.doi.org/10.1063/1.865834 (11 pages) | Cited 6 times

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The convection arising in a cylindrical container, heated from the ends and designed for a measurement of Soret coefficient, is examined. A three‐dimensional method using a pseudostationary scheme with a finite differences technique is used. Attention is focused on a horizontal cylinder with an aspect ratio of 6, a Prandtl number of 0.6, and a Schmidt number of 60. The influence of convection on the separation and on the mass fraction profiles is examined for moderate Grashof numbers (0.01≤GrH≤10) and realistic Soret parameters (−0.75≤S≤1). A domain is found where the flow has no influence on the separation, corresponding to a ‘‘separation’’ regime. Extensions of the results to different Prandtl and Schmidt numbers and to larger aspect ratios are proposed.
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66.10.C- Diffusion and thermal diffusion
47.27.T- Turbulent transport processes

Vaporization of irradiated droplets

R. L. Armstrong, P. J. O’Rourke, and A. Zardecki

Phys. Fluids 29, 3573 (1986); http://dx.doi.org/10.1063/1.865783 (9 pages) | Cited 16 times

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The vaporization of a spherically symmetric liquid droplet subject to a high‐intensity laser flux is investigated on the basis of a hydrodynamic description of the system composed of the vapor and ambient gas. In the limit of the convective vaporization, the boundary conditions at the fluid–gas interface are formulated by using the notion of a Knudsen layer in which translational equilibrium is established. This leads to approximate jump conditions at the interface. For homogeneous energy deposition, the hydrodynamic equations are solved numerically with the aid of the CON1D computer code (‘‘CON1D: A computer program for calculating spherically symmetric droplet combustion,’’ Los Alamos National Laboratory Report No. LA‐10269‐MS, December, 1984), based on the implict continuous–fluid Eulerian (ICE) [J. Comput. Phys. 8, 197 (1971)] and arbitrary Lagrangian–Eulerian (ALE) [J. Comput. Phys. 14, 1227 (1974)] numerical mehtods. The solutions exhibit the existence of two shock waves propagating in opposite directions with respect to the contact discontinuity surface that separates the ambient gas and vapor.
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47.40.-x Compressible flows; shock waves
79.20.Ds Laser-beam impact phenomena
47.27.T- Turbulent transport processes
68.03.Fg Evaporation and condensation of liquids

Generalized random forcing in random‐walk turbulent dispersion models

B. L. Sawford

Phys. Fluids 29, 3582 (1986); http://dx.doi.org/10.1063/1.865784 (4 pages) | Cited 23 times

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The Kramers–Moyal expansion is used to derive an infinite hierarchy of Eulerian moment conservation equations from a random‐walk model with non‐Gaussian random forcing, thus generalizing the Langevin‐equation–Fokker–Planck analysis of van Dop et al. [H. van Dop, F. T. M. Nieuwstadt, and J. C. R. Hunt, Phys. Fluids 28, 1639 (1985)]. By imposing the condition that an initially well‐mixed state should remain so, equations for random forcing moments of arbitrary order are derived in terms of the Eulerian velocity moments of the turbulence. This procedure makes explicit the equivalence of the different procedures used by van Dop et al. and Thomson [D. J. Thomson, Q. J. R. Meteorol. Soc. 110, 1107 (1984)] to derive the first few forcing moments and extends their results. It is then shown that the random forcing approximation implies an infinite hierarchy of Eulerian closure assumptions, the first few of which were derived by van Dop et al. The analysis is extended to a class of rescaled random‐walk equations, and it is shown that the version developed by Wilson et al. [J. D. Wilson, B. J. Legg, and D. J. Thomson, Boundary‐Layer Meteorol. 27, 163 (1983)] is unique in that it alone is realizable for inhomogeneous Gaussian turbulence and then has Gaussian random forcing.
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47.27.T- Turbulent transport processes
92.10.Lq Turbulence, diffusion, and mixing processes in oceanography
92.60.hk Convection, turbulence, and diffusion

Turbulent passive scalar field of a small Prandtl number

J. Qian

Phys. Fluids 29, 3586 (1986); http://dx.doi.org/10.1063/1.865785 (4 pages) | Cited 7 times

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The statistical‐mechanics theory of the passive scalar field convected by turbulence, developed in an earlier paper [Phys. Fluids 28, 1299 (1985)], is extended to the case of a small molecular Prandtl number. The set of governing integral equations is solved by the equation‐error method. The resultant scalar‐variance spectrum for the inertial range is F(k)∼x−5/3/[1+1.21x1.67(1+0.353x2.32)], where x is the wavenumber scaled by Corrsin’s dissipation wavenumber. This result reduces to the − (5)/(3) law in the inertial‐convective range. It also approximately reduces to the − (17)/(3) law in the inertial‐diffusive range, but the proportionality constant differs from Batchelor’s by a factor of 3.6.
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47.27.T- Turbulent transport processes
47.27.Gs Isotropic turbulence; homogeneous turbulence
05.20.-y Classical statistical mechanics

Microbubble skin friction reduction on an axisymmetric body

S. Deutsch and J. Castano

Phys. Fluids 29, 3590 (1986); http://dx.doi.org/10.1063/1.865786 (8 pages) | Cited 14 times

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A reduction in skin friction drag is shown when gas is introduced into the liquid turbulent boundary layer of a submerged axisymmetric body. The 89 mm diameter, 632 mm long body has a cylindrical balance 273 mm long. Free stream speeds in the 305 mm diameter tunnel are as high as 17 m/sec, giving length Reynolds number of up to 10 million. In general, skin friction reduction is shown to increase with increasing free stream speed. At high speeds, helium injection is shown to be more effective at reducing skin friction than is air injection. Maximum skin friction reduction is near 80%—a value in good agreement with the maximum value observed in the flat plate work of Madavan et al. [Phys. Fluids 27, 356 (1984)]. While maximum skin friction reduction was found at a free stream speed of 5 m/sec for the flat plate geometry, maximum skin friction reduction was at a free stream speed of 17 m/sec for the axisymmetric geometry.
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47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
47.35.-i Hydrodynamic waves
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.27.T- Turbulent transport processes

Evolution of flow in the developing region of the mixing layer with a skew laminar wake as an initial condition

Jiun‐Jih Miau and Sture K. F. Karlsson

Phys. Fluids 29, 3598 (1986); http://dx.doi.org/10.1063/1.865787 (10 pages) | Cited 2 times

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The mixing layer was studied at a Reynolds number (U1δ∗/ν) of 270 and at six velocity ratios ranging from 1.0 to 0.46. Velocity measurements were carried out in the developing region of the mixing layer. Results show that naturally developing velocity fluctuations reach the maximum at a certain stream location in the developing region, then decay, and that the streamwise velocity fluctuation increases again in the further downstream region where the mean flow approaches the hyperbolic‐tangent shape. There is an indication that the fluctuating motion initiated in the wake region with its characteristic scale can pick up additional energy in the downstream hyperbolic‐tangent mean‐flow region, although stability theory predicts a most unstable length scale that is substantially larger.
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47.27.W- Boundary-free shear flow turbulence
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.60.-i Flow phenomena in quasi-one-dimensional systems
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

Inverse energy cascade in two‐dimensional turbulence

J. Qian

Phys. Fluids 29, 3608 (1986); http://dx.doi.org/10.1063/1.865788 (4 pages) | Cited 2 times

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The closure method developed in earlier papers [J. Qian, Phys. Fluids 26, 2098 (1983); 27, 2412 (1984)] is applied to the study of the inverse energy cascade in two‐dimensional turbulence. The resultant inertial‐range energy spectrum is E(k)=2.58g0.244ϵ2/3k−5/3. Here g is a localization factor and ϵ is the rate of energy cascade. This result is compatible with the numerical experiments by Lilly [D. K. Lilly, Phys. Fluids Suppl. II 12, 24 (1969)], Siggia and Aref [E. D. Siggia and H. Aref, Phys. Fluids 24, 171 (1981)], and Frisch and Sulem [U. Frisch and P. L. Sulem, Phys. Fluids 27, 1921 (1984)].
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47.27.Gs Isotropic turbulence; homogeneous turbulence
47.20.-k Flow instabilities

Coherent structures in the far field of a turbulent wake

L. W. B. Browne, R. A. Antonia, and D. K. Bisset

Phys. Fluids 29, 3612 (1986); http://dx.doi.org/10.1063/1.865789 (6 pages) | Cited 19 times

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The topology of a typical group of large‐scale coherent structures in the far‐field of a slightly heated cylinder wake is clearly delineated by using averages of the velocity vector components conditioned on the occurrence of spatially coherent temperature fronts. Velocities are determined relative to a frame of reference traveling with the approximate convection velocity of the structures. When the results for a number of positions across the wake are assembled a clear topology picture of a typical group of structures in the plane of the main shear is obtained. The contributions of the coherent and random motions of all structures to the momentum and heat transports have been determined. In all cases the contribution that results from the random motion is larger than that of the coherent motion. This difference is more pronounced for the momentum transport than for the lateral heat transport.
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47.27.N- Wall-bounded shear flow turbulence
47.27.T- Turbulent transport processes
47.60.-i Flow phenomena in quasi-one-dimensional systems

Ionization behind strong normal shock waves in argon

A. Kaniel, O. Igra, G. Ben‐Dor, and M. Mond

Phys. Fluids 29, 3618 (1986); http://dx.doi.org/10.1063/1.865790 (8 pages) | Cited 5 times

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The ionization of argon by strong normal shock waves is studied. The conservation equations are solved to yield the plasma behavior behind the shock wave front. Very good agreement is obtained between experimental findings and the present numerical results for the electron number density, plasma density, and degree of ionization, especially at the electron avalanche region of the relaxation zone. The high accuracy of the present numerical solutions in reproducing the electron avalanche is attributed to the use of accurate threshold collision cross sections for excitation of argon by electron collisions. To support this claim it is demonstrated that if different assumptions were used to describe the ionization process, then the computed results would be different only upstream of the electron avalanche region, i.e., it is shown that the proposed model for ionizing shock waves enables a highly accurate reproduction of the electron avalanche but is less accurate in predicting its exact location.
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52.50.Lp Plasma production and heating by shock waves and compression
52.25.Fi Transport properties

Dissociation–association equilibrium of magnetic particle chains in homogeneous magnetic fields

H. E. Wilhelm

Phys. Fluids 29, 3626 (1986); http://dx.doi.org/10.1063/1.865791 (5 pages)

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An idealized statistical theory of chaining in a dilute suspension of macroscopic magnetic particles in a rarefied gas is presented when an external homogeneous magnetic field is present. The primary colloidal particles are assumed to be spherical, of the same size, and to have saturated magnetic moments. The magnetochemical potentials and the association–dissociation equations are derived for chains consisting of v≥1 magnetic grains, in dependence of the temperature T, the density Nv of chains, and the homogeneous magnetic field B0. High field intensities B0 are shown to shift the chain length distribution F=F(v) in favor of long chains, v≫1, whereas increasing temperatures T move the maximum of this statistical distribution to smaller chain lengths, v→1. The theory appears to be in qualitative agreement with oven experiments using an external magnetic field for the alignment and stabilization of the chains.
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82.20.Db Transition state theory and statistical theories of rate constants
82.30.Nr Association, addition, insertion, cluster formation
82.30.Lp Decomposition reactions (pyrolysis, dissociation, and fragmentation)
75.50.Mm Magnetic liquids

Alternatives to the Euler and Navier–Stokes equations for monatomic gases

D. S. Butler

Phys. Fluids 29, 3631 (1986); http://dx.doi.org/10.1063/1.865792 (4 pages)

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The Chapman–Enskog approximation scheme is not uniformly convergent because it does not approximate sufficiently the behavior of molecules in the high‐speed tail of a distribution. Asymptotic analysis of the binary collision term in the Boltzmann equation is used to show that collisions involving high‐speed molecules can redistribute molecules within an energy level more easily than between levels. Chapman–Enskog theory is reformulated by assuming near equilibrium, only within each energy level, instead of over all energy levels.
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51.10.+y Kinetic and transport theory of gases

Nonlinear gyrokinetic theory, the direct interaction approximation, and anomalous thermal transport in tokamaks

W. K. Hagan and E. A. Frieman

Phys. Fluids 29, 3635 (1986); http://dx.doi.org/10.1063/1.865793 (4 pages) | Cited 11 times

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Invariance properties under scale transformations of the nonlinear gyrokinetic Vlasov and heat transport equations are used to examine anomalous thermal transport due to drift wave turbulence. To fully exploit the gyrokinetic expansion, separation of the fluctuations from the background by means of averaging is required. This leads to a statistical description of the system and the use of the direct interaction approximation. The invariance properties of the gyrokinetic and statistical descriptions produce the same results for χ, the thermal diffusivity. For a collisionless, low‐β, quasineutral plasma in a general magnetic field, a unique result is derived for χ.
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52.55.Fa Tokamaks, spherical tokamaks
52.25.Fi Transport properties
52.35.Ra Plasma turbulence
52.25.Dg Plasma kinetic equations

Mode conversion of a propagating to nonpropagating wave

R. A. Cairns and C. N. Lashmore‐Davies

Phys. Fluids 29, 3639 (1986); http://dx.doi.org/10.1063/1.865794 (4 pages) | Cited 8 times

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A previous theory that gives a simple expression for the transmission coefficient through a mode conversion region, in terms of the local wave dispersion properties, is examined further in the special case where a propagating wave interacts with a localized resonant response. For this case it is shown how the theory can be derived, starting from Maxwell’s equations and the plasma conductivity tensor, and a particular example is analyzed by way of illustration.
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52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma
52.50.Gj Plasma heating by particle beams
94.20.Bb Wave propagation

Geometric optics at lower hybrid frequencies

K. S. Riedel

Phys. Fluids 29, 3643 (1986); http://dx.doi.org/10.1063/1.865795 (5 pages)

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Geometric optics is analyzed at lower hybrid frequencies using a realistic scaling of the cold plasma conductivity tensor. An explicit example displays the inadequacy of standard geometric optics in treating spatially varying plasmas. A new term is added to the ray Hamiltonian to remove this inconsistency. An adiabatic invariant, corresponding to the poloidal rotation of the ray, is introduced. The cold plasma waves can develop a singularity only at those points where the flux surface is tangent to upper and lower hybrid resonance surfaces, thus supporting the conjecture that heating occurs only at these points. The only other spatial points where singularities may develop in the geometric optics ray equations are the cyclotron resonances.
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52.50.Gj Plasma heating by particle beams

Drift and tearing modes in a sheared cylinder

John R. Cary and Barry S. Newberger

Phys. Fluids 29, 3648 (1986); http://dx.doi.org/10.1063/1.865796 (11 pages)

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Drift and tearing modes in a sheared cylindrical collisionless plasma column are studied. A set of differential equations in the radial coordinate is derived with small gyroradius and low‐β expansion. The finite‐β effects include curvature drifts, gradient‐B drifts, and the parallel magnetic field perturbation. Algebraic elimination reduces the resulting set of equations to a fourth‐order system. Analysis shows that bad curvature does not drive the collisionless modes unstable.
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52.35.Kt Drift waves
52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)
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.)
52.35.Qz Microinstabilities (ion-acoustic, two-stream, loss-cone, beam-plasma, drift, ion- or electron-cyclotron, etc.)
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