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Previous Issue

Dec 1989

Volume 1, Issue 12, pp. 1911-2064


Simulations of turbulent thermal convection

L. Sirovich, S. Balachandar, and M. R. Maxey

Phys. Fluids A 1, 1911 (1989); http://dx.doi.org/10.1063/1.857516 (4 pages) | Cited 24 times

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A direct numerical simulation of thermal convection between horizontal plane boundaries has been performed, at a Rayleigh number Ra=9800 Rac, where Rac is the critical Rayleigh number for the onset of convection (Pr=0.72). The flow is found to be fully turbulent and analysis of the probability distributions for temperature fluctuations indicates that this is within the ‘‘hard turbulence’’ regime, as defined by the Chicago group. Good agreement is shown to exist between their experiments and the present simulation.
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47.27.T- Turbulent transport processes
44.25.+f Natural convection
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

On the effective viscosity of a nondilute emulsion of two Stokes fluids with small capillary number

T. Miloh and Y. Benveniste

Phys. Fluids A 1, 1915 (1989); http://dx.doi.org/10.1063/1.857517 (11 pages) | Cited 1 time

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A rigorous analytical framework is presented for the computation of the effective viscosity of a neutrally buoyant nondilute emulsion of two immiscible Newtonian Stokes fluids. The capillary number, which is a relative measure of viscous forces that tend to distort the drop and of the interfacial tension that favors sphericity, is assumed to be small. Thus drop distortion is ignored to first order and sphericity is preserved under small shear rates. The so‐called ‘‘direct method,’’ which does not involve any energy concepts, is used and also is shown to be equivalent to the traditional approach based on the dissipation function. The micromechanics model is based on the ‘‘generalized self‐consistent model’’ commonly used in composite media. At low concentrations the present theoretical prediction reduces to Taylor’s formula [Proc. R. Soc. London Ser. A 138, 41 (1932)] and is also compared against other approximate theories and experimental data for the nondilute case. The agreement is in general surprisingly good. The present model is also shown to fall between some existing bounds, which result from the application of various variational principles. A critical comparison between these bounds is also given.
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82.70.Kj Emulsions and suspensions
47.40.-x Compressible flows; shock waves

Shear stabilization of the capillary breakup of a cylindrical interface

Mathew J. Russo and Paul H. Steen

Phys. Fluids A 1, 1926 (1989); http://dx.doi.org/10.1063/1.857518 (12 pages) | Cited 10 times

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A cylindrical interface containing a viscous liquid set into axial motion is subject to a capillary and to a surface‐wave instability. Clues from previous studies suggest that, even though both mechanisms separately are destabilizing, under certain circumstances their mutual interaction can lead to a stable interface; shear can stabilize capillary breakup. These clues lead the authors to consider an axial flow through an annular cross section bounded on the inside by a rigid rod and on the outside by a deformable interface. The competition between the two mechanisms is studied through the temporal growth of infinitesimal axisymmetric and nonaxisymmetric disturbances. This examination of temporal stability shows that, indeed, for geometries corresponding to thin annular layers both instabilities can be completely suppressed—disturbances of all wavelengths decay.
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47.20.-k Flow instabilities
68.03.Cd Surface tension and related phenomena
68.03.-g Gas-liquid and vacuum-liquid interfaces

Convection in rotating binary mixtures. III. Galerkin models

Jayanta K. Bhattacharjee

Phys. Fluids A 1, 1938 (1989); http://dx.doi.org/10.1063/1.857519 (11 pages) | Cited 2 times

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A few‐mode Galerkin truncation is used to set up Lorenz models for convection in rotating binary mixtures. Idealized as well as realistic boundary conditions are treated. An extended model to handle Küppers–Lortz instability is studied. For idealized boundary conditions the nonlinear terms cause the Hopf bifurcation to the traveling wave state to be backward. Finite amplitude traveling waves are expected for negative values of the separation parameter. For Prandtl numbers less than unity, a codimension three‐point should be seen. The amplitude equation near the codimension three‐point is discussed. Realistic boundary conditions, however, make the possibility of observing the codimension three‐point remote, even in 3He–4He mixtures.
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47.27.T- Turbulent transport processes
47.32.Ef Rotating and swirling flows
47.20.-k Flow instabilities

The film formation dynamics in spin coating

Taku Ohara, Yoichiro Matsumoto, and Hideo Ohashi

Phys. Fluids A 1, 1949 (1989); http://dx.doi.org/10.1063/1.857520 (11 pages) | Cited 20 times

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Thin film formation using the process of spin coating is investigated. The liquid film and surrounding gas phase two‐dimensional (2‐D) full governing equations with applicable boundary conditions are formulated. The heat and mass transfer that occurs in the gas and liquid phase and across the free surface, including the evaporation of solvent, are taken into account. The governing equations and boundary conditions are then reduced to a 1‐D case based on the variables radial dependency. The detailed film formation process that commences at the start of the spinning and ends with the dry‐up of the coated film is numerically simulated by utilizing the 1‐D governing equations. The complex effects of various process parameters, e.g., spinning speed, initial solute concentration, and disk heating, are clarified by the present numerical analysis. It was found that the final film thickness is mainly determined at the time when the film thinning rate resulting from radial convection has the same order as the film thinning rate resulting from solvent evaporation.
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85.40.Bh Computer-aided design of microcircuits; layout and modeling
44.30.+v Heat flow in porous media
68.15.+e Liquid thin films
66.20.-d Viscosity of liquids; diffusive momentum transport

The effects of streamwise vortices on transition in the plane channel

Bart A. Singer, Helen L. Reed, and Joel H. Ferziger

Phys. Fluids A 1, 1960 (1989); http://dx.doi.org/10.1063/1.857521 (12 pages) | Cited 6 times

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The effect of streamwise vorticity on the three‐dimensional breakdown of two‐dimensional Tollmien–Schlichting waves in a plane‐channel flow is studied via direct numerical simulation. Streamwise vortices of the strength inherent to most transition experiments are shown to alter the relative importance of the subharmonic and fundamental modes and to explain discrepancies observed between theory, previous computations, and experiments in both the plane channel and in the flat‐plate boundary layer. It is shown that without the inclusion of the vortices, the computations support the theory; with inclusion of the vortices, the computations support the experiments. This work demonstrates the importance of combining theory, experiments, and computations in the study of transition in both internal and external applications.
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47.60.-i Flow phenomena in quasi-one-dimensional systems
47.20.-k Flow instabilities
47.15.Cb Laminar boundary layers

Onset of turbulence in oscillating flow at low Womersley number

U. H. Kurzweg, E. R. Lindgren, and B. Lothrop

Phys. Fluids A 1, 1972 (1989); http://dx.doi.org/10.1063/1.857469 (4 pages) | Cited 14 times

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Measurements on the onset of turbulence in oscillating flow of water in small diameter tubes are presented. Observations, based upon the streaming birefringence method, show that the heretofore observed radius independent onset criterion for turbulence fails to hold as the tube radius and oscillation frequency become small. In particular, it is found that with decreasing values of Womersley number, oscillating flows become increasingly stable.
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47.27.Cn Transition to turbulence
47.60.-i Flow phenomena in quasi-one-dimensional systems

Upstream advancing columnar disturbances in two‐dimensional stratified flow of finite depth

Hideshi Hanazaki

Phys. Fluids A 1, 1976 (1989); http://dx.doi.org/10.1063/1.857470 (12 pages) | Cited 15 times

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A numerical study of the two‐dimensional flow of linearly stratified Boussinesq fluid past a vertical flat plate in a channel of finite depth is described. It is found that there are time‐dependent oscillations in each vertical mode of the upstream advancing columnar disturbances which correspond to the unsteadiness in the drag coefficient found in previous experiments. The long‐time behavior of the upstream columnar disturbances shows that the time‐averaged strength of each mode approaches some constant value that is not zero. This determines the drag coefficient in the long‐time limit. In many points the numerical solutions of the Navier–Stokes equation agree with the solutions of the forced Korteweg–de Vries (KdV) equation with a cubic nonlinear term or the forced KdV–Burgers equation. It is also suggested that the strong downstream columnar disturbances predicted by linear theory for steady flow do not exist.
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47.35.-i Hydrodynamic waves
47.55.Hd Stratified flows

The interaction between a counter‐rotating vortex pair in vertical ascent and a free surface

Daniel L. Marcus and Stanley A. Berger

Phys. Fluids A 1, 1988 (1989); http://dx.doi.org/10.1063/1.857471 (13 pages) | Cited 10 times

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The inviscid, two‐dimensional interaction between a pair of counter‐rotating line vortices and a free surface has been studied. A solution to the linearized, small‐disturbance problem has been thoroughly explored. For the nonlinear problem numerical calculations were carried out for Froude numbers representing a range of very weak to very strong vortices. Strong vortices are little affected by the presence of the surface, rising to form a bubblelike disturbance; weaker vortices follow paths like vortices approaching a plane boundary. The experimentally observed scarring phenomena—surface depressions whose axes are perpendicular to the flow plane—are seen in the numerical results.
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47.27.W- Boundary-free shear flow turbulence
47.32.Ef Rotating and swirling flows
47.35.-i Hydrodynamic waves

On the interaction of vortex rings and pairs with a free surface for varying amounts of surface active agent

L. P. Bernal, A. Hirsa, J. T. Kwon, and W. W. Willmarth

Phys. Fluids A 1, 2001 (1989); http://dx.doi.org/10.1063/1.857472 (4 pages) | Cited 29 times

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Observations are reported of the interaction with a free surface of vortex rings and vortex pairs moving normal to the surface when different amounts of surface active agents are present on the surface. At a vortex ring Reynolds number Γ/ν≈3800, the interaction with a contaminated free surface results in the generation of secondary and tertiary vortex rings that limited the outward motion of the vortex ring core. When the experiment was repeated with a cleaner surface the formation of the secondary vortex ring was delayed so that the outward motion and stretching of the vortex ring core was much more than for the contaminated surface. At a Reynolds number Γ/ν≈18 000, the vortex pair was observed to rebound from the free surface contrary to what one would expect for an inviscid flat boundary. When the surface was cleaned by draining away a portion of the contaminated surface water the amount of rebound was reduced. These changes in interaction are believed to be caused by the reduction in concentration of the surface active agent which, in turn, results in a reduced generation of secondary vorticity ahead of the vortex ring or pair before and during the interaction with the surface.
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47.32.Ef Rotating and swirling flows
68.03.Cd Surface tension and related phenomena
68.03.-g Gas-liquid and vacuum-liquid interfaces

Numerical calculation of stable three‐dimensional tertiary states in grooved‐channel flow

Cristina H. Amon and Anthony T. Patera

Phys. Fluids A 1, 2005 (1989); http://dx.doi.org/10.1063/1.857473 (5 pages) | Cited 33 times

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Numerical simulations of the early transition process in periodic grooved‐channel flow are presented. For Reynolds numbers, R<Rc,1 =O(100), the two‐dimensional steady flow is stable to all disturbances; at R=Rc,1 the flow undergoes a supercritical Hopf bifurcation to a nonlinear two‐dimensional steady‐periodic state; for R>Rc,2 >Rc,1 the wavy two‐dimensional flow is unstable to a classical linear three‐dimensional secondary instability; and for some range of Reynolds number above Rc,2 the secondary instability saturates in a steady‐periodic, three‐dimensional, low‐order equilibrium. The three‐dimensional equilibria owe their existence and stability to the narrow band nature of grooved‐channel‐flow secondary instability, which in turn reflects the low‐Reynolds‐number supercritical form of the grooved‐channel‐flow primary bifurcation. The contrast between the low‐order, weak transition in ‘‘inflectional’’ complex‐geometry channels and the abrupt, snap‐through transition in (subcritical‐primary broadband‐secondary) planar channels illustrates the important role of primary criticality in the early transition process.
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47.27.Cn Transition to turbulence
47.27.N- Wall-bounded shear flow turbulence
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking

The curvature of material surfaces in isotropic turbulence

S. B. Pope, P. K. Yeung, and S. S. Girimaji

Phys. Fluids A 1, 2010 (1989); http://dx.doi.org/10.1063/1.857474 (9 pages) | Cited 31 times

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Direct numerical simulation is used to study the curvature of material surfaces in isotropic turbulence. The Navier–Stokes equation is solved by a 643 pseudospectral code for constant‐density homogeneous isotropic turbulence, which is made statistically stationary by low‐wavenumber forcing. The Taylor‐scale Reynolds number is 39. An ensemble of 8192 infinitesimal material surface elements is tracked through the turbulence. For each element, a set of exact ordinary differential equations is integrated in time to determine, primarily, the two principal curvatures k1 and k2. Statistics are then deduced of the mean‐square curvature M= (1)/(2) (k21+k22), and of the mean radius of curvature R=(k21+k22)−1/2. Curvature statistics attain an essentially stationary state after about 15 Kolmogorov time scales. Then the area‐weighted expectation of R is found to be 12η, where η is the Kolmogorov length scale. For moderate and small radii (less than 10η) the probability density function (pdf) of R is approximately uniform, there being about 5% probability of R being less than η. The uniformity of the pdf of R, for small R, implies that the expectation of M is infinite. It is found that the surface elements with large curvatures are nearly cylindrical in shape (i.e., ‖k1‖≫‖k2‖ or ‖k2‖≫‖k1‖), consistent with the folding of the surface along nearly straight lines. Nevertheless the variance of the Gauss curvature K=k1k2 is infinite.
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47.27.Gs Isotropic turbulence; homogeneous turbulence
82.33.Vx Reactions in flames, combustion, and explosions
47.90.+a Other topics in fluid dynamics (restricted to new topics in section 47)

Sweeping decorrelation in isotropic turbulence

Shiyi Chen and Robert H. Kraichnan

Phys. Fluids A 1, 2019 (1989); http://dx.doi.org/10.1063/1.857475 (6 pages) | Cited 50 times

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Tennekes [J. Fluid Mech. 67, 561 (1975)] estimated the time decorrelation of inertial‐range excitation in isotropic turbulence by assuming effective statistical independence of the one‐time distributions of inertial‐range and energy‐range excitation. This picture has been challenged by Yakhot, Orszag, and She [Phys. Fluids A 1, 184 (1989)], who studied forced turbulence by renormalization‐group (RNG) methods. The analysis given in the present paper leads to the conclusion that (a) precise coherence between energy‐range and inertial‐range excitation is needed to inhibit sweeping effects; (b) in the case of randomly forced turbulence, this coherence is impossible and Tennekes’ picture is unavoidable; and (c) the RNG analysis does not demonstrate inhibition of sweeping; instead, it discards sweeping effects at the outset. To augment the present study, an advected passive scalar is examined by computer simulation. Sweeping effects on small scales survive even in the case of long‐time advection by a frozen velocity field. The observed probability distributions resemble those for the alignment of vorticity and velocity observed in flow simulations.
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47.27.Gs Isotropic turbulence; homogeneous turbulence
47.27.T- Turbulent transport processes
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

The dynamics of helical decaying turbulence

Wolfgang Polifke and Leonid Shtilman

Phys. Fluids A 1, 2025 (1989); http://dx.doi.org/10.1063/1.857476 (9 pages) | Cited 24 times

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The dynamics of helical decaying homogeneous turbulence is investigated in direct numerical simulations at moderate Reynolds numbers. A new initialization procedure is presented that allows one to control both the energy and the helicity spectral density of the initial flow field. It is observed that large initial helicity impedes the transfer of energy toward smaller scales, inhibits the buildup of enstrophy, and reduces dissipation for several turnover times. Also, the skewness and flatness of the velocity derivatives reach values typical of turbulence much later than in comparable flows without helicity. However, these effects are significant only if the helicity of the flow is quite high. In simulations with small or vanishing initial helicity it is found that the fluctuations of the average helicity and the helicity spectral density lie within the range suggested by a quasi‐Gaussian approximation. This suggests that at moderate Reynolds number spontaneous fluctuations of helicity are not large enough to directly influence the energy transfer.
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47.27.Gs Isotropic turbulence; homogeneous turbulence

Passive scalar tagging for the study of coherent structures in the plane mixing layer

B. R. Ramaprian, N. D. Sandham, M. G. Mungal, and W. C. Reynolds

Phys. Fluids A 1, 2034 (1989); http://dx.doi.org/10.1063/1.857477 (8 pages)

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Data obtained from the two‐dimensional numerical simulation of a plane mixing layer have been used to study the feasibility of tagging one side of the flow by a passive scalar and using the instantaneous concentration of the scalar to detect the typical coherent events in the flow. The study has shown that this technique works quite satisfactorily and yields results similar to those obtained by using the instantaneous vorticity as a detection criterion. The contribution from the coherent events to the time‐averaged turbulent momentum and scalar transport has been estimated. It is found that this contribution is of the same order as the time‐mean transport during most of the dynamical evolution of the coherent structure. However, it may attain very large values for short periods of time in the neighborhood of pairing. The increase is particularly spectacular in the case of the Reynolds shear stress. While the present findings obtained from a two‐dimensional simulation seem to support earlier results obtained from actual experiments, it is desirable to conduct additional studies with three‐dimensional simulations when they become available.
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47.27.-i Turbulent flows

Numerical analysis of the Poiseuille and thermal transpiration flows between two parallel plates on the basis of the Boltzmann equation for hard‐sphere molecules

Taku Ohwada, Yoshio Sone, and Kazuo Aoki

Phys. Fluids A 1, 2042 (1989); http://dx.doi.org/10.1063/1.857478 (8 pages) | Cited 117 times

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The Poiseuille and thermal transpiration flows of a rarefied gas between two parallel plates are investigated on the basis of the linearized Boltzmann equation for hard‐sphere molecules and diffuse reflection boundary condition. The velocity distribution functions of the gas molecules as well as the gas velocity and heat flow profiles and mass fluxes are obtained for the whole range of the Knudsen number with good accuracy by the numerical method recently developed by the authors.
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47.45.-n Rarefied gas dynamics
51.10.+y Kinetic and transport theory of gases

Kinetic theory for binary mixtures of smooth, nearly elastic spheres

J. T. Jenkins and F. Mancini

Phys. Fluids A 1, 2050 (1989); http://dx.doi.org/10.1063/1.857479 (8 pages) | Cited 69 times

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Existing Chapman–Enskog solution procedures for binary mixtures of hard, perfectly elastic spheres are extended to hard, slightly dissipative spheres, and the associated constitutive relations are calculated. Then a steady, homogeneous shear flow is analyzed and the behavior of the mixture viscosity is determined as the diameter ratio, volume ratio, and total volume fraction are varied.
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51.10.+y Kinetic and transport theory of gases
45.05.+x General theory of classical mechanics of discrete systems

Unified Kadomtsev–Petviashvili equation

Xue‐Nong Chen

Phys. Fluids A 1, 2058 (1989); http://dx.doi.org/10.1063/1.857480 (3 pages) | Cited 3 times

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The problem of shallow water waves propagating over slowly varying topography is considered. The fluid is assumed to be weakly viscous and the effects of viscosity can be considered only in the boundary layer on the bottom. By the methods of multiple scales and matched asymptotics, the Boussinesq theory is extended for this problem and a unified Kadomtsev–Petviashvili equation is obtained, in which viscous, topographic, and transverse modulational effects are incorporated.
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47.35.-i Hydrodynamic waves
47.15.Cb Laminar boundary layers

Energy transfer in turbulence

George Treviño

Phys. Fluids A 1, 2061 (1989); http://dx.doi.org/10.1063/1.857481 (4 pages)

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It is theoretically established that energy transfer in nonhomogeneous turbulence occurs in two distinct scale‐independent ‘‘modes.’’ The physical significance of these modes is examined. Further, evidence is presented that suggests the existence of a conservation principle that governs the transfer of energy between turbulence eddies of differing size. A possible algebraic form of such a principle is formulated.
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47.27.-i Turbulent flows
47.55.-t Multiphase and stratified flows
47.10.-g General theory in fluid dynamics
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