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Sep 1990

Volume 2, Issue 9, pp. 1517-1694


Gallery of Fluid Motion

Helen L. Reed

Phys. Fluids A 2, 1517 (1990); http://dx.doi.org/10.1063/1.857601 (11 pages) | Cited 1 time

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This article displays winning photographs from the seventh Annual Fluid Mechanics Photo Contest held at the November 1989 meeting of the American Physical Society, Division of Fluid Dynamics, Palo Alto, California.
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82.33.Vx Reactions in flames, combustion, and explosions
47.27.W- Boundary-free shear flow turbulence
07.68.+m Photography, photographic instruments; xerography

Nonlocality in a forced two‐dimensional turbulence

Koji Ohkitani

Phys. Fluids A 2, 1529 (1990); http://dx.doi.org/10.1063/1.857818 (3 pages) | Cited 16 times

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Nonlocality of the enstrophy cascade is revealed numerically by showing that the palinstrophy production is dominated by extremely elongated wave‐number triads. More than 85% of the palinstrophy production comes from such triads whose ratio of the smallest wave number to the middle is less than that of the dissipation length to the diameter of the coherent vortices. Such high nonlocality casts some doubt on the universality of the scaling law of energy spectrum.
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47.27.Gs Isotropic turbulence; homogeneous turbulence
05.45.-a Nonlinear dynamics and chaos

Hydrodynamic dispersion and pore geometry in consolidated rock

G. A. Gist, A. H. Thompson, A. J. Katz, and R. L. Higgins

Phys. Fluids A 2, 1533 (1990); http://dx.doi.org/10.1063/1.857602 (12 pages) | Cited 20 times

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Experimental measurements of the dispersion of tracer particles in flow through natural porous media are compared with a percolation model. The experiments show that tracer dispersion is a sensitive function of the width of the pore‐size distribution as measured by mercury capillary pressure. Measurements of capillary pressure (or electrical conductivity) are used to estimate the geometric correlation length of the dominant flow path in the rock. Percolation theory is used to derive a power‐law relationship between the correlation length and the ratio of the dispersivity to the average grain size. The experimental value of the power‐law exponent is in agreement with the theoretical prediction. Measurements on samples containing a residual saturation of wetting epoxy show no significant change in dispersion behavior. This result mediates against dispersion models requiring trapping in dead‐end pores. Tracer concentration profiles exhibit anomalous long‐time tails in two cases. In carbonate rocks, we associate long‐time tails with macroscopic permeability heterogeneities. In sandstones, long‐time tails occur in samples with a very narrow pore‐size distribution. These samples may have permeability heterogeneities as a result of defects in the packing density. In the limit of low flow velocity, the long‐time tail disappears, suggesting a convective mechanism associated with flow heterogeneities at a millimeter‐or‐larger scale.
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47.56.+r Flows through porous media
47.10.-g General theory in fluid dynamics

Small‐angle neutron scattering of sheared concentrated dispersions: Microstructure along principal flow axes

C. G. de Kruif, J. C. van der Werff, S. J. Johnson, and R. P. May

Phys. Fluids A 2, 1545 (1990); http://dx.doi.org/10.1063/1.857561 (12 pages) | Cited 8 times

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Using a novel parallel‐plate flow cell, the shear‐induced distortion of the structure factor S(k) for concentrated hard‐sphere dispersions by small‐angle neutron scattering is examined. The flow cell is vertically mounted, and the angle of incidence of the neutrons can be varied by rotating the flow cell as a whole. Thus data can be collected in many planes including those containing the principal flow axes. Dispersions containing sterically stabilized silica spheres of 40 nm radius, with volume fractions from 0.03 to 0.45, are studied. The Peclet number is varied between 0 and 1.0, and measured scattering patterns for wave vectors 0<k<0.3 nm−1 are measured. Contour plots for S(k) in part of the shear plane are presented for the first time. Based on the shear‐induced distortion of S(k), it is proposed that particle density increases along the compressional and vorticity axes, but decreases along the extensional axis.
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61.05.fg Neutron scattering (including small-angle scattering)
82.70.Dd Colloids

Taylor vortices in short fluid columns with large radius ratio

C. A. Bielek and E. L. Koschmieder

Phys. Fluids A 2, 1557 (1990); http://dx.doi.org/10.1063/1.857562 (7 pages) | Cited 4 times

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The formation of Taylor vortices after sudden starts of the inner cylinder has been studied experimentally in fluid columns with aspect ratios Γ=3.0, 3.25, 3.5, and 3.75, with radius ratio η=0.605, bounded by resting top and bottom boundaries. It has been found that the aspect ratio of the column has a profound effect on the number of Taylor vortices formed in the column. Anomalous three‐vortex flows have been found with Γ=3.0, 3.25, and 3.75, but not with Γ=3.5. Anomalous three‐vortex flows do not form directly after a sudden start, but originate from the decay of anomalous four‐vortex patterns with Γ=3.0 and Γ=3.25, and from six‐vortex patterns with Γ=3.75.
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47.20.-k Flow instabilities

Taylor vortex flow between eccentric coaxial rotating spheres

P. Bar‐Yoseph, A. Solan, R. Hillen, and K. G. Roesner

Phys. Fluids A 2, 1564 (1990); http://dx.doi.org/10.1063/1.857563 (10 pages) | Cited 8 times

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The rotationally symmetric, incompressible, spherical Couette flow between two spheres is examined, where the inner one rotates and the outer one is at rest. The investigation was done by means of a finite‐element program that solves the axisymmetric Navier–Stokes equations. Both concentric and eccentric spherical gaps are considered for two different radii ratios of a medium sized gap. The emphasis is laid upon the development of Taylor vortices out of the basic laminar flow, the transition between flow modes and the effect of eccentricities of different magnitudes. In the concentric case, the transition from the basic flow to a flow with two pairs of Taylor vortices is investigated by a steady as well as a transient analysis. The transition from the basic flow to a flow with one pair of Taylor vortices is examined by a steady analysis using a mesh that is asymmetric about the equator and also by introducing a geometrical perturbation in the form of a small eccentricity. A hysteresis for this transition is found. As the eccentricity is increased, the magnitude of the hysteresis decreases until it disappears. Comparisons of the flow patterns with experimental results show good agreement.
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47.20.Hw Morphological instability; phase changes
47.15.-x Laminar flows

Solitons induced by boundary conditions from the Boussinesq equation

Ru Ling Chou and C. K. Chu

Phys. Fluids A 2, 1574 (1990); http://dx.doi.org/10.1063/1.857564 (11 pages) | Cited 3 times

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Solitons induced by boundary excitation were first investigated numerically by Bona et al. [Philos. Trans. R. Soc. London, Ser. A 302, 457 (1981)] and by Chu et al. [Commun. Pure Appl. Math. 36, 495 (1983)] using the Korteweg–de Vries (KdV) equation. In this paper, their work is extended by considering various time‐dependent boundary conditions and different unperturbed water depths. Then solitons induced from Boussinesq equations under similar conditions are studied, in order to remove the restriction in the KdV equation of propagation in only one direction. Thus soliton head‐on collisions (as well as overtaking collisions) and reflections can be treated. The results from these two fully nonlinear equations are compared and they agree extremely well. The results of solitons induced by random boundary values are unexpected and particularly interesting.
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47.35.-i Hydrodynamic waves
41.20.Jb Electromagnetic wave propagation; radiowave propagation

The linear stability of steady circular Couette flow with a small radial temperature gradient

Jyh‐Chen Chen and Jer‐Yow Kuo

Phys. Fluids A 2, 1585 (1990); http://dx.doi.org/10.1063/1.857565 (7 pages) | Cited 10 times

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The linear stability of steady circular Couette flow with a small radial temperature gradient has been investigated. The outer cylinder is assumed stationary, while the inner cylinder is rotated with a constant angular speed. The interaction of the radial temperature gradient with both gravity and centrifugal potentials is taken into account in the formulation of the stability problem. The critical Reynolds number is found to be dependent on the ratio of the centrifugal and gravitational potentials, the Prandtl number, and the temperature difference between the cylinders. Unlike previous theoretical results, the present results agree qualitatively with those obtained experimentally.
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47.20.-k Flow instabilities
47.15.Cb Laminar boundary layers
47.32.Ef Rotating and swirling flows

Molecular‐diffusive effects in penetrative convection

H. J. S. Fernando and L. J. Little

Phys. Fluids A 2, 1592 (1990); http://dx.doi.org/10.1063/1.857566 (5 pages) | Cited 5 times

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An experimental study was performed to investigate the influence of molecular diffusion on turbulent entrainment during penetrative convection. The entrainment coefficient E was determined as a function of the Richardson number Ri and Peclet number Pe. It appears that, in parameter ranges 65<Ri<150 and 103<Pe<104, E is a function of Ri, independent of Pe, which indicates inertial‐buoyancy dominated mixing and the unimportance of molecular diffusive effects. At high interfacial stabilities, 30<Ri<300, the entrainment law was found to be given by E∼Ri−1.
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47.55.Hd Stratified flows
47.27.T- Turbulent transport processes
47.27.W- Boundary-free shear flow turbulence

Soret‐driven convection coupled to the morphology of a solid–liquid interface

Layachi Hadji and Mark Schell

Phys. Fluids A 2, 1597 (1990); http://dx.doi.org/10.1063/1.857567 (10 pages) | Cited 4 times

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The importance of Soret‐driven convection in solidification processes is illustrated through an analysis of the coupling between convective currents and the deformations in a solid–liquid interface. The interface appears on freezing an upper portion of a layer of a dilute binary fluid. The presence of the interface and the amount of the solid strongly affect the stability properties of the liquid mixture and, in turn, the state of the liquid determines the patterns formed on the interface. Marginal stability curves are constructed by plotting the critical Rayleigh number and the critical wave number against the thickness of the solid layer. At small values of a positive separation ratio, increases in the thickness of the solid layer are found to have a destabilizing effect, the static state becomes unstable at smaller values of the Rayleigh number, whereas at larger values for the separation ratio this effect disappears. As the separation ratio is increased, a change of slope at zero thickness in the solid layer, from negative to positive, occurs in the plots of the critical wave number. For the case of a sufficiently large separation ratio, a weakly nonlinear analysis leads to the prediction of a bifurcation diagram that is characterized by two regions of bistability. A stable stationary convective structure consisting of down‐hexagons appears through a subcritical bifurcation and for a small range of Rayleigh numbers coexists with the static state. Squares become stable at higher Rayleigh numbers and for a small parameter range coexist with down‐hexagons. These stationary structures, down‐hexagons and squares, are imprinted as patterns on the solid–liquid interface through the action of the convective currents. It is deduced that down‐hexagons appear as a result of the coupling of the convective motion in the melt with the deformations in the interface and do not occur in the absence of solidification.
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44.30.+v Heat flow in porous media
68.08.-p Liquid-solid interfaces
68.43.-h Chemisorption/physisorption: adsorbates on surfaces
81.10.Fq Growth from melts; zone melting and refining

The fine structure in the Strouhal–Reynolds number relationship of the laminar wake of a circular cylinder

Michael König, Holger Eisenlohr, and Helmut Eckelmann

Phys. Fluids A 2, 1607 (1990); http://dx.doi.org/10.1063/1.857568 (8 pages) | Cited 43 times

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There is experimental evidence that at least three discontinuities in the Strouhal number–Reynolds number relationship in the Reynolds number range 50–160 may exist under certain conditions. The appearance of discontinuities depends on how the cylinder is bounded at both ends, the aspect ratio, and the turbulence level of the oncoming flow. The discontinuity at Re≊90 observed by Tritton [J. Fluid Mech. 6, 547 (1959)] is therefore a three‐dimensional effect. The discontinuities in the shedding frequency are accompanied by sudden changes in the shedding angle. Parallel vortex shedding results in the highest possible shedding frequency.
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47.32.Ef Rotating and swirling flows
47.15.Cb Laminar boundary layers
47.60.-i Flow phenomena in quasi-one-dimensional systems

Axisymmetric wakes behind a slender body including zero‐momentum configurations

Hiroshi Higuchi and Toshi Kubota

Phys. Fluids A 2, 1615 (1990); http://dx.doi.org/10.1063/1.857569 (9 pages) | Cited 13 times

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An experimental investigation of turbulent axisymmetric wakes including the zero‐momentum case was carried out. Mean and fluctuation velocity profiles were measured and self‐similar profiles were observed that decayed very rapidly when the momentum was adjusted to be zero. The wake behavior was found to be sensitive to any small mismatch of momentum and the relaxation zone strongly depended on the intensity and scale of the turbulence in the initial wake.
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47.27.W- Boundary-free shear flow turbulence
47.40.Dc General subsonic flows

On the interaction between a strong vortex pair and a free surface

Peder A. Tyvand

Phys. Fluids A 2, 1624 (1990); http://dx.doi.org/10.1063/1.857570 (11 pages) | Cited 4 times

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The initial motion of a pair of strong vortices suddenly created close to a free surface is calculated analytically by means of a Taylor expansion in time. While weak vortices moving toward a free surface repel each other [see Hydrodynamics (Cambridge U.P., Cambridge, 1932)], strong vortices attract each other to the leading order. But, they cannot merge and annihilate each other because of nonlinear free‐surface effects. Several features of the solution depend on whether or not the vortices are below a critical depth. At the critical depth the two vortex points span an angle of 120° with respect to the surface center. The dominating gravitational effects are investigated.
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47.15.ki Inviscid flows with vorticity

Surface waves in closed basins under principal and autoparametric resonances

A. H. Nayfeh and J. F. Nayfeh

Phys. Fluids A 2, 1635 (1990); http://dx.doi.org/10.1063/1.857571 (14 pages) | Cited 5 times

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The method of multiple scales is used to analyze the nonlinear response of the surface of a liquid in a cylindrical container to a principal parametric resonant excitation in the presence of a two‐to‐one internal (autoparametric) resonance. Four autonomous first‐order ordinary‐differential equations are derived for the modulation of the amplitudes and phases of the two modes involved in the internal resonance when the higher mode is being excited by a principal parametric resonance. The modulation equations are used to determine the periodic oscillations and their stability. The force‐response curves exhibit the jump and saturation phenomena as well as a Hopf bifurcation, whereas the frequency‐response curves exhibit the jump phenomenon and supercritical and subcritical Hopf bifurcations. Limit‐cycle solutions of the modulation equations are found between the Hopf frequencies; they correspond to aperiodic motions of the liquid surface. All limit cycles deform and lose stability by either pitchfork or cyclic‐fold bifurcations as the excitation frequency or amplitude is varied. The pitchfork bifurcation breaks the symmetry of the limit cycles whereas the cyclic‐fold bifurcation causes cyclic jumps, which may result in a transition to chaos. Period‐three motions are found in a very narrow range of the excitation frequency.
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47.35.-i Hydrodynamic waves
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
47.52.+j Chaos in fluid dynamics

Turbulent thermal convection in a finite domain: Part I. Theory

L. Sirovich and H. Park

Phys. Fluids A 2, 1649 (1990); http://dx.doi.org/10.1063/1.857572 (10 pages) | Cited 35 times

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Determination of the empirical eigenfunctions for turbulent flows, which result from the Karhunen–Loève procedure, is considered in some generality for fully inhomogeneous flows. Group theoretical considerations are shown to lead to considerable increases in an available database. In addition, group representation procedures are shown to lead to substantial simplification. In fact, for the application considered here, a nonmanageable problem is reduced to one that is solvable. The general methods and techniques presented here are applied to the case of Rayleigh–Bénard convection in a finite box. In addition, indication is made of how to apply the procedures to several other cases. Some results of applying the method of empirical eigenfunctions to a numerical simulation of this particular flow [H. Park and L. Sirovich, Phys. Fluids A 2, 1659 (1990)] are presented here.
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47.27.T- Turbulent transport processes

Turbulent thermal convection in a finite domain: Part II. Numerical results

H. Park and L. Sirovich

Phys. Fluids A 2, 1659 (1990); http://dx.doi.org/10.1063/1.857573 (10 pages) | Cited 25 times

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A pseudospectral method is used to solve the Boussinesq equations for a fully inhomogeneous turbulent flow. The numerical data are analyzed using the empirical eigenfunction technique. As a result of the underlying inhomogeneity of the flow, the eigenfunctions (structures) are inhomogeneous in all three directions. This is the first instance in which fully three‐dimensional empirical eigenfunctions have been calculated. The generated basis set is extremely efficient at depicting the flow. The first eigenfunction captures almost 60% of the average energy. The eigenfunctions are an optimal basis for capturing the energy of the flow and more than 95% of the energy is captured by the first 100 eigenfunctions. Ten classes of eigenfunctions are present and examples of each are shown. The average Nusselt number for the bounded geometry is found to be lower than that for a correspondong homogeneous case and the physics causing this decrease is analyzed and discussed.
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47.27.T- Turbulent transport processes

Tensorial volume of turbulence revisited

S. C. Kassinos and W. C. Reynolds

Phys. Fluids A 2, 1669 (1990); http://dx.doi.org/10.1063/1.857574 (9 pages) | Cited 1 time

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A corrected tensorial turbulent volume transport equation, which is exact for uniform density flows, is derived from the Navier–Stokes equations. For homogeneous turbulence, the new terms appearing in the correct equation account for the effect of the pressure velocity correlation and of the mean velocity gradient. The correct tensorial volume equation is closed only for the case of isotropic homogeneous turbulence. To solve the equation for the anisotropic case a model for the velocity spectrum is required. When applied to the cases of isotropic expansion, incompressible axisymmetric contraction, and shearing of initially isotropic turbulence, the correct equation predicts the same time evolution for the tensorial volume that rapid distortion theory does.
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47.27.Gs Isotropic turbulence; homogeneous turbulence
47.10.-g General theory in fluid dynamics

A critical comparison of turbulence models for homogeneous shear flows in a rotating frame

Charles G. Speziale, Thomas B. Gatski, and Nessan Mac Giolla Mhuiris

Phys. Fluids A 2, 1678 (1990); http://dx.doi.org/10.1063/1.857575 (7 pages) | Cited 17 times

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A variety of turbulence models, including five second‐order closures and four two‐equation models, are tested for the problem of homogeneous turbulent shear flow in a rotating frame. The model predictions for the time evolution of the turbulent kinetic energy and dissipation rate, as well as those for the equilibrium states, are compared with the results of physical and numerical experiments. Most of the two‐equation models predict the same results for all rotation rates, in which there is an exponential time growth of the turbulent kinetic energy and dissipation rate. The second‐order closures are qualitatively superior since, consistent with physical and numerical experiments, they only predict this type of unstable flow for intermediate rotation rates in the range −0.1≤Ω/S≤0.6. For rotation rates outside this range, there is an exchange of stabilities with a solution whose kinetic energy and dissipation rate decay with time. Although the second‐order closures are superior to the two‐equation models, there are still problems with the quantitative accuracy of their predictions.
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47.27.Gs Isotropic turbulence; homogeneous turbulence

A k‐ϵ model for turbulent mixing in shock‐tube flows induced by Rayleigh–Taylor instability

Serge Gauthier and Michel Bonnet

Phys. Fluids A 2, 1685 (1990); http://dx.doi.org/10.1063/1.857576 (10 pages) | Cited 43 times

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A k‐ϵ model for turbulent mixing induced by Rayleigh–Taylor instability is described. The classical linear closure relations are supplemented with algebraic relations in order to be valid under strong gradients. Calibrations were made against two shock‐tube experiments (Andronov et al. [Sov. Phys. JETP 44, 424 (1976); Sov. Phys. Dokl. 27, 393 (1982)] and Houas et al. [Proceedings of the 15th International Symposium on Shock Waves and Shock Tubes (Stanford U.P., Stanford, CA, 1986)]) using the same set of constants. The new interpretation of the experimental data of Brouillette and Sturtevant [Physica D 37, 248 (1989)], where the mixing length is discriminated from the wall jet, requires a different numerical value for the Rayleigh–Taylor source term coefficient. A detailed physical study is given in both cases. It turns out that the spectrum is narrower in the Brouillette and Sturtevant case than in the Andronov et al. case but the small length scales are of the same magnitude.
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47.27.T- Turbulent transport processes
47.20.Hw Morphological instability; phase changes
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
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