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Oct 1989

Volume 1, Issue 10, pp. 1611-1749


A novel method to promote parallel vortex shedding in the wake of circular cylinders

M. Hammache and M. Gharib

Phys. Fluids A 1, 1611 (1989); http://dx.doi.org/10.1063/1.857306 (4 pages) | Cited 40 times

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Slanted vortex shedding dominates the wake of circular cylinders of finite aspect ratio in the Reynolds number range of 72–158. Parallel vortex shedding can be induced in the wake of a circular cylinder by imposing a symmetric pressure boundary condition at the two ends of the cylinder. This condition can be achieved by positioning two upstream circular cylinders of larger diameter normal to it. The resulting Strouhal–Reynolds number curve shows no discontinuity. Also, the turbulent transition in the wake of a circular cylinder could be delayed by using this technique.
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47.27.W- Boundary-free shear flow turbulence
47.32.Ef Rotating and swirling flows
47.27.Cn Transition to turbulence

Organized motion in a very high Reynolds number jet

M. G. Mungal and D. K. Hollingsworth

Phys. Fluids A 1, 1615 (1989); http://dx.doi.org/10.1063/1.857527 (9 pages) | Cited 27 times

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Direct visual observations of a high Reynolds number jet are presented. The jet consists of the exhaust plume of a TITAN IV rocket motor, which was discharged upward during ground‐based testing producing an estimated Reynolds number of about 2×108. An overall view of the first 2000 ft of the resulting plume is observed and discussed. Image processing is used to enhance the plume appearance and reveal significant events associated with the jet evolution. The most striking finding is the progression of organized structures up through the jet, similar to those observed in laboratory flows at Reynolds numbers of 104. Significant differences are also seen between the time‐averaged scalar field, which appears more Gaussian, and the instantaneous scalar field, which appears more top hat. It is concluded that the organization is associated with inviscid instability mechanisms that are Reynolds number independent, and that large‐scale organization is an integral part of the evolution of such flows, and not a remnant of transitional behavior.
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47.27.W- Boundary-free shear flow turbulence
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)

Combined side wall and bottom wall effects on the Stokes velocity of a disk moving broadside

Jeffrey F. Trahan, R. F. Folse, and R. G. Hussey

Phys. Fluids A 1, 1625 (1989); http://dx.doi.org/10.1063/1.857528 (7 pages) | Cited 4 times

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The effect of a solid boundary on the Stokes velocity of a circular disk of zero thickness moving broadside is known in two cases: (i) when the boundary is an infinite plane parallel to the plane of the disk, and (ii) when the boundary is a cylindrical tube of infinite length coaxial with the disk. Results are presented of an experiment in which both boundary effects are significant and it is shown that there is a smooth transition from a region in which the cylindrical side wall is dominant to a region in which the plane bottom wall is dominant. Measurements with disks of different thickness indicate that results for zero thickness can be obtained by linear extrapolation. The recent results for a sphere obtained by Sano [J. Phys. Soc. Jpn. 56, 2713 (1987)] suggest a way of obtaining an empirical correction to the side wall effect. An empirical correction to the bottom wall effect is also presented, and the two corrections are found to overlap for a significant range.
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47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.15.G- Low-Reynolds-number (creeping) flows
47.55.Hd Stratified flows

Particle distribution functions in suspensions

Jacob Rubinstein and Joseph B. Keller

Phys. Fluids A 1, 1632 (1989); http://dx.doi.org/10.1063/1.857529 (10 pages) | Cited 8 times

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Equations are derived for the temporal variation of the one‐ and two‐particle position distribution functions in a suspension. The fluid is assumed to be incompressible, viscous, and in slow motion, i.e., to be undergoing Stokes flow. External forces such as gravity are included, but Brownian motion is omitted. The resulting system of equations for the one‐particle distribution and for the mean velocity of a particle resemble the Vlasov–Poisson system for the charge density and the electric field in a plasma. The existence and uniqueness of the solution of this system is proved for a nearly uniform distribution of spherical particles. This shows that in this case the equations do not break down because of shock formation or other nonlinear effects.
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47.55.Kf Particle-laden flows
47.10.-g General theory in fluid dynamics
82.70.Kj Emulsions and suspensions

Transport of gas bubbles in capillaries

John Ratulowski and Hsueh‐Chia Chang

Phys. Fluids A 1, 1642 (1989); http://dx.doi.org/10.1063/1.857530 (14 pages) | Cited 69 times

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The pressure drop and wetting film thickness for isolated bubbles and bubble trains moving in circular and square capillaries are computed. An arclength‐angle formulation of a composite lubrication equation allows for the numerical matching of the lubrication solution of the transition region to the static profiles away from the channel wall. This technique is shown to extend the classical matched asymptotic analysis of Bretherton for circular capillaries to higher capillary numbers Ca. More importantly, it allows the study of finite bubbles, which are shown to resemble infinitely long bubbles in film thickness and pressure drop if their lengths exceed the channel width. The numerical study of bubble trains, verified by a matched asymptotic analysis, shows a surprising result that the pressure drop across one member bubble is identical to that of an isolated bubble at low capillary numbers. This analysis of square capillaries neglects azimuthal flow and is only valid for Ca>3.0×10−3. Nevertheless the film radius and pressure drop of a bubble traveling in a square capillary above this capillary number are computed. These results are conveniently summarized in a correlation for the apparent viscosity of bubbles as a function of foam texture and capillary geometry and dimension.
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47.55.Kf Particle-laden flows
47.15.G- Low-Reynolds-number (creeping) flows

The hydrodynamic interaction of two slowly evaporating spheres

Hasan N. Oguz, Andrea Prosperetti, and Dario Antonelli

Phys. Fluids A 1, 1656 (1989); http://dx.doi.org/10.1063/1.857531 (10 pages) | Cited 3 times

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The Stokes flow induced by the slow evaporation or condensation of two spheres is studied. The phase‐change velocity is prescribed and uniform over the surfaces of the spheres. Exact expressions are obtained for the streamfunction and the drag forces. Simpler expressions applicable to a variety of limit cases (distant spheres, a source and a sphere, and a sphere and a plane) are presented. When only one sphere is evaporating, depending on the distance from the other sphere, the flow may exhibit a variety of interesting behaviors such as smooth‐boundary separation, closed recirculating eddies, and infinite open eddies.
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47.15.G- Low-Reynolds-number (creeping) flows
47.55.Kf Particle-laden flows
64.70.F- Liquid-vapor transitions

Weakly nonlinear behavior of periodic disturbances in two‐layer Couette–Poiseuille flow

Yuriko Renardy

Phys. Fluids A 1, 1666 (1989); http://dx.doi.org/10.1063/1.857548 (11 pages) | Cited 16 times

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The stability of a plane Couette–Poiseuille flow consisting of two layers of different fluids is analyzed using methods of bifurcation theory. The fluids have different viscosities and densities, and there is surface tension at the interface. The center manifold theorem is used to justify the derivation of the final amplitude evolution equation. The nonlinear calculations are carried out with two alternative approaches. One approach is to keep the combined volume flux fixed, and the other is to keep the pressure gradient in the horizontal direction fixed. Numerical results are presented for some Couette flow profiles and a Poiseuille flow profile at low speeds, showing that traveling waves are supported at the interface. A computation at a high speed is also presented. The derivation and numerical results are compared with those of a formal approach, employing multiple scales, which has been used on related problems.
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47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
47.55.Hd Stratified flows
47.15.Cb Laminar boundary layers
68.03.Kn Dynamics (capillary waves)
68.05.-n Liquid-liquid interfaces

Stability of core‐annular flow in a rotating pipe

Howard H. Hu and Daniel D. Joseph

Phys. Fluids A 1, 1677 (1989); http://dx.doi.org/10.1063/1.857532 (9 pages) | Cited 6 times

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The linear stability of core‐annular flow in rotating pipes is analyzed. Attention is focused on the effects of rotating the pipe and the difference in density of the two fluids. Both axisymmetric and nonaxisymmetric disturbances are considered. Major effects of the viscosity ratio, interfacial tension, radius ratio, and Reynolds number are included. It is found that for two fluids of equal density the rotation of the pipe stabilizes the axisymmetric (n=0) modes of disturbances and destabilizes the nonaxisymmetric modes. Except for small R, where the axisymmetric capillary instability is dominant, the first azimuthal mode of disturbance ‖n‖=1 is the most unstable. When the heavier fluid is outside centripetal acceleration of the fluid in the rotating pipe is stabilizing; there exists a critical rotating speed above which the flow is stabilized against capillary instability for certain range of small R. When the lighter fluid is outside the flow is always unstable.
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47.20.-k Flow instabilities
47.55.Kf Particle-laden flows
47.32.Ef Rotating and swirling flows
47.60.-i Flow phenomena in quasi-one-dimensional systems

The effect of viscosity stratification on the stability of a free surface flow at low Reynolds number

D. S. Loewenherz and C. J. Lawrence

Phys. Fluids A 1, 1686 (1989); http://dx.doi.org/10.1063/1.857533 (8 pages) | Cited 25 times

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A zero Reynolds number approximation to the Orr–Sommerfeld equation is used to assess the effects that viscosity stratification has on the stability of a very viscous flow on an incline when surface tension is negligible. Results indicate that for a two‐layer system with uniform density, the flow is always unstable when the viscosity of the upper layer is greater than that of the lower layer, regardless of the thickness of the upper layer. The wavenumber of the fastest growing mode is on the order of the inverse of the thickness of the upper layer, implying that the instability is manifested in waves having finite wavelength, whereas previous research on this topic has focused on a long wavelength approximation. It is further shown that neutral stability is independent of the angle of inclination of the underlying slope, although the growth rate of any instability is not. The results suggest that the transverse surficial ridges, which commonly occur on the surfaces of rock glacier forms, may be the product of a flow instability arising from the differing viscosities of the layers that comprise such features.
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47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.15.G- Low-Reynolds-number (creeping) flows
47.55.Hd Stratified flows

Supercritical free‐surface flow with a stagnation point due to a submerged source

Hocine Mekias and Jean‐Marc Vanden‐Broeck

Phys. Fluids A 1, 1694 (1989); http://dx.doi.org/10.1063/1.857534 (4 pages) | Cited 16 times

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Two‐dimensional free‐surface flow produced by a submerged source in a fluid of finite depth is considered. It is assumed that there is a stagnation point on the free surface immediately above the source. The shape of the free surface and the flow of the fluid are determined numerically by series truncation for various values of the Froude number F. It is found that there is a flow for each value of F ≥1.22. In addition, a local solution is constructed to describe the flow near the stagnation point as F→∞.
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47.10.-g General theory in fluid dynamics

Turbulence spectrum of strongly conductive temperature field in a rapidly stirred fluid

J. Chasnov, V. M. Canuto, and R. S. Rogallo

Phys. Fluids A 1, 1698 (1989); http://dx.doi.org/10.1063/1.857535 (3 pages) | Cited 2 times

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In an earlier paper [Phys. Fluids 31, 2065 (1988)], a numerical simulation of a passive scalar field convected by a frozen velocity field, i.e., a velocity field with an infinite correlation time, was performed. In this paper, a simulation of a passive scalar field convected by a velocity field which is rapidly stirred at all scales of motion, i.e., a velocity field with near zero correlation time, is performed. For an energy spectrum of the form E(k)∝k−5/3, the temperature spectrum G(k) is found to obey G(k)∝k−11/3 when conductive effects are dominant. A theoretical model is proposed which obtains the above result by representing the transfer of scalar variance by an eddy conductivity, whose correlation time is limited by the correlation time of the velocity field.
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47.27.T- Turbulent transport processes
47.27.Gs Isotropic turbulence; homogeneous turbulence

Coherent structure interactions in a two‐stream plane turbulent mixing layer with impulsive acoustic excitation

Ben O. Latigo

Phys. Fluids A 1, 1701 (1989); http://dx.doi.org/10.1063/1.857557 (15 pages)

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Periodic plane acoustic waves consisting of four discrete pulses are used to trigger the Kelvin–Helmholtz (KH) instability at the origin of an initially laminar plane mixing layer. The resulting coherent large‐scale structures (CLSS) which grow and interact with their neighbors are followed downstream with hot‐wire probes traversed across the mixing layer to a Reynolds number Re=1.5×106. The Reynolds number here is based on downstream distance x and the velocity difference (U1−U2). The continuous hot‐wire time record is conditionally sampled with respect to the tone bursts and the samples are phase averaged to reveal the CLSS footprints. Optimum phase averages are obtained using an iterative correlation technique that corrects for phase jitters due to turbulence. An enhanced study of the CLSS is therefore made possible. The ensembles reveal a vivid picture of vortex pairing between the initial eddies as well as the significant role played by the CLSS in momentum transport; hence turbulence mixing.
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47.27.W- Boundary-free shear flow turbulence
47.27.T- Turbulent transport processes
47.90.+a Other topics in fluid dynamics (restricted to new topics in section 47)

On mixing in an elliptic turbulent free jet

W. R. Quinn

Phys. Fluids A 1, 1716 (1989); http://dx.doi.org/10.1063/1.857536 (7 pages) | Cited 29 times

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This paper documents the results of an experimental study of the mean flow and turbulence characteristics of a turbulent free jet of air issuing, into still air surroundings, from a sharp‐edged elliptical slot of aspect ratio 5. The measured quantities, which were obtained with hot‐wire anemometry as a flow diagnostic tool, include the mean streamwise velocity, the turbulence intensities, the Reynolds shear stress, the transport of some of the Reynolds stresses, and the flatness and skewness of the distributions of the streamwise velocity fluctuations. Two switches of the major and minor axes were observed and it was found that the jet attains an axisymmetric shape at about 30 equivalent slot diameters downstream of the exit plane. Also, the jet, compared to a turbulent free jet from a sharp‐edged round slot of the same exit area, was found to entrain ambient fluid faster both in the near and far flow fields.
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47.27.W- Boundary-free shear flow turbulence

The dynamics of low initial disturbance turbulent jets

R. E. Drubka, P. Reisenthel, and H. M. Nagib

Phys. Fluids A 1, 1723 (1989); http://dx.doi.org/10.1063/1.857537 (13 pages) | Cited 16 times

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Recent experimental results in axisymmetric free jets are discussed with an emphasis on the dynamics of their self‐forced states. The role played by the initial shear‐layer instabilities and their coupling with subsequent jet instabilities is examined to reveal key mechanisms and scaling relations.
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47.27.W- Boundary-free shear flow turbulence
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)

The absolute‐convective transition in subsonic mixing layers

S. Pavithran and L. G. Redekopp

Phys. Fluids A 1, 1736 (1989); http://dx.doi.org/10.1063/1.857496 (4 pages) | Cited 24 times

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The stability properties of subsonic mixing layers described by hyperbolic‐tangent profiles of both velocity and temperature are studied. The impulse response of the flow is examined to classify the instability as being of either absolute or convective type. The boundary of the absolute‐convective transition is defined as a function of the velocity ratio, the temperature ratio, and the Mach number.
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47.20.-k Flow instabilities
47.40.Dc General subsonic flows
47.27.W- Boundary-free shear flow turbulence

Higher‐order corrections to the axisymmetric interactions of nearly touching spheres

D. J. Jeffrey

Phys. Fluids A 1, 1740 (1989); http://dx.doi.org/10.1063/1.857497 (3 pages) | Cited 4 times

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Two unequal spheres are immersed in an axisymmetric low‐Reynolds‐number flow and are separated by a small nondimensional distance ϵ. The forces and stresslets exerted by the spheres on the fluid are calculated asymptotically to O(ϵ ln ϵ), in order to improve the convergence of numerical calculations of the same quantities. The main obstacle to the extension to O(ϵ ln ϵ) was the breakdown of the usual lubrication approach at higher orders in ϵ. The method adopted here obtains expressions for the functions of immediate interest, but does so by postponing the resolution of the fundamental difficulties until a higher order in ϵ.
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47.15.G- Low-Reynolds-number (creeping) flows

On hydrodynamic diffusion and drift in sheared suspensions

Donald L. Koch

Phys. Fluids A 1, 1742 (1989); http://dx.doi.org/10.1063/1.857498 (4 pages) | Cited 9 times

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It is shown that a migration or drift of particles induced by inhomogeneities in the average shear rate will occur in a suspension of spheres with purely hydrodynamic interactions, even in the absence of inertial effects. Two relationships between the drift velocity, the hydrodynamic tracer‐ and gradient‐diffusion coefficients for the suspended particles, and the diffusivity for a fluid‐phase chemical tracer are derived.
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05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
47.15.G- Low-Reynolds-number (creeping) flows
47.15.-x Laminar flows
47.60.-i Flow phenomena in quasi-one-dimensional systems

Eckhaus instabilities in generalized Landau–Ginzburg equations

David S. Riley and Stephen H. Davis

Phys. Fluids A 1, 1745 (1989); http://dx.doi.org/10.1063/1.857499 (3 pages) | Cited 1 time

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The effect of Eckhaus instabilities is shown to be mitigated by an increase in order of a Landau–Ginzburg equation.
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47.20.Ky Nonlinearity, bifurcation, and symmetry breaking

Nonlinear stability of a laminar flow past a two‐dimensional grid

Vincenzo Coscia

Phys. Fluids A 1, 1747 (1989); http://dx.doi.org/10.1063/1.857500 (3 pages)

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Sufficient conditions for nonlinear stability of an exact solution to the Navier–Stokes equations (Kovasznay flow) are given by use of the energy method. These results markedly improve on earlier ones obtained by Lin and Tobak [Phys. Fluids 30, 3388 (1987)].
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47.20.-k Flow instabilities
47.15.-x Laminar flows
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