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Jul 2002

Volume 14, Issue 7, pp. L45-L56, 2029-2581

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Stokes-flow instability due to interfacial surfactant

Alexander L. Frenkel and David Halpern

Phys. Fluids 14, L45 (2002); http://dx.doi.org/10.1063/1.1483838 (4 pages) | Cited 26 times

Online Publication Date: 20 May 2002

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The linear stability of a two-fluid shear flow with an insoluble surfactant on the flat interface is investigated in the Stokes approximation. Gravity is neglected in order to isolate the Marangoni effect of the surfactant. In contrast to all earlier studies of related fluid systems, we encounter (i) the destabilization (here, of a shear flow) caused solely by the introduction of an interfacial surfactant and (ii) the destabilization (here, of a system with a surfactant) caused solely by the imposition of a Stokes flow. Asymptotic long-wave expressions for the growth rates are obtained. © 2002 American Institute of Physics.
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47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)

Experimental studies on the shape and path of small air bubbles rising in clean water

Mingming Wu and Morteza Gharib

Phys. Fluids 14, L49 (2002); http://dx.doi.org/10.1063/1.1485767 (4 pages) | Cited 33 times

Online Publication Date: 23 May 2002

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This Letter reports experiments on the shape and path of air bubbles (diameter range 0.1–0.2 cm) rising in clean water. We find that bubbles in this diameter range have two steady shapes, a sphere and an ellipsoid, depending on the size of the capillary tube from which they detach. The spherical bubbles move significantly slower than the ellipsoidal ones of equivalent volume. Bubbles with diameter less than about 0.15 cm rise rectilinearly. The larger spherical bubbles follow zigzag paths while the larger ellipsoidal bubbles follow spiral paths. © 2002 American Institute of Physics.
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47.55.D- Drops and bubbles

Onset of the second wake: Dependence on the Reynolds number

Peter Vorobieff, Daniel Georgiev, and Marc S. Ingber

Phys. Fluids 14, L53 (2002); http://dx.doi.org/10.1063/1.1486450 (4 pages) | Cited 4 times

Online Publication Date: 31 May 2002

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The second wake transition occurs in the far wake of a bluff body. This transition destroys the Bénard–von Kármán vortex street originating in the near wake and produces a secondary vortex street with a lower characteristic frequency. We characterize the onset of the second wake for Reynolds numbers 50<Re<800 in a nearly two-dimensional soap film flow. The dimensionless distance between the cylinder and the onset of the second wake decreases with Reynolds number consistently with Re−1/2 power law. Our two-dimensional far-wake numerical simulations are in good agreement with the experiment. © 2002 American Institute of Physics.
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47.27.wb Turbulent wakes
47.32.C- Vortex dynamics
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Mechanical imperfections effect on the minimum volume stability limit of liquid bridges

M. Gómez, I. E. Parra, and J. M. Perales

Phys. Fluids 14, 2029 (2002); http://dx.doi.org/10.1063/1.1476780 (14 pages) | Cited 3 times

Online Publication Date: 13 May 2002

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The bifurcation to unstable equilibrium shapes in the neighborhood of the minimum volume stability limit of liquid bridges has been described by using the Lyapunov–Schmidt technique. Prior to the bifurcation analysis, the stability limits of axisymmetric liquid bridges (both that of maximum and that of minimum volume) have been analytically calculated when the liquid bridge supports are two circular, coaxial disks. The interface shapes have been parametrically described and the parameters corresponding to the marginally stable shapes have been determined in terms of elliptic variables. Bifurcation equations have been obtained analytically describing the behavior near the critical points previously calculated and the effect of small axisymmetric imperfections has been considered. The considered imperfections are inequality in the diameter of the supporting disks, small body forces due to an axial gravity, and liquid bridge rotation as a solid body. © 2002 American Institute of Physics.
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47.20.Ky Nonlinearity, bifurcation, and symmetry breaking

Dynamic wall modeling for large-eddy simulation of complex turbulent flows

Meng Wang and Parviz Moin

Phys. Fluids 14, 2043 (2002); http://dx.doi.org/10.1063/1.1476668 (9 pages) | Cited 54 times

Online Publication Date: 17 May 2002

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The efficacy of large-eddy simulation (LES) with wall modeling for complex turbulent flows is assessed by considering turbulent boundary-layer flows past an asymmetric trailing-edge. Wall models based on turbulent boundary-layer equations and their simpler variants are employed to compute the instantaneous wall shear stress, which is used as approximate boundary conditions for the LES. It is demonstrated that, as first noted by Cabot and Moin [Flow Turb. Combust. 63, 269 (2000)], when a Reynolds-averaged Navier–Stokes type eddy viscosity is used in the wall-layer equations with nonlinear convective terms, its value must be reduced to account for only the unresolved part of the Reynolds stress. A dynamically adjusted mixing-length eddy viscosity is used in the turbulent boundary-layer equation model, which is shown to be considerably more accurate than the simpler wall models based on the instantaneous log law. This method predicts low-order velocity statistics in good agreement with those from the full LES with resolved wall-layers, at a small fraction of the original computational cost. In particular, the unsteady separation near the trailing-edge is captured correctly, and the prediction of surface pressure fluctuations also shows promise. © 2002 American Institute of Physics.
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47.27.-i Turbulent flows
47.27.nb Boundary layer turbulence
47.10.-g General theory in fluid dynamics

Miscible displacements in capillary tubes: Influence of Korteweg stresses and divergence effects

Ching-Yao Chen and Eckart Meiburg

Phys. Fluids 14, 2052 (2002); http://dx.doi.org/10.1063/1.1481507 (7 pages) | Cited 26 times

Online Publication Date: 17 May 2002

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The question is addressed as to whether Korteweg stresses and/or divergence effects can potentially account for discrepancies observed between conventional Stokes flow simulations (Chen and Meiburg) and experiments (Petitjeans and Maxworthy) for miscible flows in capillary tubes. An estimate of the vorticity and stream function fields induced by the Korteweg stresses is presented, which shows these stresses to result in the formation of a vortex ring structure near the tip of the concentration front. Through this mechanism the propagation velocity of the concentration front is reduced, in agreement with the experimental observations. Divergence effects, on the other hand, are seen to be very small, and they have a negligible influence on the tip velocity. As a result, we can conclude that they are not responsible for the discrepancies between experiments and conventional Stokes simulations. © 2002 American Institute of Physics.
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47.55.Kf Particle-laden flows
47.60.-i Flow phenomena in quasi-one-dimensional systems

Thermomagnetic convection of magnetic fluids in a cylindrical geometry

Adrian Lange

Phys. Fluids 14, 2059 (2002); http://dx.doi.org/10.1063/1.1480264 (6 pages) | Cited 4 times

Online Publication Date: 17 May 2002

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The thermomagnetic convection of magnetic fluids in a cylindrical geometry subjected to a homogeneous magnetic field is studied. The study is motivated by a novel thermal instability [W. Luo et al., Phys. Rev. Lett. 82, 4134 (1999)]. As model system a composite cylinder with inner heating is considered which reflects the symmetry of the experimentally setup. The general condition for the existence of a potentially unstable stratification in the magnetic fluid is derived. Within a linear stability analysis the critical external induction for the onset of thermomagnetic convection is determined for dilute and nondilute magnetic fluids. The difference between both thresholds allows to test experimentally whether a test sample is a dilute fluid or not. © 2002 American Institute of Physics.
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47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.27.T- Turbulent transport processes

Some characteristics of entrainment at a cylindrical turbulence boundary

Joseph Mathew and Amit J. Basu

Phys. Fluids 14, 2065 (2002); http://dx.doi.org/10.1063/1.1480831 (8 pages) | Cited 27 times

Online Publication Date: 17 May 2002

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Over the last 30 years, turbulent entrainment has come to be viewed as a large-scale process, directed by coherent structures, and described as engulfing. With turbulence simulations, we examined the process of entrainment directly, as growth of vorticity and concentration along fluid particle pathlines which were computed simultaneously. Our results indicate that the process is more often small scale. Growth occurs close to the turbulence boundary, within small radial displacements, and in times which are smaller than local large-scale times. These observations can be cast into a model to show that overall rates can be predicted by large-scale quantities even though the process occurs at small scales; the only requirement is a fixed relationship across scales as in fully developed turbulent flows. So it is not inconsistent that engulfment can be a successful, and accepted, model for fully developed flows even if it is not the more frequent process. © 2002 American Institute of Physics.
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47.27.E- Turbulence simulation and modeling
47.27.nb Boundary layer turbulence
47.32.C- Vortex dynamics
47.27.wg Turbulent jets

Optimal rotary control of the cylinder wake in the laminar regime

B. Protas and A. Styczek

Phys. Fluids 14, 2073 (2002); http://dx.doi.org/10.1063/1.1476671 (15 pages) | Cited 21 times

Online Publication Date: 20 May 2002

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In this paper we develop the Optimal Control Approach to the rotary control of the cylinder wake. We minimize the functional which represents the sum of the work needed to resist the drag force and the work needed to control the flow, where the rotation rate math(t) is the control variable. Sensitivity of the functional to control is determined using the adjoint equations. We solve them in the “vorticity” form, which is a novel approach and leads to computational advantages. Simulations performed at Re = 75 and Re = 150 reveal systematic decrease of the total power and drag achieved using a very small amount of control effort. We investigate the effect of the optimization horizon on the performance of the algorithm and the correlation of the optimal controls with the changes of the flow pattern. The algorithm was also applied to the control of the subcritical flow at Re = 40, however, no drag reduction was achieved in this case. Based on this, limits of the performance of the algorithm are discussed. © 2002 American Institute of Physics.
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47.27.wb Turbulent wakes
47.85.L- Flow control
47.15.-x Laminar flows
47.54.-r Pattern selection; pattern formation

Numerical investigations of small-amplitude disturbances in a boundary layer with impinging shock wave at Ma = 4.8

Alessandro Pagella, Ulrich Rist, and Siegfried Wagner

Phys. Fluids 14, 2088 (2002); http://dx.doi.org/10.1063/1.1480265 (14 pages) | Cited 5 times

Online Publication Date: 20 May 2002

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The stability behavior of a laminar boundary layer with shock boundary layer interaction and small amplitude disturbances is investigated by linear stability theory and direct numerical simulation. By a complex interaction of several physical properties, the impinging shock wave locally influences stability behavior of the boundary layer, dependent on its shock strength, applied disturbance frequency, and disturbance propagation angle with respect to the flow direction (obliqueness angle). Due to the displacement of the boundary layer near shock impingement and the according Reynolds number effect in this area, the boundary layer is locally destabilized. The displacement of the boundary layer also produces an increase of the thickness of local regions of relative supersonic speed, which promotes second mode instability. For the results obtained by direct numerical simulation nonparallel effects could be identified and quantified. Taking these nonparallel effects into account, linear stability theory is able to represent the stability behavior of wall distant disturbance amplitude maxima having small obliqueness angles for the cases investigated here. For larger obliqueness angles and disturbance amplitudes at or close to the wall the agreement between linear stability theory and direct numerical simulation declines considerably. © 2002 American Institute of Physics.
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47.15.Cb Laminar boundary layers
47.15.Fe Stability of laminar flows
47.40.Nm Shock wave interactions and shock effects

The effect of weak inertia on the emptying of a tube

Alain de Ryck

Phys. Fluids 14, 2102 (2002); http://dx.doi.org/10.1063/1.1480267 (7 pages) | Cited 9 times

Online Publication Date: 21 May 2002

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We present an extension of the classical axisymmetric Bretherton theory giving the thickness of the liquid film left on the walls of a drained tube, treating the case of weak inertia by a regular perturbation method. The results obtained by numerical integration fit Taylor’s [J. Fluid Mech. 10, 161 (1961)] experiments, obtained with viscous fluids (glycerine and strong sucrose solutions), and Aussillous and Quéré’s [Phys. Fluids 12, 2367 (2000)] experiments with low viscosity liquids (hexamethyldisiloxane and water) when inertia becomes important. The discrepancies observed between the theory and high Reynolds numbers experiments (Re>1000) are commented on. © 2002 American Institute of Physics.
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68.15.+e Liquid thin films
47.60.-i Flow phenomena in quasi-one-dimensional systems

On the phase velocity effect of nonlinear interactions between surface gravity waves

Mitsuhiro Tanaka, Catherine Phan Van, and Olivier Oldrini

Phys. Fluids 14, 2109 (2002); http://dx.doi.org/10.1063/1.1481742 (4 pages) | Cited 2 times

Online Publication Date: 22 May 2002

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The change of phase velocity of a train of surface gravity waves due to nonlinear interaction with another train of surface gravity waves is investigated. Three different expressions for the change of phase velocity have been derived from Zakharov-type equations, and it is confirmed that all these expressions are equivalent with each other, as well as with the classical result of Longuet-Higgins and Phillips. The theory for the interaction between two wave trains is also extended naively to that among component waves in a continuous energy spectrum, and the validity of this extension is assessed by comparing with direct numerical simulations based on the primitive equations. © 2002 American Institute of Physics.
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47.35.-i Hydrodynamic waves

Unsteady mixed convection in a horizontal channel with protruding heated blocks and a rectangular vortex promoter

Qinghua Wang and Yogesh Jaluria

Phys. Fluids 14, 2113 (2002); http://dx.doi.org/10.1063/1.1480832 (15 pages) | Cited 6 times

Online Publication Date: 23 May 2002

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The objective of this research is to study the resonance oscillatory flow in a channel and the resulting effect on thermal transport, leading to cooling enhancement in electronic systems. The unsteady mixed convection through a horizontal channel with two isolated protruding blocks on the bottom wall has been studied numerically. For this geometry, at moderate Reynolds numbers, the flow is found to separate at the leading edge of the first block, and then reattach at the top surface of the second block. At a given Grashof number, when Re exceeds a critical value, vortex is shed only from the second block, and rolls over the bottom wall with its size decaying, while one or two recirculating cells are trapped in the groove. The base vortex shedding frequency is dependent on the buoyancy level Gr/Re2. The critical value of Re is much lower when perturbation is introduced by a rectangular or square promoter in the channel. The frequency and amplitude of perturbation are changed by adjusting the geometry of the promoter. An improved fluid exchange between the main flow and the recirculating cell occurs when the promoter is employed. The effects of frequency and perturbation amplitude on the flow and on the heat transfer are investigated. The study consists of three parts. The first studies the developing flow in the grooved channel; the second investigates the vortex shedding from a rectangular promoter confined in a smooth channel; and the last studies the effect of resonance by tuning the frequency of vortex shedding. © 2002 American Institute of Physics.
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47.27.T- Turbulent transport processes
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.32.C- Vortex dynamics
47.35.-i Hydrodynamic waves
85.40.-e Microelectronics: LSI, VLSI, ULSI; integrated circuit fabrication technology

Simultaneous measurements of all three components of velocity and vorticity vectors in a lobed jet flow by means of dual-plane stereoscopic particle image velocimetry

Hui Hu, Tetsuo Saga, Toshio Kobayashi, and Nubuyuki Taniguchi

Phys. Fluids 14, 2128 (2002); http://dx.doi.org/10.1063/1.1481741 (11 pages) | Cited 2 times

Online Publication Date: 23 May 2002

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Results from an advanced particle image velocimetry (PIV) technique, named as dual-plane stereoscopic PIV technique, for making simultaneous measurements of all three components of velocity and vorticity vectors are presented for a lobed jet flow. The dual-plane stereoscopic PIV technique uses polarization conservation characteristic of Mie scattering to achieve simultaneous stereoscopic PIV measurements at two spatially separated planes. Unlike “classical” PIV systems or conventional stereoscopic PIV systems, which can only get one component of vorticity vectors, the present dual-plane stereoscopic PIV system can provide all three components of velocity and vorticity distributions in fluid flows instantaneously and simultaneously. The evolution and interaction characteristics of the large-scale streamwise vortices and azimuthal Kelvin–Helmholtz vortices in the lobed jet flow are revealed very clearly and quantitatively from the simultaneous measurement results of the dual-plane stereoscopic PIV system. A discussion about the satisfaction of the measurement results of the present dual-plane stereoscopic PIV system to mass conservation equation is also conducted in the present paper to evaluate the error levels of the measurement results. © 2002 American Institute of Physics.
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47.27.wg Turbulent jets
47.32.C- Vortex dynamics

Statistical mechanics of strong and weak point vortices in a cylinder

Oliver Bühler

Phys. Fluids 14, 2139 (2002); http://dx.doi.org/10.1063/1.1483305 (11 pages) | Cited 7 times

Online Publication Date: 23 May 2002

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The motion of 100 point vortices in a circular cylinder is simulated numerically and compared with theoretical predictions based on statistical mechanics. The novel aspect considered here is that the vortices have greatly different circulation strengths. Specifically, there are 4 strong vortices and 96 weak vortices, the net circulation in either group is zero, and the strong circulations are five times larger than the weak circulations. As envisaged by Onsager [Nuovo Cimento, Suppl. 6, 279 (1949)], such an arrangement leads to a substantial amplification of statistical trends such as the preferred clustering of the strong vortices in either same-signed or oppositely signed pairs, depending on the overall energy level. To prepare the ground, this behavior is illustrated here first by a simple toy model with exactly solvable statistics. A microcanonical ensemble based on the conserved total energy E and angular momentum M for the whole vortex system is then used, in which the few strong vortices are treated as a subsystem in contact with a reservoir composed of the many weak vortices. It is shown that allowing for the finite size of this reservoir is essential in order to predict the statistics of the strong vortices accurately. Notably, this goes beyond the standard canonical ensemble with positive or negative temperature. A certain approximation is then shown to allow a single random sample of uniformly distributed vortex configurations to be used to predict the strong vortex statistics for all possible values of E and M. Detailed predictions for the energy, two-vortex, and radial distribution functions of the strong vortices are then made for comparison with three simulated cases of near-zero M and low, neutral, or high E. It is found that the statistical mechanics predictions compare remarkably well with the numerical results, including a prediction of vortex accumulation at the cylinder wall for low values of E. © 2002 American Institute of Physics.
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47.32.C- Vortex dynamics
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.11.-j Computational methods in fluid dynamics
05.20.Jj Statistical mechanics of classical fluids
02.60.Cb Numerical simulation; solution of equations
05.20.Gg Classical ensemble theory

Self-organization of quasi-two-dimensional turbulence in stratified fluids in square and circular containers

S. R. Maassen, H. J. H. Clercx, and G. J. F. van Heijst

Phys. Fluids 14, 2150 (2002); http://dx.doi.org/10.1063/1.1480263 (20 pages) | Cited 18 times

Online Publication Date: 23 May 2002

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Laboratory experiments on decaying quasi-2D (two-dimensional) turbulence have been performed in stratified fluids in both square and circular containers. The turbulence was generated by towing an array of vertical cylinders through the container, which was filled with either a two-layer or a linearly stratified fluid. By varying the grid configuration a different amount of angular momentum could be added to the initial flow. The evolution of the flow was visualized by 2D particle tracking velocimetry. The observed decay scenario has been investigated with emphasis on the evolution of the kinetic energy and the enstrophy of the horizontal flow, vortex statistics and the angular momentum of the flow. In particular it is shown that the experiments in both the square and the circular container support the observations from numerical simulations of decaying 2D turbulence in bounded domains with no-slip walls. Two striking examples are the experimental observation of the spontaneous spin-up phenomenon (in the square-container experiments) and the confirmation that the angular momentum of the flow in the circular-container experiment is better conserved than the total kinetic energy of the flow. The role of the initial nonzero net angular momentum on the decay of quasi-2D turbulence is investigated for both geometries and indications for an acceleration of the self-organization process are presented. © 2002 American Institute of Physics.
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47.55.Hd Stratified flows
47.32.C- Vortex dynamics
47.27.N- Wall-bounded shear flow turbulence

Conditionally filtered scalar dissipation, scalar diffusion, and velocity in a turbulent jet

Danhong Wang and Chenning Tong

Phys. Fluids 14, 2170 (2002); http://dx.doi.org/10.1063/1.1481744 (16 pages) | Cited 26 times

Online Publication Date: 23 May 2002

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Conditionally filtered conserved scalar (temperature) dissipation (CFD), diffusion, and conditionally filtered velocity are studied experimentally in the fully developed region of a turbulent jet with a jet Reynolds number Rej = UjDj/ν of 40 000. These variables are the unclosed terms in the transport equation of the conserved scalar filtered density function. One-dimensional box filters of widths Δ ranging from 30 to 496 scalar dissipation scales (ηϕ) as well as a two-dimensional box filter (Δ/ηϕ = 90) which consists of three discrete sensors are used to obtain filtered variables. Taylor’s hypothesis is used to perform the streamwise filtering. The means of these conditionally filtered variables conditional on the resolvable-scale scalar fluctuations 〈ϕ〉L and the subgrid-scale (SGS) variance 〈ϕ″2〉L indicate two regimes of the SGS scalar mixing. For large SGS variance (〈ϕ″2〉L/〈ϕ″2〉>1) the SGS scalar exhibits similarities to scalars in initially binary mixing at early times, suggesting existence of diffusion-layer-like structure and nonequilibrium SGS scalar. The nonequilibrium is further evidenced by the observed large SGS mechanical-to-scalar time scale ratio and large SGS variance production-to-dissipation ratio. These characteristics have not been previously observed in fully developed flows. For small SGS variance the conditionally filtered variables indicate well-mixed SGS scalar. The results also show that the SGS advection is only significant at large SGS variance. Our measurements also suggest that the dependence of the scalar dissipation (and the filtered dissipation) on large-scale scalar fluctuations is caused primarily by the fluctuations in the spectral transfer and that the conditional CFD is directly affected mostly by scales near the filter scale. The present study suggests that the nonequilibrium effects related to sheet-like structures are important for modeling the conditionally filtered variables. © 2002 American Institute of Physics.
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47.27.wg Turbulent jets
47.11.-j Computational methods in fluid dynamics

Effects of subgrid-scale modeling on time correlations in large eddy simulation

Guo-Wei He, R. Rubinstein, and Lian-Ping Wang

Phys. Fluids 14, 2186 (2002); http://dx.doi.org/10.1063/1.1483877 (8 pages) | Cited 26 times

Online Publication Date: 24 May 2002

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The effects of the unresolved subgrid-scale (SGS) motions on the energy balance of the resolved scales in large eddy simulation (LES) have been investigated actively because modeling the energy transfer between the resolved and unresolved scales is crucial to constructing accurate SGS models. But the subgrid scales not only modify the energy balance, they also contribute to temporal decorrelation of the resolved scales. The importance of this effect in applications including the predictability problem and the evaluation of sound radiation by turbulent flows motivates the present study of the effect of SGS modeling on turbulent time correlations. This paper compares the two-point, two-time Eulerian velocity correlation in isotropic homogeneous turbulence evaluated by direct numerical simulation (DNS) with the correlations evaluated by LES using a standard spectral eddy viscosity. It proves convenient to express the two-point correlations in terms of spatial Fourier decomposition of the velocity field. The LES fields are more coherent than the DNS fields: their time correlations decay more slowly at all resolved scales of motion and both their integral scales and microscales are larger than those of the DNS field. Filtering alone is not responsible for this effect: in the Fourier representation, the time correlations of the filtered DNS field are identical to those of the DNS field itself. The possibility of modeling the decorrelating effects of the unresolved scales of motion by including a random force in the model is briefly discussed. The results could have applications to the problem of computing sound sources in isotropic homogeneous turbulence by LES. © 2002 American Institute of Physics.
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47.11.-j Computational methods in fluid dynamics
47.27.Gs Isotropic turbulence; homogeneous turbulence
47.27.Sd Turbulence generated noise

Measurement of an unexpectedly large shear-induced self-diffusivity in a dilute suspension of spheres

Isidro E. Zarraga and David T. Leighton

Phys. Fluids 14, 2194 (2002); http://dx.doi.org/10.1063/1.1483304 (8 pages) | Cited 19 times

Online Publication Date: 28 May 2002

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We report the measurement of unexpectedly large shear-induced diffusivities for various sized tracers in a dilute suspension of noncolloidal spheres in simple shear. The suspension was sheared in a narrow gap Couette device at low Reynolds number, and the tracer diffusivities parallel to the velocity gradient D were obtained using an orbit-time technique. It is shown that the presence of even a dilute concentration ϕ of particles renders an otherwise smooth tracer trajectory strongly stochastic and the resulting diffusivity is linear in ϕ in this limit, indicating irreversible displacements at the pair interaction level. The measured values of the diffusivity, however, are at least an order of magnitude larger than that predicted by current theories. In a previous study, Beimfohr et al. [Proc. DOE/NSF Workshop, Ithaca, NY (1993)] likewise obtained values for D larger than that predicted by theory, but the discrepancy was attributed to the large eccentricity (average aspect ratio = 1.19) of the particles used. In the present study, very nearly spherical ground acrylic particles were used, yet diffusivities of the same order of magnitude as that obtained by Beimfohr et al. were measured. Various possible causes for this anomalous diffusivity were explored and tested in the course of our investigation, including the effect of inertial lift and possible non-Newtonian properties of the base fluid, but none proved sufficiently large to account for the observed behavior. © 2002 American Institute of Physics.
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66.10.C- Diffusion and thermal diffusion
47.55.Kf Particle-laden flows
82.70.Kj Emulsions and suspensions
47.50.-d Non-Newtonian fluid flows

Transient coating flow of a thin non-Newtonian fluid film

Kyu-Tae Kim and Roger E. Khayat

Phys. Fluids 14, 2202 (2002); http://dx.doi.org/10.1063/1.1483306 (14 pages) | Cited 8 times

Online Publication Date: 28 May 2002

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The interplay between non-Newtonian effects, gravity, and substrate topography is examined in this theoretical study for the transient two-dimensional flow of a thin non-Newtonian film. The study is a continuation of the previous work by Khayat and Welke [Phys. Fluids 13, 355 (2001)], which focused on the influence of inertia on a Newtonian film. The fluid emerges from a channel and is driven by a pressure gradient maintained inside the channel. The substrate is assumed to be stationary and of arbitrary shape. The flow is dictated by the thin-film equations of the “boundary layer” type, which are solved by expanding the flow field in terms of orthonormal modes in the transverse direction and using the Galerkin projection, combined with a time-stepping implicit scheme, and integration along the flow direction. Gravity and substrate topography can have a significant effect on transient behavior, but this effect varies significantly, depending on whether the fluid is Newtonian, shear thinning or shear thickening. Wave formation and propagation, as well as steady film flow are examined. It is found that shear-thickening fluids tend to accumulate near the channel exit, exhibiting a standing wave that grows with time. This behavior clearly illustrates the difficulty faced with coating shear-thickening fluids at any level of inertia. The influence of the substrate topography has been explored in the case of undulated substrate. © 2002 American Institute of Physics.
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47.50.-d Non-Newtonian fluid flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.35.-i Hydrodynamic waves
47.27.-i Turbulent flows
68.15.+e Liquid thin films

Shape stability of unsteadily translating bubbles

Anil J. Reddy and Andrew J. Szeri

Phys. Fluids 14, 2216 (2002); http://dx.doi.org/10.1063/1.1483840 (9 pages) | Cited 8 times

Online Publication Date: 28 May 2002

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In this paper the problem of shape stability is considered, for a bubble with time-dependent radius, translating unsteadily in a flow. This situation can be brought about, for example, by forcing with an acoustic traveling wave. The equation governing translation was derived in a previous work [Reddy and Szeri (unpublished)]. Here, the equations governing the amplitudes of shape modes are derived using domain perturbation theory, following a classical paper by Plesset. Contrary perhaps to intuition, results show that driving at the natural frequency of volume oscillations is not necessarily the ideal forcing to engender a shape instability. Moreover, severe radial oscillations can have a stabilizing effect on shape oscillations. The results suggest the possibility of destroying bubbles selectively by size. © 2002 American Institute of Physics.
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47.55.D- Drops and bubbles
47.20.-k Flow instabilities

Fourth-order nonlinear evolution equations for counterpropagating capillary-gravity wave packets on the surface of water of infinite depth

Suma Debsarma and K. P. Das

Phys. Fluids 14, 2225 (2002); http://dx.doi.org/10.1063/1.1476669 (10 pages) | Cited 1 time

Online Publication Date: 29 May 2002

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Asymptotically exact nonlocal fourth-order nonlinear evolution equations are derived for two counterpropagating capillary-gravity wave packets on the surface of water of infinite depth. On the basis of these equations a stability analysis is made for a uniform standing capillary-gravity wave for longitudinal perturbation. The instability conditions and an expression for the maximum growth rate of instability are obtained. Significant deviations are noticed between the results obtained from third-order and fourth-order nonlinear evolution equations. © 2002 American Institute of Physics.
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47.35.-i Hydrodynamic waves
47.20.-k Flow instabilities

Ergodic theory and experimental visualization of invariant sets in chaotically advected flows

Igor Mezić and Fotis Sotiropoulos

Phys. Fluids 14, 2235 (2002); http://dx.doi.org/10.1063/1.1480266 (9 pages) | Cited 9 times

Online Publication Date: 29 May 2002

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We analyze a recently proposed experimental technique for constructing Poincaré maps in flows exhibiting chaotic advection and develop the theoretical framework that explains the reasons for the success of this approach. The technique is nonintrusive and, thus, simple to implement. Planar laser-induced fluorescence is employed to collect a sufficiently long sequence of instantaneous light intensity fields on the plane of section of the Poincaré map (defined by the laser sheet). The invariant sets of the flow are visualized by time-averaging the instantaneous images and plotting iso-contours of the so resulting mean light intensity field. By linking the Eulerian time averages of light intensity at fixed points in space with the Lagrangian time averages along particle paths passing through these points, we show that ergodic theory concepts can be used to show that this procedure will indeed visualize invariant sets of the Poincaré map. As the technique is based on time-averaging, we discuss the rates of convergence and show that inside regular islands the convergence is fast. An example is presented from the application of this technique to visualize the intricate web of regular islands within a steady, three-dimensional vortex breakdown bubble. © 2002 American Institute of Physics.
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47.52.+j Chaos in fluid dynamics

Interfacial gravity currents. I. Mixing and entrainment

B. R. Sutherland

Phys. Fluids 14, 2244 (2002); http://dx.doi.org/10.1063/1.1483303 (11 pages) | Cited 9 times

Online Publication Date: 29 May 2002

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Experiments are performed to examine mixing and transport due to an intrusive gravity current in a two- and three-layer fluid. Successive passages of the intrusion act to increase the depth of the middle layer. The observed broadening rates and the deposition of potential energy are compared with theories that neglect mixing and entrainment processes. As the middle layer widens, a transition in the mass transport by the intrusion is observed: in a two-layer fluid the intrusion transports mass along the entire length of the interface; in a three-layer fluid with sufficiently deep middle layer the intrusion transports mass over a limited distance and simultaneously excites large-amplitude internal wave modes and solitary internal waves. © 2002 American Institute of Physics.
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47.35.-i Hydrodynamic waves
47.55.Hd Stratified flows

Rayleigh–Bénard flow of a rarefied gas and its attractors. I. Convection regime

S. Stefanov, V. Roussinov, and C. Cercignani

Phys. Fluids 14, 2255 (2002); http://dx.doi.org/10.1063/1.1483837 (15 pages) | Cited 20 times

Online Publication Date: 29 May 2002

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In this paper we investigate the long time behavior (final state) of the Rayleigh–Bénard (RB) flow of a rarefied monatomic gas for a set of the nondimensional Knudsen and Froude numbers in the intervals Kn ∊ [1.0×10−3,4×10−2], Fr ∊ [1.0×10−1,1.5×103]. For the most part of the computations the third nondimensional parameter, the ratio of the cold and hot wall temperatures is fixed to Tc/Th = 0.1, corresponding to a large temperature difference (Th serves as reference temperature), for which the RB system is believed to reach most of the possible final states (attractors). The low Knudsen numbers allow the problem to be investigated numerically by using two completely different methods: direct simulation Monte Carlo (DSMC) method (molecular approach) and finite difference (FD) method (continuum approach based on the model of compressible viscous heat conducting gas with state-dependent transport coefficients). As a result the effect of rarefaction on the onset of convection in the two-dimensional case is studied and the zone of convection is delineated. The gravitational instability of the RB system is analyzed by using the exact solution of pure-conduction state. As a result two analytical conditions for large and small Froude numbers, respectively, are suggested as exterior bounds of the zone of convection. Both DSMC and FD calculations, which are in good agreement in the considered set of the governing parameters, confirm the validity of these estimations. The observed hysteresis loops between the found out co-existing attractors within the zone of convection is another finding of the presented study. The results for the lowest Knudsen number considered (Kn = 0.001), where a set of qualitatively new regimes and final states have been found, are presented separately in paper II. © 2002 American Institute of Physics.
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47.45.-n Rarefied gas dynamics
47.20.-k Flow instabilities
47.27.T- Turbulent transport processes
47.11.-j Computational methods in fluid dynamics
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