Phys. Fluids (1994-Present) - Physics of Fluids

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On the evolution of maximum turbulent kinetic energy production in a channel flow

F. Laadhari

Phys. Fluids 14, L65 (2002); http://dx.doi.org/10.1063/1.1511731 (4 pages) | Cited 11 times

Online Publication Date: 6 September 2002

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The Reynolds number effects on turbulent kinetic energy production and mean transport terms in near-wall turbulent channel flow are investigated analytically and with the help of direct numerical simulations (DNS). Using the momentum equation for turbulent channel flow, an analytical expression for the envelope of turbulent kinetic energy production curves is derived. It is shown that this envelope coincides with the wall-normal position at which the turbulent and viscous shear stress are equal. The DNS results carried out corroborate this finding and assess other quantitative details, namely the evolution of the peak of kinetic energy production and of its wall-normal position in terms of the Reynolds number. Empirical relations for the envelopes of the mean momentum transport terms and for their extrema position are also derived. © 2002 American Institute of Physics.

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47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.27.E-	Turbulence simulation and modeling

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Continuous chain of bubbles in concentrated polymeric solutions

Igor L. Kliakhandler

Phys. Fluids 14, 3375 (2002); http://dx.doi.org/10.1063/1.1501284 (5 pages) | Cited 4 times

Online Publication Date: 16 August 2002

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Motion of bubbles in a liquid is a ubiquitous yet very nontrivial phenomenon. The available body of knowledge and even its language connotation consider bubbles only as a discrete, detached from each other, units. It turns out that in concentrated polymer solutions bubbles may form a qualitatively new structure. The experimental study reported below shows that bubbles may form a very stable, continuous, slowly rising, connected long chain similar to beads, or bubble “sausage.” © 2002 American Institute of Physics.

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47.55.D-	Drops and bubbles
47.50.-d	Non-Newtonian fluid flows

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An experimental and numerical study of the spatial evolution of unidirectional nonlinear water-wave groups

Lev Shemer, Eliezer Kit, and Haiying Jiao

Phys. Fluids 14, 3380 (2002); http://dx.doi.org/10.1063/1.1501908 (11 pages) | Cited 7 times

Online Publication Date: 16 August 2002

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Spatial evolution of nonlinear narrow-spectrum deep-water wave groups is studied experimentally in a wave tank. The experimental results are compared with the computations based on the unidirectional Zakharov equation and the Dysthe model. The very good agreement between the computational results based on both models with the experiments prompted an attempt to perform simulations for a wider initial spectral width, that formally violate the assumptions adopted in the derivation of the Dysthe model. The accuracy of the results based on the Dysthe model is checked against the solutions of the Zakharov equation, which is free of restrictions on the spectral width. Conclusions regarding the domain of validity of the Dysthe model are drawn. © 2002 American Institute of Physics.

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47.35.-i	Hydrodynamic waves
92.10.Hm	Ocean waves and oscillations

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Experimental study of wave characteristics on a thin layer of de/anti-icing fluid

S. Özgen, M. Carbonaro, and G. S. R. Sarma

Phys. Fluids 14, 3391 (2002); http://dx.doi.org/10.1063/1.1501282 (12 pages) | Cited 2 times

Online Publication Date: 28 August 2002

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Several series of experiments were conducted in order to investigate wave formation and wave characteristics on a thin layer of de/anti-icing fluid using a nonintrusive technique. The configuration consists of a thin layer of de/anti-icing fluid deposited on the lower wall of the wind tunnel section, sheared by a turbulent airflow. Beyond a critical value of the wind speed, two-dimensional surface waves could be observed. The characteristics of these waves like the wavelength and the wave speed could be measured using the light absorption technique. The main purpose of the study is to augment the already existing experimental data for wave characteristics of Newtonian liquid layers in the literature. The non-Newtonian character and the high viscosities of the fluids used render these experiments and their results original. The results obtained from the experiments have been compared with the results of an already existing code utilizing linear stability theory and the agreement was seen to be very good provided that the liquid film is not too thin. © 2002 American Institute of Physics.

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47.35.-i

Hydrodynamic waves

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A glimpse of hydrodynamics beyond the Navier–Stokes equations

D. Baganoff

Phys. Fluids 14, 3403 (2002); http://dx.doi.org/10.1063/1.1502659 (11 pages)

Online Publication Date: 28 August 2002

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A solution of Maxwell’s moment equations is obtained for the steady, one-dimensional flow through a normal shock wave in a Maxwellian gas. The solution method makes use of a new representation for the conservation equations, a closure relation for a single third-order moment, and a spatially integrated form of Maxwell’s equations of transfer. The integrated equations of transfer act as constraints in evaluating two sets of coefficients introduced in the conservation equations and the single closure relation. A total of only four coefficients are found to be fully sufficient when comparisons are made with results from the direct simulation Monte Carlo method, which show excellent agreement across all hydrodynamic variables including two fourth-order moments which the theory predicts. © 2002 American Institute of Physics.

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47.10.-g

General theory in fluid dynamics

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The influence of developed cavitation on the flow of a turbulent shear layer

Claudia O. Iyer and Steven L. Ceccio

Phys. Fluids 14, 3414 (2002); http://dx.doi.org/10.1063/1.1501541 (18 pages) | Cited 18 times

Online Publication Date: 28 August 2002

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Developed cavitation in a shear layer was studied experimentally in order to determine the effect that the growth and collapse of cavitation have on the dynamics of shear flows. Planar particle imaging velocimetry (PIV) was used to measure the velocity field, the vorticity, strain rates, and Reynolds stresses of the flow downstream of the cavitating and noncavitating shear layer; the flow pressures and void fraction were also measured. The flow downstream of a cavitating shear flow was compared to the noncavitating shear flow. For cavitating shear layers with void fractions of up to 1.5%, the growth rate of the shear layer and the mean flow downstream of the shear layer were modified by the growth and collapse of cavitation bubbles. The cross-stream velocity fluctuations and the Reynolds stresses measured downstream of the cavitating shear layer were reduced compared to the entirely noncavitating flow. This result is inconsistent with a scaling of the shear stress within the shear flow based on the mean flow. The decrease in the cross-stream fluctuations and Reynolds stresses suggests that the cavitation within the cores of strong streamwise vortices has decreased the coupling between the streamwise and cross-stream velocity fluctuations. © 2002 American Institute of Physics.

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47.27.nb	Boundary layer turbulence
47.55.dp	Cavitation and boiling
47.32.C-	Vortex dynamics
47.55.D-	Drops and bubbles

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Instabilities and drop formation in cylindrical liquid jets in reduced gravity

A. P. R. Edwards, B. P. Osborne, J. M. Stoltzfus, T. Howes, and T. A. Steinberg

Phys. Fluids 14, 3432 (2002); http://dx.doi.org/10.1063/1.1501825 (7 pages) | Cited 2 times

Online Publication Date: 3 September 2002

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The effects of convective and absolute instabilities on the formation of drops formed from cylindrical liquid jets of glycerol/water issuing into still air were investigated. Medium-duration reduced gravity tests were conducted aboard NASA’s KC-135 and compared to similar tests performed under normal gravity conditions to aid in understanding the drop formation process. In reduced gravity, the Rayleigh–Chandrasekhar Equation was found to accurately predict the transition between a region of absolute and convective instability as defined by a critical Weber number. Observations of the physics of the jet, its breakup, and subsequent drop dynamics under both gravity conditions and the effects of the two instabilities on these processes are presented. All the normal gravity liquid jets investigated, in regions of convective or absolute instability, were subject to significant stretching effects, which affected the subsequent drop and associated geometry and dynamics. These effects were not displayed in reduced gravity and, therefore, the liquid jets would form drops which took longer to form (reduction in drop frequency), larger in size, and more spherical (surface tension effects). Most observed changes, in regions of either absolute or convective instabilities, were due to a reduction in the buoyancy force and an increased importance of the surface tension force acting on the liquid contained in the jet or formed drop. Reduced gravity environments allow better investigations to be performed into the physics of liquid jets, subsequently formed drops, and the effects of instabilities on these systems. In reduced gravity, drops form up to three times more slowly and as a consequence are up to three times larger in volume in the theoretical absolute instability region than in the theoretical convective instability region. This difference was not seen in the corresponding normal gravity tests due to the masking effects of gravity. A drop is shown to be able to form and detach in a region of absolute instability, and spanning the critical Weber number (from a region of convective to absolute instability) resulted in a marked change in dynamics and geometry of the liquid jet and detaching drops. © 2002 American Institute of Physics.

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47.27.wg	Turbulent jets
47.20.Dr	Surface-tension-driven instability
47.20.Bp	Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
47.55.D-	Drops and bubbles
47.27.T-	Turbulent transport processes

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Effects of vertical vibration on hopper flows of granular material

C. R. Wassgren, M. L. Hunt, P. J. Freese, J. Palamara, and C. E. Brennen

Phys. Fluids 14, 3439 (2002); http://dx.doi.org/10.1063/1.1503354 (10 pages) | Cited 14 times

Online Publication Date: 3 September 2002

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The discharge of granular material from a hopper subject to vertical sinusoidal oscillations was investigated using experiments and discrete element computer simulations. With the hopper exit closed, side-wall convection cells are observed, oriented such that particles move up along the inclined walls of the hopper and down at the center line. The convection cells are a result of the granular bed dilation during free fall and the subsequent interaction with the hopper walls. The mass discharge rate for a vibrating hopper scaled by the discharge rate without vibration reaches a maximum value at a dimensionless velocity amplitude just greater than 1. Further increases in the velocity decrease the discharge rate. This decrease occurs due to a decrease in the bulk density of the discharging material when vibration is applied. © 2002 American Institute of Physics.

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47.55.Kf	Particle-laden flows
45.70.Mg	Granular flow: mixing, segregation and stratification
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.35.-i	Hydrodynamic waves
47.27.T-	Turbulent transport processes
47.80.-v	Instrumentation and measurement methods in fluid dynamics
47.11.-j	Computational methods in fluid dynamics

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A technique for real-time visualization of flow structure in high-speed flows

Brian Thurow, James Hileman, Walter Lempert, and Mo Samimy

Phys. Fluids 14, 3449 (2002); http://dx.doi.org/10.1063/1.1503802 (4 pages) | Cited 10 times

Online Publication Date: 3 September 2002

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A newly developed MHz rate imaging system that provides real-time flow visualization is described. The technique utilizes a custom-built Nd:YAG pulse burst laser and an ultra high-speed digital camera and is capable of capturing 17 images over 150 microseconds. The system was used to visualize a Mach 1.3 (M_c = 0.6) axisymmetric jet. Sample results indicate the potential of the technique to provide detailed information on the dynamic characteristics of large-scale structures. A two-dimensional cross-correlation technique was used to calculate the convective velocity of large-scale structures. Present results generally agree with the findings of earlier investigations that indicate a significant deviation of the convective velocity from theoretical predictions. © 2002 American Institute of Physics.

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47.80.-v	Instrumentation and measurement methods in fluid dynamics
47.40.Ki	Supersonic and hypersonic flows
42.60.By	Design of specific laser systems
42.62.-b	Laser applications
47.27.wg	Turbulent jets

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Structure functions and energy dissipation dependence on Reynolds number

G. Boffetta and G. P. Romano

Phys. Fluids 14, 3453 (2002); http://dx.doi.org/10.1063/1.1504449 (6 pages) | Cited 4 times

Online Publication Date: 3 September 2002

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The dependence of the statistics of energy dissipation on the Reynolds number is investigated in an experimental jet flow. In a range of about one decade of Re_λ (from about 200 to 2000) the adimensional mean energy dissipation is found to be independent on Re_λ, while the higher moments of dissipation show a power-law dependence. The scaling exponents are found to be consistent with a simple prediction based on the multifractal model for inertial range structure functions. This is an experimental confirmation of the connection between inertial range quantities and dissipation statistics predicted by the multifractal approach. © 2002 American Institute of Physics.

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47.27.wg	Turbulent jets
47.11.-j	Computational methods in fluid dynamics
05.45.Df	Fractals

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Near wake of an impulsively started disk

H. Johari and K. Stein

Phys. Fluids 14, 3459 (2002); http://dx.doi.org/10.1063/1.1502267 (16 pages) | Cited 2 times

Online Publication Date: 5 September 2002

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The near wake of an impulsively started disk was studied computationally by a finite element code with a Smagorinsky turbulence model. The shear layer separating from the disk lip rolled up into a symmetric starting vortex ring at first. As time evolved, the vortex stretched in the downstream direction and flow instabilities caused the vortex ring to become wavy eventually leading to the breakup of the ring. The complete breakup and shedding of the starting vortex ring took a time of approximately 14D/U, where D is the disk diameter and U is the freestream velocity. The starting vortex ring circulation attained a plateau of ≈ 2.6UD at a time of about 4D/U, in good agreement with the experimental findings by Balligand (2000). The radial circulation profiles are Gaussian during the symmetric phase and collapse together at a time of 4D/U. Beyond this time, the vortex ring celerity is constant and vorticity extends to the symmetry axis. The base pressure coefficient becomes positive as the vortex ring moves away from the disk and remains positive until the ring is completely shed. The breakup of the starting vortex ring is concurrent with the appearance of an azimuthal pressure gradient and core flow. Following the breakup of the starting vortex ring, the flow became three-dimensional and settled into an open wake. The mean drag and base pressure coefficients were nearly constant after a time of approximately 30D/U and matched very well against experimental data. © 2002 American Institute of Physics.

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47.27.wb	Turbulent wakes
47.27.-i	Turbulent flows
47.32.C-	Vortex dynamics
47.20.-k	Flow instabilities
02.70.Dh	Finite-element and Galerkin methods

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Transient growth in Taylor–Couette flow

Hristina Hristova, Sébastien Roch, Peter J. Schmid, and Laurette S. Tuckerman

Phys. Fluids 14, 3475 (2002); http://dx.doi.org/10.1063/1.1502658 (10 pages) | Cited 6 times

Online Publication Date: 5 September 2002

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Transient growth due to non-normality is investigated for the Taylor–Couette problem with counter-rotating cylinders as a function of aspect ratio η and Reynolds number Re. For all Re ⩽ 500, transient growth is enhanced by curvature, i.e., is greater for η<1 than for η = 1, the plane Couette limit. For fixed Re<130 it is found that the greatest transient growth is achieved for η between the Taylor–Couette linear stability boundary, if it exists, and one, while for Re>130 the greatest transient growth is achieved for η on the linear stability boundary. Transient growth is shown to be approximately 20% higher near the linear stability boundary at Re = 310, η = 0.986 than at Re = 310, η = 1, near the threshold observed for transition in plane Couette flow. The energy in the optimal inputs is primarily meridional; that in the optimal outputs is primarily azimuthal. Pseudospectra are calculated for two contrasting cases. For large curvature, η = 0.5, the pseudospectra adhere more closely to the spectrum than in a narrow gap case, η = 0.99. © 2002 American Institute of Physics.

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47.32.C-	Vortex dynamics
47.15.-x	Laminar flows
47.20.-k	Flow instabilities

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Impact of water drops on small targets

A. Rozhkov, B. Prunet-Foch, and M. Vignes-Adler

Phys. Fluids 14, 3485 (2002); http://dx.doi.org/10.1063/1.1502663 (17 pages) | Cited 21 times

Online Publication Date: 5 September 2002

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The collision of water drops against small targets was studied experimentally by means of a high-speed photography technique. The drop impact velocity was about 3.5 m/s. Drop diameters were in the range of 2.8–4.0 mm. The target was a stainless steel disk of 3.9 mm diameter. The drop spread beyond the target like a central cap surrounded by a thin, slightly conical lamella bounded by a thicker rim. By mounting a small obstacle near the target, surface-tension driven Mach waves in the flowing lamella were generated, which are formally equivalent to the familiar compressibility driven Mach waves in gas dynamics. From the measurement of the Mach angle, the values of some flow parameters could be obtained as functions of time, which provided insight into the flow structure. The liquid flowed from the central cap to the liquid rim through the thin lamella at constant momentum flux. At a certain stage of the process, most of the liquid accumulated in the rim and the internal part of the lamella became metastable. In this situation, a rupture wave propagating through the metastable internal part of the lamella caused the rim to retract while forming outwardly directed secondary jets. The jets disintegrated into secondary droplets due to the Savart–Plateau–Rayleigh instability. Prior to the end of the retraction, an internal circular wave of rupture was formed. It originated at the target and then it propagated to meet the retracting rim. Their meeting resulted in a crown of tiny droplets. A theoretical analysis of the ejection process is proposed. © 2002 American Institute of Physics.

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47.55.D-	Drops and bubbles
47.80.-v	Instrumentation and measurement methods in fluid dynamics
68.08.Bc	Wetting
47.35.-i	Hydrodynamic waves
42.65.Re	Ultrafast processes; optical pulse generation and pulse compression
07.68.+m	Photography, photographic instruments; xerography
47.27.wg	Turbulent jets
47.40.-x	Compressible flows; shock waves

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Streaming flows in a channel with elastic walls

I. V. Shugan, N. N. Smirnov, and J. C. Legros

Phys. Fluids 14, 3502 (2002); http://dx.doi.org/10.1063/1.1504081 (10 pages)

Online Publication Date: 5 September 2002

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The two-way coupling model for wave motion in a two-phase medium “fluid–elastic walls” accounting for interaction between those phases is considered within the frames of the boundary layer type approximation. An asymptotic linearized model including Navier–Stokes equations for the viscous incompressible fluid and the deformable plate motion equations for elastic walls is analyzed within a wide range of governing parameters variations. The dispersion relationship for different Reynolds numbers shows different oscillation regimes. The structure of the fluid flow is studied in detail for the two asymptotic limit cases of high and low Reynolds numbers. The results show that the intensity of fluid mass transfer induced in a fluid-filled channel with vibrating walls increases when increasing the vibrational Reynolds number. Contrary to the existing opinion, which considers the traveling wave regime of wall oscillations to be the basic mechanism generating the fluid flow, it is proved that the mean flux induced by standing waves could surpass the flux induced by the traveling waves in a range of one order of Reynolds number. © 2002 American Institute of Physics.

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47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.55.Kf	Particle-laden flows

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Cavitation inception following shock wave passage

C. D. Ohl

Phys. Fluids 14, 3512 (2002); http://dx.doi.org/10.1063/1.1503351 (10 pages) | Cited 14 times

Online Publication Date: 5 September 2002

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Cavitation bubble nucleation following the passage of an extracorporeal shock wave lithotripter pulse is investigated experimentally and numerically. In the experiments two configurations are considered: Free passage of the shock wave, and reflection of the shock wave from a rigid reflector. The nucleation and the early growth phase of the bubbles including radial and translatory motion is compared with a commonly used model for bubble dynamics, the Gilmore model, which is coupled to a one-dimensional model for translatory motion. Reasonable agreement is found for the predicted translatory motion of the bubble center; however, considerable disagreement between a simple cavitation inception theory and the experiment exists: Cavitation bubbles expand later than predicted pointing to a more complex inception scenario than a single stabilized gas pocket. A hypothesis is proposed to explain the delayed growth of the bubbles. Additional findings are the formation of bands with diminished bubble activity, which very much resemble the structure found by Sokolov et al. (2001). High-speed photographs suggest that bubble–bubble interaction plays an important role in the formation of structured bands. © 2002 American Institute of Physics.

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47.55.dp	Cavitation and boiling
47.40.Nm	Shock wave interactions and shock effects
47.55.D-	Drops and bubbles

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Effective-medium theories for predicting hydrodynamic transport properties of bidisperse suspensions

Sangkyun Koo and Ashok S. Sangani

Phys. Fluids 14, 3522 (2002); http://dx.doi.org/10.1063/1.1503352 (12 pages) | Cited 4 times

Online Publication Date: 5 September 2002

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Effective-medium theories for predicting conditionally averaged velocity field and hydrodynamic transport coefficients of monodisperse suspensions are extended to bidisperse suspensions. The predictions of the theory are shown to agree very well with the results of direct numerical simulations of bidisperse suspensions with hard-sphere configurations up to volume fractions at which phase separation in bidisperse hard-sphere systems are observed. © 2002 American Institute of Physics.

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47.55.Kf	Particle-laden flows
82.70.Kj	Emulsions and suspensions
64.75.-g	Phase equilibria
61.20.Gy	Theory and models of liquid structure
02.60.Cb	Numerical simulation; solution of equations

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Radial oscillations of encapsulated microbubbles in viscoelastic liquids

Damir B. Khismatullin and Ali Nadim

Phys. Fluids 14, 3534 (2002); http://dx.doi.org/10.1063/1.1503353 (24 pages) | Cited 33 times

Online Publication Date: 5 September 2002

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The small-amplitude radial oscillations of a gas microbubble encapsulated by a viscoelastic solid shell and surrounded by a slightly compressible viscoelastic liquid are studied theoretically. The Kelvin–Voigt and 4-constant Oldroyd models are used to describe the viscoelastic properties of the shell and liquid, respectively. The equation for radial oscillation is derived using the method of matched asymptotic expansions. Based on this equation, we present the expressions for damping coefficients and scattering cross sections at the fundamental frequency and at twice that frequency. The numerical maximization of the amplitude-frequency response function shows that the resonance frequency for the encapsulated microbubble highly depends on viscous damping, and therefore, significantly differs from the undamped natural frequency. The effects of the shell and liquid parameters on the resonance frequency and scattering cross sections are analyzed. © 2002 American Institute of Physics.

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47.55.D-	Drops and bubbles
47.35.-i	Hydrodynamic waves
47.50.-d	Non-Newtonian fluid flows

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Interfacial gravity currents. II. Wave excitation

A. P. Mehta, B. R. Sutherland, and P. J. Kyba

Phys. Fluids 14, 3558 (2002); http://dx.doi.org/10.1063/1.1503355 (12 pages) | Cited 11 times

Online Publication Date: 5 September 2002

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We examine the response of a two- and three-layer salt-stratified fluid to the collapse of a mixed region intruding along the middle layer. For sufficiently deep middle layers, the intrusion (an interfacial gravity current) excites a double-humped solitary wave appearing in the interfacial layer in front of the intrusion head. When the solitary wave is generated the current stops propagating. Trailing the intrusion are large-amplitude trapped internal waves. We study the effect of middle-layer depth and density difference to determine the conditions under which a solitary wave is generated. We propose that this transition occurs because the intrusion resonantly couples with trapped internal waves for a sufficiently thick interface.© 2002 American Institute of Physics.

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47.35.-i	Hydrodynamic waves
47.55.Hd	Stratified flows

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Experimental study of gravity-driven dense suspension jets

Maxime Nicolas

Phys. Fluids 14, 3570 (2002); http://dx.doi.org/10.1063/1.1504447 (7 pages) | Cited 11 times

Online Publication Date: 5 September 2002

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This article presents experimental results from a study of a jet of dense suspension falling under gravity in a quiescent liquid bath of miscible liquid. The initial jet velocity v₀ scales with the square of the initial jet diameter. Four different flow behaviors are observed. The jet remains cylindrical and stable when viscous forces are dominant. A capillary-like instability with formation of blobs occurs when a Reynolds number based on the particle diameter and a free-falling velocity is over unity. The blobs are stable and settle without changing shape only for a blob Reynolds number below a critical number. Dispersion of the jet particles is observed when the particle Reynolds number is over 1, and an atomization behavior occurs when particle inertia is large compared to viscous forces, i.e., when the Stokes number of the particles is large compared to unity. © 2002 American Institute of Physics.

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47.55.Kf	Particle-laden flows
47.27.wg	Turbulent jets
47.20.-k	Flow instabilities

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Potential model of a two-dimensional Bunsen flame

Bruno Denet

Phys. Fluids 14, 3577 (2002); http://dx.doi.org/10.1063/1.1504448 (7 pages) | Cited 6 times

Online Publication Date: 5 September 2002

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The Michelson–Sivashinsky equation, which models the nonlinear dynamics of premixed flames, has been recently extended to describe oblique flames. This approach was extremely successful to describe the behavior on one side of the flame, but some qualitative effects involving the interaction of both sides of the front were left unexplained. We use here a potential flow model, first introduced by Frankel, to study numerically this configuration. Furthermore, this approach allows us to provide a physical explanation of the phenomena occuring in this geometry by means of an electrostatic analogy. © 2002 American Institute of Physics.

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47.70.Fw	Chemically reactive flows
82.33.Vx	Reactions in flames, combustion, and explosions

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A stirrer for magnetohydrodynamically controlled minute fluidic networks

Shizhi Qian, Jianzhong Zhu, and Haim H. Bau

Phys. Fluids 14, 3584 (2002); http://dx.doi.org/10.1063/1.1504713 (9 pages) | Cited 15 times

Online Publication Date: 5 September 2002

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Magnetohydrodynamics may potentially provide a convenient means for controlling fluid flow and stirring fluids in minute fluidic networks. The branches of such fluidic networks consist of conduits with rectangular cross sections. Each conduit has two individually controlled electrodes positioned along opposing walls and additional disk-shaped electrodes deposited in the conduit’s interior away from its sidewalls. The network is positioned in a uniform magnetic field. When one applies a potential difference between a disk-shaped electrode and two wall electrodes acting in tandem, circulatory motion is induced in the conduit. When the potential difference alternates periodically across two or more such configurations, complicated (chaotic) motions evolve. As the period of alternation increases, so does the complexity of the flow. We derive a two-dimensional, time-independent expression for the magnetohydrodynamic creeping flow around a centrally positioned disk-shaped electrode in the limit of zero radius. With the aid of this expression, the trajectories of passive tracers are computed as functions of the alternations protocol and the electrodes’ locations. The theoretical results are qualitatively compared with flow visualization experiments. © 2002 American Institute of Physics.

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47.85.L-	Flow control
47.65.-d	Magnetohydrodynamics and electrohydrodynamics
47.32.-y	Vortex dynamics; rotating fluids
47.52.+j	Chaos in fluid dynamics

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An evaluation of linear instability waves as sources of sound in a supersonic turbulent jet

Kamran Mohseni, Tim Colonius, and Jonathan B. Freund

Phys. Fluids 14, 3593 (2002); http://dx.doi.org/10.1063/1.1501545 (8 pages) | Cited 8 times

Online Publication Date: 5 September 2002

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Mach wave radiation from supersonic jets is revisited to better quantify the extent to which linearized equations represent the details of the actual mechanism. To this end, we solve the linearized Navier–Stokes equations (LNS) with precisely the same mean flow and inflow disturbances as a previous direct numerical simulation (DNS) of a perfectly expanded turbulent M = 1.92 jet [Freund et al., AIAA J. 38, 2023 (2000)]. We restrict our attention to the first two azimuthal modes, n = 0 and n = 1, which constitute most of the acoustic field. The direction of peak radiation and the peak Strouhal number matches the DNS reasonably well, which is in accord with previous experimental justification of the linear theory. However, it is found that the sound pressure level predicted by LNS is significantly lower than that from DNS. In order to investigate the discrepancy, individual frequency components of the solution are examined. These confirm that near the peak Strouhal number, particularly for the first helical mode n = 1, the amplification of disturbances in the LNS closely matches the DNS. However, away from the peak frequency (and generally for the azimuthal mode n = 0), modes in the LNS are damped while those in the DNS grow at rates comparable to those at the peak Strouhal number. © 2002 American Institute of Physics.

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47.27.wg	Turbulent jets
47.40.Ki	Supersonic and hypersonic flows
47.20.-k	Flow instabilities

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Instability of time-dependent wind-driven ocean gyres

Paul C. F. van der Vaart, Henk M. Schuttelaars, Daniel Calvete, and Henk A. Dijkstra

Phys. Fluids 14, 3601 (2002); http://dx.doi.org/10.1063/1.1503804 (15 pages) | Cited 4 times

Online Publication Date: 5 September 2002

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The wind-driven ocean circulation at midlatitudes is susceptible to several types of instabilities. One of the simplest models of these flows is the quasigeostrophic barotropic potential vorticity equation in an idealized ocean basin. In this model, the route to complex spatio/temporal flows is through successive bifurcations. The aim of this study is to describe the physics of the destabilization process of a periodic wind-driven flow associated with a secondary bifurcation. Although bifurcation theory has proven to be a valuable tool to determine the physical mechanisms of destabilization of fluid flows, the analysis of the stability of time-dependent (for example, periodic) flows, using this methodology, is computationally unpractical, due to the large number of degrees-of-freedom involved. The approach followed here is to construct a low-order model using numerical Galerkin projection of the full model equations onto the dynamically active eigenmodes. The resulting reduced model is shown to capture the local dynamics of the full model. The physical mechanism of the destabilization of the periodic wind-driven flow is deduced from the reduced model. While there are several stabilizing processes, notably rectification, the destabilization occurs due to time-dependent increase of the background horizontal shear in the flow. © 2002 American Institute of Physics.

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92.10.af	Thermohaline convection
92.60.Gn	Winds and their effects
47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking

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Vector level identity for dynamic subgrid scale modeling in large eddy simulation

Youhei Morinishi and Oleg V. Vasilyev

Phys. Fluids 14, 3616 (2002); http://dx.doi.org/10.1063/1.1504450 (8 pages) | Cited 12 times

Online Publication Date: 5 September 2002

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The most commonly used dynamic subgrid scale model is based on the Smagorinsky eddy viscosity model with the model coefficient computed dynamically through the tensor level identity by Germano et al. However, the tensor level identity does not explicitly account for the effect of the discretization of the governing equations, and thus the computational results strongly depend on grid resolution, especially in a simulation with poor resolution. In this paper, we propose a new dynamic procedure with the vector level identity, which takes the effect of grid resolution into consideration. The new procedure is tested for the dynamic Smagorinsky eddy viscosity model with the vector level identity. All computational tests were done on turbulent channel flow. The numerical results confirm that the mean velocity profile computed using the new subgrid scale model does not depend on the grid resolution. © 2002 American Institute of Physics.

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47.11.-j	Computational methods in fluid dynamics
47.27.E-	Turbulence simulation and modeling
47.60.-i	Flow phenomena in quasi-one-dimensional systems

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A new variational approach to gas flow in a rotating system

Richard J. Babarsky, Ira W. Herbst, and Houston G. Wood

Phys. Fluids 14, 3624 (2002); http://dx.doi.org/10.1063/1.1504451 (17 pages) | Cited 3 times

Online Publication Date: 5 September 2002

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Onsager’s classic treatment of axisymmetric, stationary flow in a rapidly rotating centrifuge is based on the theorem of minimum entropy production. For the case of end-driven flows, this approach yields a sixth-order, self-adjoint equation (the “pancake” equation) for a master potential, χ, whose second-order radial derivative is equivalent to axial mass flow. This formulation allows for a straightforward application of mass flow conditions on the axial boundaries, and χ provides a theoretical foundation for describing axial mass-driven flow in a centrifuge. Alternatively, several authors have described axisymmetric flow in a centrifuge by a sixth-order partial differential equation for temperature. So far, however, there has been no established theoretical connection between Onsager’s minimum principle and the thermal problem. This topic is considered in this paper and the corresponding derivation also results in a self-adjoint problem, in this case in terms of a temperature potential, Φ. Moreover, it may be shown that the corresponding variational form of the thermal problem is equivalent to the original Onsager entropy integral. The resulting Euler equation in the temperature potential Φ gives rise to a radial operator, M₆, which, in terms of the composition of fundamental third-order operators (i.e., M₆ = L₃L3∗ where L₃ is the radial shear operator and L3∗ is the radial heat flux operator), is the commutation of the original “pancake” operator, L₆ (i.e., L₆ = L3∗L₃). Furthermore, based on this relationship, M₆ and L₆ are shown to be isospectral except for the point 0, which is an eigenvalue of M₆ but not of L₆. © 2002 American Institute of Physics.

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