Phys. Fluids A (1989-1993) - Physics of Fluids

Select this Article		The 1990 François Naftali Frenkiel Award for Fluid Mechanics Phys. Fluids A 3, 1 (1991); http://dx.doi.org/10.1063/1.3480470 (1 page) Full Text: \| Download PDF
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Remobilizing surfactant retarded fluid particle interfaces. I. Stress‐free conditions at the interfaces of micellar solutions of surfactants with fast sorption kinetics

Kathleen J. Stebe, Shi‐Yow Lin, and Charles Maldarelli

Phys. Fluids A 3, 3 (1991); http://dx.doi.org/10.1063/1.857862 (18 pages) | Cited 38 times

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Surfactant molecules adsorb onto the interfaces of moving fluid particles and are convected to regions in which the surface flow converges. Accumulation of surfactant in these regions creates interfacial tension gradients that retard the surface flow. In this study it is argued theoretically and demonstrated experimentally that fluid movement on the surface of a drop or bubble can remain unhindered in the presence of a single adsorbed surfactant if, relative to the convective rate of transport of adsorbed surfactant along the surface, desorption is fast, and the bulk concentration is high enough so that diffusion away from the particle is fast. For this circumstance, a uniform surface concentration of surfactant is maintained, and no gradients in surface tension arise to retard the surface velocity. The fluid particle flow behaves as it would in the absence of surfactant save that it has a reduced, uniform surface tension. The remobilization of surfactant‐laden interfaces of fluid particles is demonstrated experimentally in a three‐phase periodic slug flow in a capillary tube in which a train of alternating air and aqueous slugs ride on an annular wetting film of fluorocarbon oil. Surfactant, dissolved in the aqueous slug phase, adsorbs onto and retards the aqueous–oil interface. The hydrodynamics of this flow is such that small changes in the mobility of this interface create large shear rates in the oil layer. This significantly increases the pressure drop required to drive the slug train at constant velocity. Three surface adsorbers are used to demonstrate surface remobilization: The polyethoxy, nonionic surfactants Triton X‐100 and Brij‐35, which have fast desorption kinetics and do not retard the surface flow at high concentrations and, as a counter example, the desorption hindered protein bovine serum albumin, which is shown to be unable to remobilize an interface even at high concentration.

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68.03.-g	Gas-liquid and vacuum-liquid interfaces
68.05.-n	Liquid-liquid interfaces
47.60.-i	Flow phenomena in quasi-one-dimensional systems

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Measurement of the drift of a droplet due to the presence of a plane

Jeffrey R. Smart and David T. Leighton

Phys. Fluids A 3, 21 (1991); http://dx.doi.org/10.1063/1.857856 (8 pages) | Cited 26 times

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The drift of a deformable droplet of low viscosity (viscosity ratio λ=0.08) in a Couette device is examined. The drift is measured both in the plane of shear (due to the rigid outer bounding walls of the Couette device) and also normal to the plane of shear (due to the upper bounding stress‐free surface). A general relationship between normal stresses induced by the deformation of a droplet in an arbitrary shear flow and the leading‐order drift normal to rigid and stress‐free plane surfaces is described theoretically. This relationship is consistent with previous theoretical predictions for droplet migration in shear flows, and is used to compare results from the drift measurement experiments with first‐order deformation theories. The measured drift velocities are in reasonable agreement with the theory of Schowalter et al. [J. Colloid Interface Sci. 26, 152 (1968)].

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47.55.Kf	Particle-laden flows
47.15.Cb	Laminar boundary layers

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Effect of convective Mach number on mixing of coaxial circular and rectangular jets

E. Gutmark, K. C. Schadow, and K. J. Wilson

Phys. Fluids A 3, 29 (1991); http://dx.doi.org/10.1063/1.857860 (8 pages) | Cited 2 times

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Rectangular supersonic free and coaxial jets were used to enhance mixing relative to a circular jet in a convective Mach number range of 0.5 to 2.2. The different convective Mach numbers were obtained by changing the central jet gas composition, the temperatures of the inner and outer flows, and the velocity of the coaxial flow. The experimental techniques used were schlieren photography, total pressure, and gas‐sampling measurements. For all test conditions the rectangular jets showed substantial improved mixing relative to a circular jet. The free jets showed high mixing in the circumferential region of the jet while the coaxial jet had a high mixing rate inside the central jet.

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47.40.Ki	Supersonic and hypersonic flows
47.27.W-	Boundary-free shear flow turbulence
82.33.Vx	Reactions in flames, combustion, and explosions
07.68.+m	Photography, photographic instruments; xerography

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Rotating, stratified flow past a shallow ridge

Kiran B. Chilakamarri and M. R. Foster

Phys. Fluids A 3, 37 (1991); http://dx.doi.org/10.1063/1.857861 (10 pages) | Cited 1 time

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Streamline patterns in experiments performed by Boyer and Biolley [Philos. Trans. R. Soc. London Ser. A 318, 411 (1986)] on flow past a shallow ridge on the floor of a channel in a rotating, stratified fluid compare very poorly with two‐dimensional theory, even though the aspect ratio of the ridge is relatively large at 3. In the present study, it is shown that a fully three‐dimensional calculation agrees quite well with the experiments, both in terms of the qualitative form of the streamline patterns, and also with respect to a quantitative measure of streamline deflection. The equations are solved by means of Fourier series across the channel and Fourier integral in the streamwise direction. The resultant double Fourier series is truncated, and the partial sum computed by machine. The form of the solution is relatively easily extended to other obstacle shapes.

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47.32.Ef	Rotating and swirling flows
47.55.Hd	Stratified flows

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Inelastic microstructure in rapid granular flows of smooth disks

Mark A. Hopkins and Michel Y. Louge

Phys. Fluids A 3, 47 (1991); http://dx.doi.org/10.1063/1.857863 (11 pages) | Cited 122 times

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Computer simulations of two‐dimensional rapid granular flows of uniform smooth inelastic disks under simple shear reveal a dynamic microstructure characterized by the local, spatially anisotropic agglomeration of disks. A spectral analysis of the concentration field suggests that the formation of this inelastic microstructure is correlated with the magnitude of the total stresses in the flow. The simulations confirm the theoretical results of Jenkins and Richman [J. Fluid Mech. 192, 313 (1988)] for the kinetic stresses in the dilute limit and for the collisional stresses in the dense limit, when the size of the periodic domain used in the simulations is a small multiple of the disk diameter. However, the kinetic and, to a lesser extent, collisional stresses both increase significantly with the size of the periodic domain, thus departing from the predictions of the theory that assumes spatial homogeneity and isotropy.

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61.20.Ja	Computer simulation of liquid structure
46.55.+d	Tribology and mechanical contacts

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Scale transition of double‐diffusive finger cells

Colin Y. Shen and George Veronis

Phys. Fluids A 3, 58 (1991); http://dx.doi.org/10.1063/1.857864 (11 pages) | Cited 6 times

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The processes that bring about the change of cell size in the evolution of salt‐finger convection are investigated with a numerical model of the convection in a Hele–Shaw cell. It is shown that the increase of cell width during the convection is produced by the vertical penetration of increasingly wider cells from the edges of the finger zone into the interior, as has been observed in a laboratory experiment. The increase of scale is also shown to occur through the merging process in which narrow finger cells merge to form wider cells. Occasionally, transition from wide to narrow scale can occur, in which case the wide finger cell splits to form two or more narrow cells. The scale transition produced by the merging, penetration, and splitting processes is shown to have the effect of maximizing the buoyancy flux generation in an evolving finger convection. This maximization is also interpreted in terms of the most rapidly growing finger mode. The effect of the scale transition on the actual magnitude of the buoyancy flux is related to the energy dissipation of fingers.

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47.55.Kf	Particle-laden flows
47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking

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The equations of nearly incompressible fluids. I. Hydrodynamics, turbulence, and waves

G. P. Zank and W. H. Matthaeus

Phys. Fluids A 3, 69 (1991); http://dx.doi.org/10.1063/1.857865 (14 pages) | Cited 45 times

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A unified analysis delineating the conditions under which the equations of classical incompressible and compressible hydrodynamics are related in the absence of large‐scale thermal, gravitational, and field gradients is presented. By means of singular expansion techniques, a method is developed to derive modified systems of fluid equations in which the effects of compressibility are admitted only weakly in terms of the incompressible hydrodynamic solutions (hence ‘‘nearly incompressible hydrodynamics’’). Besides including molecular viscosity self‐consistently, the role of thermal conduction in an ideal fluid is also considered. With the inclusion of heat conduction, it is found that two distinct routes to incompressibility are possible, distinguished according to the relative magnitudes of the temperature, density, and pressure fluctuations. This leads to two distinct models for thermally conducting, nearly incompressible hydrodynamics—heat‐fluctuation‐dominated hydrodynamics (HFDH’s) and heat‐fluctuation‐modified hydrodynamics (HFMD’s). For the HFD case, the well‐known classical passive scalar equation for temperature is derived as one of the nearly incompressible fluid equations and temperature and density fluctuations are predicted to be anticorrelated. For HFM fluids, a new thermal transport equation, in which compressible acoustic effects are present, is obtained together with a more‐complicated ‘‘correlation’’ between temperature, density, and pressure fluctuations. Although the equations of nearly incompressible hydrodynamics are envisaged principally as being applicable to homogeneous turbulence and wave propagation in low Mach number flow, it is anticipated that their applicability is likely to be far greater.

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47.40.-x	Compressible flows; shock waves
47.27.-i	Turbulent flows
96.60.Vg	Particle emission, solar wind

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Recurrence and chaotic behavior resulting from nonlinear interaction between long and short waves

Takao Yoshinaga, Mamoru Wakamiya, and Tsunehiko Kakutani

Phys. Fluids A 3, 83 (1991); http://dx.doi.org/10.1063/1.857866 (7 pages) | Cited 4 times

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Long time asymptotic behavior resulting from nonlinear interaction between long and short waves is examined numerically by using the Fourier expansion method. A slightly modulated short wave is adopted as an initial condition. The results exhibit recurrence or chaotic motion, depending upon the magnitude of the control parameters involved in the governing equations. It is found that the chaotic motion is possible, even in a case for which only a single unstable mode exists in the Fourier modes.

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52.35.Mw	Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
02.60.-x	Numerical approximation and analysis

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An experimental investigation of the natural transition of an untuned planar jet

F. O. Thomas and K. M. K. Prakash

Phys. Fluids A 3, 90 (1991); http://dx.doi.org/10.1063/1.857867 (16 pages) | Cited 13 times

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The result of an experimental investigation into the natural near‐field transition of an untuned planar jet at moderate Reynolds number is presented. Here the term ‘‘untuned’’ refers to the case where the ratio of the thin shear layer instability frequency to the jet column frequency is not given by an integer power of 2, so that a sequence of shear layer vortex pairing or amalgamation events is incapable of yielding the jet column frequency near the end of the potential core. This case is of interest because the jet shear layer instability must undergo more dramatic frequency and phase adjustments in order to satisfy the downstream jet column constraint. This provides a unique opportunity to investigate how instabilities that scale with the jet column interact with those that scale with the nascent shear layer instability to configure the initial evolution of the natural planar jet. Auto‐bicoherence spectra are used in conjunction with conventional power spectra in order to provide quantitative measurements of the nonlinear phase coupling between wave triads that characterizes the near‐field transition of the natural planar jet. These measurements are complemented by two‐point correlation, coherence, and phase spectra that document the streamwise evolution and cross‐stream symmetry of structural patterns in the flow throughout the initial, interaction, and early self‐preserving regions. These measurements indicate that the wave interactions that characterize the planar jet near‐field transition are quite different from the sequence of subharmonic instabilities that typically characterize the planar mixing layer. In particular, suppression of the subharmonic instability and the formation of modulating sidebands are observed. The modulation occurs at the jet column frequency and the measurements suggest that this has an origin that is due to a kinematic effect associated with the lateral oscillation of the nascent shear layers near the nozzle lip. The origin of this oscillation appears fully consistent with Biot–Savart induction from the downstream region of the flow associated with the loss of symmetry of the large‐scale vorticity field.

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47.27.W-	Boundary-free shear flow turbulence
47.15.-x	Laminar flows

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Transitions toward turbulence in a curved channel

S. B. Bland and W. H. Finlay

Phys. Fluids A 3, 106 (1991); http://dx.doi.org/10.1063/1.857870 (9 pages) | Cited 10 times

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A numerical study of the transitions that occur with increasing Reynolds number in a curved channel with radius ratio η=0.875 is performed using spectral simulations of the three‐dimensional, incompressible, time‐dependent Navier–Stokes equations. Periodic boundary conditions are used in the spanwise and streamwise directions. At Reynolds number Re=6.31 Re_c temporally periodic wavy (twisting) Dean vortices occur (Re_c is the Reynolds number for the transition from laminar curved channel Poiseuille flow to steady, streamwise‐oriented Dean vortices). At Re=8.84 Re_c, a three‐frequency flow is discovered in which two new incommensurate frequencies modulate the wavy vortices. At Re=10.10 Re_c the two modulation frequencies are phase locked producing a two‐frequency modulated wavy vortex flow that is similar in some ways to that seen in Taylor–Couette flow. The spatial and temporal characteristics of the modulation frequencies are discussed.

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47.27.Cn	Transition to turbulence
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.20.-k	Flow instabilities

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Statistics of helicity fluctuations in homogeneous turbulence

Wolfgang Polifke

Phys. Fluids A 3, 115 (1991); http://dx.doi.org/10.1063/1.857871 (15 pages) | Cited 4 times

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The statistics and dynamical significance of helicity fluctuations in turbulent flows are investigated. A random‐phase or quasi‐Gaussian approximation (QGA) is employed to obtain expectation values of the magnitude of helicity fluctuations in reflectionally symmetric ensembles of turbulent flows. It is shown that the QGA is compatible with Kolmogorov‐type scaling arguments supplemented by elementary statistical considerations. If follows from the scaling properties of the viscous term in the helicity balance equation that in the absence of phase correlations helicity is an adiabatic invariant of fully developed turbulent flows. Possible consequences of this invariance for decaying flows are discussed. In direct numerical simulations of decaying and forced turbulence it is found that at large scales the fluctuations of helicity are well described by the QGA, and as such not strong enough to directly influence the energy transfer. The helicity fluctuations at large wave numbers, on the other hand, are repeatedly observed to deviate significantly from the QGA, indicating the presence of small‐scale phase coherence. The coherence seems to be sufficiently strong to break the adiabatic invariance of helicity. The nature of the observed fluctuations suggests that the invariance properties of helicity may not be held responsible for the buildup of the correlations. In the light of these results it is questionable whether helicity fluctuations can play a fundamental role in the organization or characterization of turbulent structures.

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47.27.Gs	Isotropic turbulence; homogeneous turbulence
47.10.-g	General theory in fluid dynamics
05.40.-a	Fluctuation phenomena, random processes, noise, and Brownian motion

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Lagrangian and Eulerian statistics obtained from direct numerical simulations of homogeneous turbulence

Kyle D. Squires and John K. Eaton

Phys. Fluids A 3, 130 (1991); http://dx.doi.org/10.1063/1.857872 (14 pages) | Cited 21 times

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Lagrangian statistics have been obtained from direct numerical simulations of isotropic turbulence and homogeneous shear flow. Quantities presented include properties of the dispersion tensor 〈X_i(t)X_j(t)〉, isoprobability contours of particle displacement, Lagrangian and Eulerian velocity autocorrelations and time scale ratios, and the eddy diffusivity tensor. The dispersion measurements from the simulations of isotropic turbulence are in good agreement with those of Warhaft [J. Fluid Mech. 144, 363 (1984)] and Stapountzis et al. [J. Fluid Mech. 165, 401 (1986)]. ‘‘Integral’’ time scales were defined as the time required for the temporal correlations to decrease to 1/e of their initial value. The ratio of T^e_L/T^e_E from the simulations of isotropic turbulence was approximately 0.8, in good agreement with the data of Sato and Yamamoto [J. Fluid Mech. 175, 183 (1987)]. The principal angle of 〈X_i(t)X_j(t)〉 from the shear flow simulations shows reasonable agreement with a similar study done by Riley (Ph.D. dissertation, The Johns Hopkins University, Baltimore, 1971). The Lagrangian time microscale was found to be consistently larger than the Eulerian microscale, presumably due to the advection of the small scales by the large scales in the Eulerian reference frame. A comparison made between the measured diffusivity tensor and measurements of Tavoularis and Corrsin [Int. J. Heat Mass Transfer 28, 265 (1985)] show reasonable agreement.

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47.27.Gs	Isotropic turbulence; homogeneous turbulence
82.70.Kj	Emulsions and suspensions

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The structure of a passive scalar field with a uniform mean gradient in rapidly sheared homogeneous turbulent flow

Michael M. Rogers

Phys. Fluids A 3, 144 (1991); http://dx.doi.org/10.1063/1.857873 (11 pages) | Cited 22 times

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The effect of an arbitrarily oriented mean passive scalar gradient on one‐point passive scalar statistics is studied in homogeneous turbulent shear flow in the limit of rapid shearing. By neglecting the nonlinear inertial transfer to small scales an analytical solution for individual Fourier modes is obtained for the case of unity Prandtl number. This solution is used to compute the development of one‐point statistics for the velocity and scalar fields in the inviscid limit. Comparisons to direct numerical simulations of the full nonlinear equations for the same flow show that in addition to describing the early time response to the imposed shear, the linear solution gives reasonable estimates of several correlation coefficients for the developed shear flow.

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47.27.Gs	Isotropic turbulence; homogeneous turbulence
47.27.N-	Wall-bounded shear flow turbulence

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Transport asymmetry in skewed turbulence

John C. Wyngaard and Jeffrey C. Weil

Phys. Fluids A 3, 155 (1991); http://dx.doi.org/10.1063/1.857874 (8 pages) | Cited 13 times

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Large‐eddy simulations have shown that passive, conservative scalars emitted into the convective boundary layer (CBL) of the atmosphere have unusual diffusion properties. A species introduced through an area source at the layer top and having zero flux through the bottom (i.e., one undergoing ‘‘top‐down’’ diffusion) has a well‐behaved eddy diffusivity, but one introduced at the bottom, with zero flux at the top (‘‘bottom‐up’’ diffusion) has a much different diffusivity profile in the same turbulence field. It is suggested that the roots of this transport asymmetry lie in the interaction between skewness of the transporting turbulence and the gradient of the flux of the transported scalar. A kinematic model is used to show that this interaction can indeed induce transport asymmetry in small‐time‐scale, homogeneous turbulence. The present simulations with a Lagrangian particle model confirm that this asymmetry extends to large‐time‐scale, inhomogeneous turbulence. A heuristic model of convective turbulence suggests that its asymmetric transport is also described by the kinematic model but with the small‐time‐scale restriction removed. In all cases the transport asymmetry effects scale with the parameter Sσ_wT_L/h, where S, σ_w, and T_L are the skewness, standard deviation, and Lagrangian integral time scale of the transporting turbulence, and h is the layer depth; a scalar flux gradient is required as well.

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47.20.Bp	Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
92.60.hk	Convection, turbulence, and diffusion
92.60.Fm	Boundary layer structure and processes

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Turbulence spectra in free convection flow

Nikolas E. Kotsovinos

Phys. Fluids A 3, 163 (1991); http://dx.doi.org/10.1063/1.857875 (5 pages) | Cited 8 times

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The results of a laboratory experiment to study the spectral density of temperature fluctuations in a fully developed round plume are presented. It is found that there is a range of low wave numbers K (the next to inertial subrange) where the spectra of temperature are proportional to K⁻³. The modification of turbulent spectrum at small wave numbers due to buoyancy forces in free convection flow is discussed.

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47.20.Bp	Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
47.55.Hd	Stratified flows

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Stochastic geometric properties of scalar interfaces in turbulent jets

Paul L. Miller and Paul E. Dimotakis

Phys. Fluids A 3, 168 (1991); http://dx.doi.org/10.1063/1.857876 (10 pages) | Cited 26 times

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Experiments were conducted in which the behavior of scalar interfaces in turbulent jets was examined, using laser‐induced fluorescence (LIF) techniques. The experiments were carried out in a high Schmidt number fluid (water), on the jet centerline, over a jet Reynolds number range of 1000≤Re≤24 000. Both two‐dimensional scalar data, c(r,t) at fixed x/d, and one‐dimensional scalar data, c(t) at fixed x/d and r/x, were analyzed using standard one‐ and two‐dimensional fractal box‐counting algorithms. Careful treatment was given to the handling of noise. Both long and short records as well as off‐centerline measurements were also investigated. The important effect of threshold upon the results is discussed. No evidence was found of a constant (power‐law) fractal dimension over the range of Reynolds numbers studied. On the other hand, the results are consistent with the computed behavior of a simple stochastic model of interface geometry.

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47.27.W-	Boundary-free shear flow turbulence
02.50.Ey	Stochastic processes
07.57.Ty	Infrared spectrometers, auxiliary equipment, and techniques
07.60.Rd	Visible and ultraviolet spectrometers
02.60.Gf	Algorithms for functional approximation

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Dynamic response of boundary‐layer turbulence to oscillatory shear

G. J. Brereton and W. C. Reynolds

Phys. Fluids A 3, 178 (1991); http://dx.doi.org/10.1063/1.857877 (10 pages) | Cited 11 times

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The temporal response of a well‐developed turbulent boundary layer to the superposition of oscillatory shear has been measured experimentally, over a wide range of frequencies. The response is primarily a periodic organization in magnitude of components of the turbulent velocity field at the forcing frequency. Oscillatory production of turbulence arises predominantly as a modulation of the mean production process in the parent boundary layer. Close to the wall, the relative phases of response of components of turbulent kinetic energy indicate that temporal redistribution of turbulent kinetic energy is driven by robust coherent motions of the underlying mean flow. The local directions of redistribution deduced from these measurements indicate a wall impingement (splatting) effect, consistent with characterizations from numerical simulation.

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47.27.N-	Wall-bounded shear flow turbulence
47.27.T-	Turbulent transport processes

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Simulation of the Kolmogorov inertial subrange using an improved subgrid model

Jeffrey R. Chasnov

Phys. Fluids A 3, 188 (1991); http://dx.doi.org/10.1063/1.857878 (13 pages) | Cited 69 times

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A subgrid model is developed and applied to a large‐eddy simulation of the Kolmogorov inertial subrange. Currently popular subgrid models are derived from models of the turbulent energy equation, resulting in a significant loss of information as a consequence of the statistical averaging performed in going from the Navier–Stokes equation to the energy equation. The subgrid model developed here is based directly on a model of the Navier–Stokes equation. The improved subgrid model contains two terms: an eddy viscosity and a stochastic force. These terms are computed from the EDQNM stochastic model representation of the momentum equation, and from a fully resolved direct numerical simulation. Use of the subgrid model in a forced large‐eddy simulation results in an energy spectrum that exhibits a clear k⁻⁵^/³ power‐law subrange with an approximate value Ko=2.1 of the Kolmogorov constant.

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47.27.-i	Turbulent flows
92.10.Lq	Turbulence, diffusion, and mixing processes in oceanography
92.60.hk	Convection, turbulence, and diffusion

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Shock wave driven by a phased implosion

R. Menikoff, K. S. Lackner, N. L. Johnson, S. A. Colgate, J. M. Hyman, and G. A. Miranda

Phys. Fluids A 3, 201 (1991); http://dx.doi.org/10.1063/1.857854 (18 pages) | Cited 3 times

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In this paper the theory of an axially phased radial implosion of a channel is developed. When the phase velocity of the implosion exceeds the sound velocity inside the channel, a planar shock wave traveling along the channel axis can develop. For the energy of the implosion system in the appropriate range, the theory predicts a stable steady‐state flow configuration. The effect of the phased implosion is for the channel wall to form a nozzle that travels along the channel axis. The flow behind the axial shock is well described by the equations for nozzle flow with an additional dynamical degree of freedom for the shape of the wall. Experiments presented here verify the theoretical predictions. The numerical simulations show the formation of the axial shock during start‐up and the approach to steady state to be in good agreement with experiment and theory. A potential application of the axially phased implosion is the design of a super shock tube.

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47.40.-x	Compressible flows; shock waves
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.60.Kz	Flows and jets through nozzles

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Steady, isentropic flows of dense gases

M. S. Cramer and L. M. Best

Phys. Fluids A 3, 219 (1991); http://dx.doi.org/10.1063/1.857855 (8 pages) | Cited 15 times

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Steady isentropic flows of fluids in their dense gas regime are examined. It is shown that the Mach number may increase, rather than decrease, with density or pressure if the specific heats of the fluid are sufficiently large. Conditions are also reported under which isentropic expansions through converging–diverging nozzles are not possible, regardless of the imposed exit pressure. In such cases, the nozzle must be replaced with one having multiple throats. Applications to external transonic flows are briefly considered.

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47.40.-x	Compressible flows; shock waves
47.60.Kz	Flows and jets through nozzles

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On unsteady flows through two sequentially connected Laval nozzles

Martin Rein and Klaus Ehrenfried

Phys. Fluids A 3, 227 (1991); http://dx.doi.org/10.1063/1.857857 (4 pages)

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The flow through two sequentially connected Laval nozzles depends on the ratio of the two throat cross sections. If the second throat is wider than the first one, two different cases are distinguishable. In steady flows solutions with a single shock can occur if the second throat is relatively wide. Within a certain range of exit pressures, two different one‐shock solutions are possible. Under these conditions the shock position depends hysteretically on the exit pressure. If the second throat is only slightly wider than the first one, either a one‐ or a two‐shock solution can be present for the same exit pressure. The unsteady transition between these solutions that can be caused by a variation of the exit pressure with time, is investigated.

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47.40.Nm	Shock wave interactions and shock effects
47.60.Kz	Flows and jets through nozzles
47.40.Hg	Transonic flows

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On falling‐film instabilities and wave breaking

S. W. Joo, S. H. Davis, and S. G. Bankoff

Phys. Fluids A 3, 231 (1991); http://dx.doi.org/10.1063/1.857858 (2 pages) | Cited 10 times

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Long‐wave instabilities of thin viscous films flowing down inclined planes are studied. Numerical solutions of the full long‐wave evolution equation show that wave profiles grow superexponentially and evolve toward breaking when the surface tension takes on realistically small values. This contrasts with the solutions of the Kuramoto–Sivashinsky equation, which do not tend toward breaking. The use of the full equation thus dispenses with the need to introduce the formally small curvature terms into the Kuramoto–Sivashinsky equation, as suggessted by Rosenau and Oron [Phys. Fluids A 1, 1763 (1989)].

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47.20.-k	Flow instabilities
47.35.-i	Hydrodynamic waves
68.15.+e	Liquid thin films
68.03.Cd	Surface tension and related phenomena

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Normalization for a turbulent boundary layer with wall suction

L. Fulachier, F. Anselmet, T. Benabid, and R. A. Antonia

Phys. Fluids A 3, 233 (1991); http://dx.doi.org/10.1063/1.857859 (3 pages) | Cited 3 times

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When a moderate suction rate is applied at the wall of a turbulent boundary layer, the normalized distributions of the Reynolds stresses, temperature variance, and heat fluxes in the inner region are analogous to those obtained without suction, provided the normalization is based on local maxima of the Reynolds shear stress and turbulent heat flux instead of the wall shear stress and the wall heat flux.

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