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

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Influence of subgrid scales on resolvable turbulence and mixing in Rayleigh–Taylor flow

William H. Cabot, Oleg Schilling, and Ye Zhou

Phys. Fluids 16, 495 (2004); http://dx.doi.org/10.1063/1.1636477 (14 pages) | Cited 5 times

Online Publication Date: 13 January 2004

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The energy transfer process and the interaction of different scales in a flow induced by the variable-density Rayleigh–Taylor instability in miscible fluids is investigated using a three-dimensional direct numerical simulation database with a spatial resolution of N_x×N_y×N_z = 512×512×2040. The method used to study the transfer of energy between the supergrid and subgrid scales in the homogeneous planes, determined by partitioning the modes into resolved and unresolved scales defined by a two-dimensional cutoff wave number k_c in Fourier space, is applied to the kinetic energy evolution equation. The treatment of the flow inhomogeneity in the direction z parallel to the acceleration is analogous to that used in the analysis of incompressible wall-bounded flows, including channel flow and Rayleigh–Bénard convection [J. A. Domaradzki et al., Phys. Fluids 6, 1583 (1994); J. A. Domaradzki and W. Liu, ibid. 7, 2025 (1995)]. Using a sharp Fourier cutoff filter, the kinetic energy transfer is decomposed into (1) the resolved part; (2) a part corresponding to the interaction between resolved and unresolved scales; and (3) a part corresponding to the interaction between unresolved scales. The sum of these last two contributions is the subgrid-scale kinetic energy transfer, which is studied in the present work. These z-dependent spectra are computed for three different cutoff wave numbers to investigate the dependence of the transfer process on the scales contributing to the subgrid interactions. The kinetic energy transfer is further decomposed into its positive and negative components corresponding to the forward and backward cascades of energy, respectively, that arise from the nonlinear modal interactions. The decomposition into resolved and unresolved scales is used to define an effective eddy viscosity and backscatter viscosity. The principal conclusions of the analysis are (1) the transfer spectra and eddy viscosities exhibit a strong dependence on the wave number cutoff; (2) the contributions from the interaction between resolved and unresolved scales dominate the contribution to the total subgrid eddy viscosities and are responsible for the cusp at large k/k_c; (3) the contributions from the interaction between unresolved scales dominate the contribution to the total subgrid eddy viscosities at small k/k_c and are responsible for the small, negative contribution (associated with an inverse energy transfer), and (4) backscatter is strongest in the regions near the boundaries of the mixing layer. The physical implications of these results for subgrid-scale modeling in a large-eddy simulation of Rayleigh–Taylor instability-induced turbulence are discussed. © 2004 American Institute of Physics.

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47.20.-k	Flow instabilities
47.27.nb	Boundary layer turbulence
47.11.-j	Computational methods in fluid dynamics
47.60.-i	Flow phenomena in quasi-one-dimensional systems

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Density waves and coherent structures in granular Couette flows

Stephen L. Conway and Benjamin J. Glasser

Phys. Fluids 16, 509 (2004); http://dx.doi.org/10.1063/1.1637348 (21 pages) | Cited 17 times

Online Publication Date: 13 January 2004

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Density inhomogeneities in granular flows can dramatically influence microscopic and macroscopic properties. Here, we numerically examine dilute rapid granular flows in the Couette geometry via large-scale particle-dynamic simulations, and characterize development of nonuniform particle distributions. For monodisperse grains we observe density waves in two- and three-dimensional computational domains of varying aspect ratios. Both fully developed and transient states are quantified using Fourier methods. For inelastic, planar (two-dimensional) flows exceeding a minimum solids fraction, one-dimensional, high-density clusters—well-known features of inelastic materials—align parallel to the walls. Above a critical streamwise length, these are destabilized by two-dimensional antisymmetric modes with wavelength ∼100 particle diameters. We relate oscillatory behavior to an underlying physical mechanism of the slow drift of clusters towards walls and their subsequent bursting. Further streamwise or spanwise expansions permit additional wave numbers to be expressed in these directions. In “shallow” three-dimensional flows, the planar wave types initially survive. As depth is increased above a critical value, cross-stream invariance experiences symmetry preserving instabilities to form coherent structures resembling steady and wavy Taylor–Couette fluid vortices. Their presence strongly impacts macroscopic behavior, as regions of sustained vorticity develop, and stresses and granular temperatures deviate by up to an order of magnitude from mean values. The influence of solids fraction, particle size, material elasticity, surface friction, polydispersity, and gravity are considered, and instabilities are found to intensify as collisional dissipation rises. For planar flows, transient and fully developed density distributions share many parametric responses with previous continuum results using kinetic theory. © 2004 American Institute of Physics.

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45.70.Mg	Granular flow: mixing, segregation and stratification
47.60.-i	Flow phenomena in quasi-one-dimensional systems

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Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at M = 2.25

S. Pirozzoli, F. Grasso, and T. B. Gatski

Phys. Fluids 16, 530 (2004); http://dx.doi.org/10.1063/1.1637604 (16 pages) | Cited 46 times

Online Publication Date: 13 January 2004

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A spatially developing supersonic adiabatic flat plate boundary layer flow (at M_∞ = 2.25 and Re_θ ≈ 4000) is analyzed by means of direct numerical simulation. The numerical algorithm is based on a mixed weighted essentially nonoscillatory compact-difference method for the three-dimensional Navier–Stokes equations. The main objectives are to assess the validity of Morkovin’s hypothesis and Reynolds analogies, and to analyze the controlling mechanisms for turbulence production, dissipation, and transport. The results show that the essential dynamics of the investigated turbulent supersonic boundary layer flow closely resembles the incompressible pattern. The Van Driest transformed mean velocity obeys the incompressible law-of-the-wall, and the mean static temperature field exhibits a quadratic dependency upon the mean velocity, as predicted by the Crocco–Busemann relation. The total temperature has been found not to be precisely uniform, and total temperature fluctuations are found to be non-negligible. Consistently, the turbulent Prandtl number is not unity, and it varies between 0.7 and 0.8 in the outer part of the boundary layer. Nonetheless, a modified strong Reynolds analogy is still verified. In agreement with the low Mach number results, the streamwise velocity component and the temperature are only weakly anti-correlated. The turbulent kinetic energy budget also shows similarities with the incompressible case provided all terms of the equation are properly scaled; indeed, the leading compressibility contributions are negligible throughout the boundary layer. © 2004 American Institute of Physics.

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47.27.nb	Boundary layer turbulence
47.40.Ki	Supersonic and hypersonic flows
47.11.-j	Computational methods in fluid dynamics
47.10.-g	General theory in fluid dynamics
47.80.-v	Instrumentation and measurement methods in fluid dynamics

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On a modified Taylor–Dean stability problem where the small gap between the cylinders varies in the azimuthal direction

P. M. Eagles

Phys. Fluids 16, 546 (2004); http://dx.doi.org/10.1063/1.1625943 (5 pages)

Online Publication Date: 22 January 2004

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We modify the classical Taylor–Dean stability problem to a case where the inner circular cylinder is rotating and the outer cylinder is fixed and noncircular in general. A method is given to determine some stability characteristics, in which the streamwise growth of a steady disturbance is calculated, in a small-gap approximation. Some particular examples are studied. If the gap width is increasing in the direction of flux of the basic steady-state flow, this flow is more unstable than for the case of constant gap width, and conversely when the gap width is decreasing. © 2004 American Institute of Physics.

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47.20.-k	Flow instabilities
47.60.-i	Flow phenomena in quasi-one-dimensional systems

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Soret effect inducing subcritical and Hopf bifurcations in a shallow enclosure filled with a clear binary fluid or a saturated porous medium: A comparative study

M. Bourich, M. Hasnaoui, M. Mamou, and A. Amahmid

Phys. Fluids 16, 551 (2004); http://dx.doi.org/10.1063/1.1636727 (18 pages) | Cited 12 times

Online Publication Date: 22 January 2004

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Soret-driven thermosolutal convection within a shallow porous or fluid layer subject to a vertical gradient of temperature is investigated analytically and numerically. The bridging between a clear fluid and Darcy porous media problems is conducted using the Brinkman–Hazen–Darcy model in its transient form. The analytical solution is derived on the basis of the parallel flow approximation, and validated numerically using a finite difference method by solving the full governing equations. The study is focused on the thermal diffusion effects on the flow intensity, and on the heat and mass transfer rates. In particular, a comparative study is made for the two limiting cases that emerge from the present investigation, namely the low porosity Darcy porous medium and the clear fluid medium. The flow behavior for both cases is qualitatively similar. The critical Rayleigh numbers for the onset of subcritical, oscillatory and stationary convection are determined explicitly as functions of the governing parameters for infinite and finite layers. At the onset of instabilities, the wavenumber is equal to zero and the oscillation frequency vanishes at the onset of Hopf bifurcation. For a finite aspect ratio enclosure, the frequency is finite and decreases as the aspect ratio increases. The codimension-2 point exists and different flow regimes are delineated. For constant heat flux boundaries, only standing oscillatory and steady waves are found to exist. The analytical and numerical results are found to be in good agreement, within the range of the governing parameters considered in the present study. The thermal diffusion effect on the flow intensity and on the heat and mass transfer is more enhanced for Darcy medium compared to the clear fluid, for which the viscous effects are significant. © 2004 American Institute of Physics.

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47.56.+r	Flows through porous media
66.10.C-	Diffusion and thermal diffusion
47.52.+j	Chaos in fluid dynamics
47.27.T-	Turbulent transport processes

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Theoretical and numerical results for spin coating of viscous liquids

Leonard W. Schwartz and R. Valery Roy

Phys. Fluids 16, 569 (2004); http://dx.doi.org/10.1063/1.1637353 (16 pages) | Cited 10 times

Online Publication Date: 26 January 2004

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A mathematical model is developed for fluid flow in the spin coating process. Spin coating employs centrifugal force to produce coatings of uniform thickness. The long-wave or lubrication approximation is used for the flow of thin liquid layers that are exposed to the air and lie on a spinning horizontal solid substrate. For low rotation rates, steady axisymmetric drop shapes can be found analytically. The stability of these drops is investigated, using an energy method, both with and without the long-wave approximation. For industrially relevant high-speed motions, we formulate and solve a theoretical and numerical model for the three-dimensional time-dependent motion of the deforming drop. We pay particular attention to the formation of “fingers” at the expanding front. The model includes viscous, capillary, gravitational, centrifugal, Coriolis, and finite-contact-angle effects. Both homogeneous and chemically heterogeneous substrates are considered. In agreement with published experiments, the model demonstrates that imperfect wetting behavior is the principal cause of fingering during spin coating. Features of the finger profiles are in close agreement with experimental observations. © 2004 American Institute of Physics.

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81.15.Lm	Liquid phase epitaxy; deposition from liquid phases (melts, solutions, and surface layers on liquids)
47.10.-g	General theory in fluid dynamics
47.11.-j	Computational methods in fluid dynamics
68.03.Cd	Surface tension and related phenomena
68.15.+e	Liquid thin films
66.20.-d	Viscosity of liquids; diffusive momentum transport
68.08.Bc	Wetting

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Pankaj Doshi and Osman A. Basaran

Phys. Fluids 16, 585 (2004); http://dx.doi.org/10.1063/1.1639015 (9 pages) | Cited 8 times

Online Publication Date: 26 January 2004

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Pinch-off dynamics of slender liquid threads of power law fluids without inertia are studied by asymptotic analysis. Because the threads are slender, their dynamics are governed by a pair of spatially one-dimensional, nonlinear evolution equations for the thread shape and axial velocity that results from a long-wave asymptotic expansion of the creeping flow equations. By means of an approach that differs from those used previously in analyses of capillary pinching of threads of Newtonian fluids, a similarity transformation is derived that reduces the evolution equations to two coupled similarity equations. As in the Newtonian case, it is shown that for each value of the power law exponent n where 0 ⩽ n ⩽ 1, there is a family of similarity solutions for capillary pinching of threads of power law fluids. For a given family of solutions, the radial and axial scales vary with time τ to pinch-off as τⁿ and τ^δ, respectively, where δ is the axial scaling exponent. It is shown that for a given family of solutions characterized by a fixed value of n, each member of the family has a different scaling exponent δ. Since the viscosity of a power law fluid varies as ∣ math

∣⁽ⁿ⁻¹⁾, where math

is the deformation rate, for each value of n a numerical method based on domain splicing is used to compute the values of the axial scaling exponent δ and the similarity solutions. © 2004 American Institute of Physics.

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47.50.-d

Non-Newtonian fluid flows

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Motion of a solid object through a pasty (thixotropic) fluid

T. Ferroir, H. T. Huynh, X. Chateau, and P. Coussot

Phys. Fluids 16, 594 (2004); http://dx.doi.org/10.1063/1.1640372 (8 pages) | Cited 16 times

Online Publication Date: 26 January 2004

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For materials assumed to be simple yield stress fluids the velocity of an object should continuously increase from zero as the applied force increases from the critical value for incipient motion. We carried out experiments of fall of a sphere in a typical, thixotropic, pasty material (a laponite suspension). We either left a sphere falling in the fluid in different initial states of structure or vibrated the fluid in a given state of structure at different frequencies. In each case three analogous regimes appear either for increasing restructuring states of the fluid or decreasing frequencies: A rapid fall at an almost constant rate; a slower fall at a progressively decreasing velocity; a slow fall at a rapidly decreasing rate finally leading to apparent stoppage. These results show that the motion of an object, due to gravity in a pasty material, is a more complex dynamical process than generally assumed for simple yield stress fluids. A simple model using the basic features of the (thixotropic) rheological behavior of these pasty materials makes it possible to explain these experimental trends. The fall of an object in such a fluid thus appears to basically follow a bifurcation process: For a sufficiently large force applied onto the object its rapid motion tends to sufficiently liquify the fluid around it so that its subsequent motion is more rapid and so on until reaching a constant velocity; on the contrary if the force applied onto the object is not sufficiently large the fluid around has enough time to restructure, which slows down the motion and so on until the complete stoppage of the object. © 2004 American Institute of Physics.

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47.55.Kf

Particle-laden flows

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Miscible displacements in capillary tubes: Effect of a preexisting wall film

Ching-Yao Chen and Eckart Meiburg

Phys. Fluids 16, 602 (2004); http://dx.doi.org/10.1063/1.1640373 (8 pages) | Cited 2 times

Online Publication Date: 26 January 2004

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For miscible displacements in capillary tubes, the impact of a preexisting wall film on the tip velocity of the displacing fluid finger is analyzed by means of axisymmetric Stokes simulations. The wall film is assumed to have the same viscosity as the displacing fluid, which is less viscous than the displaced fluid. The finger of the displacing fluid is seen to move in a quasisteady fashion, with a tip velocity below the centerline velocity of an equivalent Poiseuille flow. The explanation for this behavior, which is in contrast to our earlier findings for miscible displacements without wall films, lies in the lubricating effect of the wall film. The condition is established for which the displaced fluid moves in a nearly solid body-like motion. In this limit, a closed expression is derived for the finger tip velocity. A comparison between the simulation data and the closed form results shows reasonable agreement, provided that the criterion for solid body-like motion is satisfied. Furthermore, results are presented for the practically relevant limit of large viscosity ratios. © 2004 American Institute of Physics.

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47.10.-g	General theory in fluid dynamics
47.60.-i	Flow phenomena in quasi-one-dimensional systems

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Impact of an oblique breaking wave on a wall

Jian-Jun Shu

Phys. Fluids 16, 610 (2004); http://dx.doi.org/10.1063/1.1644145 (5 pages) | Cited 2 times

Online Publication Date: 29 January 2004

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The intention of this paper is to study impact force of an oblique-angled slamming wave acting on a rigid wall. In the present study the analytical approach is pursued based on a technique proposed by Shu (Proceedings of the International Conference on Applied Mathematics & Mathematical Physics, Sylhet, Bangladesh, 2000). A nonlinear theory in the context of potential flow is presented for determining accurately the free-surface profiles immediately after an oblique breaking wave impingement on the rigid vertical wall that suddenly starts from rest. The small-time expansion is taken as far as necessary to include the accelerating effect. The analytical solutions for the free-surface elevation are derived up to the third order. The results derived in this paper are of particular interest to the marine and offshore engineering industries, which will find the information useful for the design of ships, coastal and offshore. © 2004 American Institute of Physics.

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47.35.-i	Hydrodynamic waves
47.11.-j	Computational methods in fluid dynamics

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Conductances between confined rough walls

F. Plouraboué, S. Geoffroy, and M. Prat

Phys. Fluids 16, 615 (2004); http://dx.doi.org/10.1063/1.1644152 (10 pages) | Cited 5 times

Online Publication Date: 29 January 2004

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Two- and three-dimensional creeping flows and diffusion transport through constricted and possibly rough surfaces are studied. Asymptotic expansions of conductances are derived as functions of the constriction local geometry. The validity range of the proposed theoretical approximations is explored through a comparison either with available exact results for specific two-dimensional aperture fields or with direct numerical computations for general three-dimensional geometries. The large validity range of the analytical expressions proposed for the hydraulic conductivity (and to a lesser extent for the electrical conductivity) opens up interesting perspectives for the simulation of flows in highly complicated geometries with a large number of constrictions. © 2004 American Institute of Physics.

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47.15.G-	Low-Reynolds-number (creeping) flows
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.11.-j	Computational methods in fluid dynamics

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Experimental investigation on cellular breakup of a planar liquid sheet from an air-blast nozzle

Jaewan Park, Kang Y. Huh, Xianguo Li, and Metin Renksizbulut

Phys. Fluids 16, 625 (2004); http://dx.doi.org/10.1063/1.1644575 (8 pages) | Cited 11 times

Online Publication Date: 29 January 2004

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The cellular breakup phenomenon is investigated experimentally for a planar liquid sheet from an air-blast nozzle. The dominant sinuous wave growing spatially downstream forms complicated cellular structures of perforated thin films and surrounding ligaments. Several characteristic parameters are measured from photographic images and compared with linear temporal analysis. The dominant wavelength is proportional to the inverse square of the relative velocity between air and liquid. The estimated breakup time matches the growth time of the most unstable wave, while the breakup length corresponds to a product of breakup time and liquid velocity. Numerical simulation shows a substantially reduced mean effective velocity near flow reattachment region of the air stream. Air turbulence seems to play a major role on initial perturbations of cellular breakup in the given nozzle configuration. The measured spatial growth rates are always less than linear predictions due to deviation from the linear regime at higher amplitudes. © 2004 American Institute of Physics.

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47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.27.-i	Turbulent flows

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Rimming flows with an axially varying viscosity

Bo Jin and Andreas Acrivos

Phys. Fluids 16, 633 (2004); http://dx.doi.org/10.1063/1.1640374 (8 pages) | Cited 4 times

Online Publication Date: 4 February 2004

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We consider rimming flows in the presence of an axially varying viscosity but with inertia and surface tension effects being negligible. First, we find that a modified lubrication analysis (MLA) presented earlier [M. Tirumkudulu and A. Acrivos, Phys. Fluids 13, 14 (2001)] can predict accurately the thickness of the film profile over the whole range of Ω, the angular velocity of the rotating cylinder, even when the fill fraction F is as large as 0.36, where the film is far from thin. This is also the case with the analysis due to Benjamin et al. [T. B. Benjamin, W. G. Pritchard, and S. J. Tavener (preprint, 1993)] except that, here, F cannot exceed 0.29. On the basis of this MLA, we propose a model to describe the three-dimensional free surface shape of rimming flows with an axially varying viscosity and show that the free surface profiles thereby obtained agree with those determined by solving numerically the three-dimensional Stokes equations. In the accompanying article, this model will be used as the basis of a stability analysis which will explain the origin of the observed particle band formation in rimming flows of suspensions containing neutrally buoyant particles [M. Tirumkudulu, A. Mileo, and A. Acrivos, Phys. Fluids 12, 1615 (2000)]. © 2004 American Institute of Physics.

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47.11.-j	Computational methods in fluid dynamics
66.20.-d	Viscosity of liquids; diffusive momentum transport
47.32.-y	Vortex dynamics; rotating fluids

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Theory of particle segregation in rimming flows of suspensions containing neutrally buoyant particles

Bo Jin and Andreas Acrivos

Phys. Fluids 16, 641 (2004); http://dx.doi.org/10.1063/1.1640375 (11 pages) | Cited 9 times

Online Publication Date: 4 February 2004

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It has recently been reported that an initially uniform suspension of neutrally buoyant particles within a partially filled horizontal rotating cylinder can, under certain conditions, segregate into bands of particles separated by regions of low particle concentration or even particle-free liquid [M. Tirumkudulu, A. Mileo, and A. Acrivos, Phys. Fluids 12, 1615 (2000)]. An explanation for this phenomenon is proposed on the basis of a model of rimming flows with an axially varying viscosity plus the experimental observation that, when the liquid contains a recirculating region (puddle), the particles segregate radially by migrating out of the puddle into the unidirectional circumferential flow. A linear stability analysis for dilute suspensions shows that such a particle distribution is unstable to axial perturbations with the surface tension being responsible for the selection of the wavelength of the most rapidly amplified disturbance. The calculated and measured spacings between the bands are in good agreement. In addition, since, in the absence of a puddle, the particle concentration appears to remain uniform throughout the cross section of the film, no axial particle segregation is predicted to occur nor has it ever been seen experimentally, even when an axial viscosity variation is imposed on the flow by cooling a preselected portion of the cylinder. © 2004 American Institute of Physics.

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47.55.Kf	Particle-laden flows
47.32.-y	Vortex dynamics; rotating fluids
47.60.-i	Flow phenomena in quasi-one-dimensional systems
68.03.Cd	Surface tension and related phenomena
66.20.-d	Viscosity of liquids; diffusive momentum transport

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Inertialess instability of a two-layer liquid film flow

W. Y. Jiang, B. Helenbrook, and S. P. Lin

Phys. Fluids 16, 652 (2004); http://dx.doi.org/10.1063/1.1642657 (12 pages) | Cited 17 times

Online Publication Date: 4 February 2004

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The physical mechanism of instability in a superposed two-layer liquid film flow down an incline plane is analyzed. If the layer adjacent to the wall is sufficiently thin and less viscous in certain two-layer parallel Newtonian liquid flows of the same density with an interface but without a free surface, the flows are stable with respect to long waves. This is the so-called “thin lubrication layer effect.” However, when a free surface exists in the two-layered flow, the flow becomes unstable even when the Reynolds number approaches zero. Thus the thin-layer lubrication effect is lost due to the presence of the free surface, and inertialess instability occurs. The reason for the loss of the lubrication effect and the mechanism of inertialess instability are explained by use of the energy budget in the mechanical energy equation. Contrary to the case of two-layer flows without a free surface, the flow with a free surface is stable if the layer adjacent to the solid wall is more viscous. The stabilization is achieved even without help from surface or interfacial tension. The mechanism of stabilization is also elucidated from an energy consideration. Navier–Stokes simulations are then performed to determine the effect of the layer viscosity ratio when nonlinear effects are included. © 2004 American Institute of Physics.

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47.55.Hd	Stratified flows
47.20.Ma	Interfacial instabilities (e.g., Rayleigh-Taylor)
68.15.+e	Liquid thin films

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Singularity method for oblate and prolate spheroids in Stokes and linearized oscillatory flow

Lisa F. Shatz

Phys. Fluids 16, 664 (2004); http://dx.doi.org/10.1063/1.1643402 (14 pages) | Cited 7 times

Online Publication Date: 4 February 2004

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This paper applies the singularity method to obtain analytic solutions for oblate spheroids in Stokes flow, and to obtain numerical results for prolate and oblate spheroids undergoing oscillatory translation, and oscillatory rotation. To apply the method to oblate spheroids, singularities are placed along an imaginary focal length. A novel method is used to determine the hydrodynamic torque by deriving Green’s functions for torque for the unsteady rotlet, stresslet, and potential quadrupole. The results agree with analytic solutions for high and low frequencies, the results of previous studies, and results calculated using the boundary element method. © 2004 American Institute of Physics.

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47.35.-i	Hydrodynamic waves
47.32.-y	Vortex dynamics; rotating fluids
47.20.Gv	Viscous and viscoelastic instabilities
02.60.Lj	Ordinary and partial differential equations; boundary value problems
02.30.-f	Function theory, analysis

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Mode-switching and nonlinear effects in compressible flow over a cavity

Michael A. Kegerise, Eric F. Spina, Sanjay Garg, and Louis N. Cattafesta

Phys. Fluids 16, 678 (2004); http://dx.doi.org/10.1063/1.1643736 (10 pages) | Cited 28 times

Online Publication Date: 4 February 2004

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Multiple distinct peaks of comparable strength in unsteady pressure autospectra often characterize compressible flow-induced cavity oscillations. It is unclear whether these different large-amplitude tones (i.e., Rossiter modes) coexist or are the result of a mode-switching phenomenon. The cause of additional peaks in the spectrum, particularly at low frequency, is also unknown. This article describes the analyses of unsteady pressure data in a cavity using time-frequency methods, namely the short-time Fourier transform (STFT) and the continuous Morlet wavelet transform, and higher-order spectral techniques. The STFT and wavelet analyses clearly show that the dominant mode switches between the primary Rossiter modes. This is verified by instantaneous schlieren images acquired simultaneously with the unsteady pressures. Furthermore, the Rossiter modes experience some degree of low-frequency amplitude modulation. An estimate of the modulation frequency, obtained from the wavelet analysis, matches the low-frequency peak seen in the autospectrum. Higher-order spectral methods were employed to investigate potential quadratic nonlinear interactions between the Rossiter modes and to determine if they are responsible for the low-frequency mode present in the autospectrum. In turn, this low-frequency mode could interact with the Rossiter modes to modulate their amplitude. Significant nonlinearities, in the form of sum and difference frequencies of the Rossiter modes, are present in the l/d = 2 cavity at M_∞ = 0.4, while nonlinear effects are much smaller in the l/d = 4 at M_∞ = 0.6. The bispectral analysis indicates that quadratic interactions between Rossiter modes in the near-field pressure are not responsible for the observed low-frequency peak in the pressure autospectrum. Furthermore, the low-frequency mode does not exhibit a strong nonlinear coupling with the Rossiter modes. © 2004 American Institute of Physics.

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47.35.-i	Hydrodynamic waves
47.40.-x	Compressible flows; shock waves
47.80.-v	Instrumentation and measurement methods in fluid dynamics
02.30.-f	Function theory, analysis

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Coupled numerical and theoretical study of the flow transition between a rotating and a stationary disk

Eric Serre, Ewa Tuliszka-Sznitko, and Patrick Bontoux

Phys. Fluids 16, 688 (2004); http://dx.doi.org/10.1063/1.1644144 (19 pages) | Cited 14 times

Online Publication Date: 4 February 2004

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Both direct numerical simulation and theoretical stability analysis are performed together in order to study the transition process to turbulence in a flow between a rotating and a stationary disk. This linear stability analysis considers the complete rotor-stator flow and then extends the results of Lingwood [J. Fluid Mech. 299, 17 (1995); 314, 373 (1996)] obtained in a single disk case. The present linear analysis also extends the former two-disk computations of Itoh [ASME FED 114, 83 (1991)], only limited to a hydrodynamic spatial instability analysis. Moreover, in the present work, this approach is completed by discussing the effects of buoyancy-driven convection on the flow stability and by absolute/convective analysis of the flow. Coupled with accurate numerical computations based on an efficient pseudo-spectral Chebyshev–Fourier method, this study brings new insight on the spatio-temporal characteristics of this flow during the first stages of transition. For instance, an exchange of stability from a steady to a periodic flow with spiral structures is observed for the first time numerically in such cavity of large aspect ratio. The nature of the first bifurcation is discussed as well as the influence on it of disturbances coming from the end-wall boundary layer. Annular and spiral patterns are observed in the unstable stationary disk layer with characteristic parameters agreeing very well with the present theoretical results. Then, these structures are interpreted in terms of type I and type II generic instabilities. Moreover, the absolute instability regions which are supposed to be strongly connected with the turbulent breakdown process are also identified and the critical Reynolds numbers of the convective/absolute transition in both Ekman and Bödewadt layers are given. © 2004 American Institute of Physics.

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47.27.Cn	Transition to turbulence
47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking
47.32.-y	Vortex dynamics; rotating fluids
47.27.T-	Turbulent transport processes
47.11.-j	Computational methods in fluid dynamics
47.27.nb	Boundary layer turbulence
02.30.Nw	Fourier analysis
02.60.Cb	Numerical simulation; solution of equations

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Rotating disk flow stability in electrochemical cells: Effect of viscosity stratification

J. Pontes, N. Mangiavacchi, A. R. Conceição, O. E. Barcia, O. R. Mattos, and B. Tribollet

Phys. Fluids 16, 707 (2004); http://dx.doi.org/10.1063/1.1644147 (10 pages) | Cited 3 times

Online Publication Date: 4 February 2004

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This work is about the effect of viscosity stratification on the hydrodynamic instability of rotating disk flow, and whether or not it can take into account experimental observations of the lowering of critical Reynolds numbers in electrochemical systems, where a viscosity stratification is assumed to result from the gradients of chemical species existing in the convective boundary layer near the disk electrode. The analysis is for temporal stability of a class of von Kármán solutions: fully three-dimensional modes are considered and the neutral curves are therefore functions of not only the Reynolds number but also the wave frequency and the two wave numbers. Global minimization over wave numbers and also over the frequency gives the critical Reynolds number. The neutral curves exhibit a two-mode structure and the dependence of both modes on parameters is studied. It is shown that viscosity stratification leads to an increase in the range of parameters where perturbations are amplified and to a reduction of the critical Reynolds number, in a wide range of perturbation frequencies. The results support the hypothesis that the current oscillations may originate from a hydrodynamic instability. © 2004 American Institute of Physics.

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47.20.Gv	Viscous and viscoelastic instabilities
66.20.-d	Viscosity of liquids; diffusive momentum transport
47.32.-y	Vortex dynamics; rotating fluids
47.27.T-	Turbulent transport processes
82.47.Jk	Photoelectrochemical cells, photoelectrochromic and other hybrid electrochemical energy storage devices

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Motion of a vortex sheet on a sphere with pole vortices

Takashi Sakajo

Phys. Fluids 16, 717 (2004); http://dx.doi.org/10.1063/1.1644148 (11 pages) | Cited 4 times

Online Publication Date: 4 February 2004

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We consider the motion of a vortex sheet on the surface of a unit sphere in the presence of point vortices fixed on north and south poles. Analytic and numerical research revealed that a vortex sheet in two-dimensional space has the following three properties. First, the vortex sheet is linearly unstable due to Kelvin–Helmholtz instability. Second, the curvature of the vortex sheet diverges in finite time. Last, the vortex sheet evolves into a rolling-up doubly branched spiral, when the equation of motion is regularized by the vortex method. The purpose of this paper is to investigate how the curvature of the sphere and the presence of the pole vortices affect these three properties mathematically and numerically. We show that some low spectra of disturbance become linearly stable due to the pole vortices and thus the singularity formation tends to be delayed. On the other hand, however, the vortex sheet, which is regularized by the vortex method, acquires complex structure of many rolling-up spirals. © 2004 American Institute of Physics.

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47.32.C-	Vortex dynamics
47.20.Cq	Inviscid instability
47.20.Ft	Instability of shear flows (e.g., Kelvin-Helmholtz)
47.10.-g	General theory in fluid dynamics

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Dynamic stretching of a planar liquid bridge

C. Mehring, J. Xi, and W. A. Sirignano

Phys. Fluids 16, 728 (2004); http://dx.doi.org/10.1063/1.1644150 (20 pages)

Online Publication Date: 4 February 2004

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A thin incompressible viscous planar free liquid film in a void and under zero gravity is analyzed by means of a reduced-dimension (lubrication) approach. Linear analysis focuses on films with harmonic modulations in the axial film velocity enforced at the ends of the planar bridge. Effects of changes in the problem parameters on the overall distortion characteristics of the film are discussed. Nonlinear film distortion and break-up are investigated for the case of temporally increasing velocity at the end of the film resulting in continuous film stretching eventually leading to film rupture. Implementation of the employed numerical model is validated for the linear limit by comparison with the analytical linear solutions and for harmonically modulated film-end velocities. Within the nonlinear analysis of the continuously stretched film bridge, several distinct film topologies are identified depending on liquid Weber number and Reynolds number, i.e., the magnitude of the stretching rate (end velocity) compared to signal propagation rates through the liquid via capillary waves and viscous action. That is, the Weber number is the square of the ratio of stretching rate to capillary wave velocity while the Reynolds number is the ratio of stretching rate to the characteristic viscous velocity. Here, film topology is typically characterized by three distinct regions, i.e., a film wedge forming at the pulling end(s), the film center region and a transition region. The size and shape of these regions greatly depend on the particular case under investigation. Film distortion characteristics observed for continuously compressed planar films conform with observations made by other authors for the similar case of contracting free liquid films. © 2004 American Institute of Physics.

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68.15.+e	Liquid thin films
47.35.-i	Hydrodynamic waves
66.20.-d	Viscosity of liquids; diffusive momentum transport

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Contact-line dynamics and damping for oscillating free surface flows

Lei Jiang, Marc Perlin, and William W. Schultz

Phys. Fluids 16, 748 (2004); http://dx.doi.org/10.1063/1.1644151 (11 pages) | Cited 6 times

Online Publication Date: 4 February 2004

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New experimental data on the frequency and damping of Faraday water waves in glass tanks are presented to demonstrate the contact-line effect on free surface flows. We find a complicated nonlinear relationship between wave frequency and amplitude near contact lines: The amplitude dispersion for decaying standing waves directly progresses from a nonlinear regime due to large amplitude to a regime due to contact-line nonlinearity. The relative damping rate is also a function of the wave amplitude, increasing significantly at smaller wave amplitude. These results are discussed in relation to different formulations of contact-line conditions for oscillatory motions and free surface flows. A new model is proposed to explain the observed amplitude scaling in the frequency and damping rate, and to relate these behaviors to slip-length and other contact-line measurements by Ting and Perlin [J. Fluid Mech. 295, 263 (1995)]. © 2004 American Institute of Physics.

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47.35.-i	Hydrodynamic waves
47.45.Gx	Slip flows and accommodation

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Velocity slip and temperature jump coefficients for gaseous mixtures. II. Thermal slip coefficient

Felix Sharipov and Denize Kalempa

Phys. Fluids 16, 759 (2004); http://dx.doi.org/10.1063/1.1644572 (6 pages) | Cited 16 times

Online Publication Date: 4 February 2004

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The thermal slip coefficient was calculated for a binary gaseous mixture on the basis of the McCormack kinetic model of the Boltzmann equation, which was solved by the discrete velocity method. The calculations were carried out for the three mixtures of noble gases: neon–argon, helium–argon, and helium–xenon. A strong influence of the potential of intermolecular interaction upon the thermal slip coefficient was observed by comparing the results based on the model of rigid spheres with those obtained for a realistic potential. An example of application of the thermal slip coefficient is given. © 2004 American Institute of Physics.

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47.45.Gx	Slip flows and accommodation
47.10.-g	General theory in fluid dynamics

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Experimental study of a supersonic jet-mixing layer interaction

E. Collin, S. Barre, and J. P. Bonnet

Phys. Fluids 16, 765 (2004); http://dx.doi.org/10.1063/1.1644574 (14 pages) | Cited 5 times

Online Publication Date: 4 February 2004

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An experimental study is performed to analyze the interaction between a control jet (CJ) and a moderately supersonic main jet. Flow visualizations and laser Doppler velocimetry methods are used. A strong instability of the CJ has been identified. The dynamic of this instability corresponds to that of the local mixing layer. Two stability scenarios are proposed, one corresponding to the local Kelvin–Helmholtz instability of the main jet, the other linked to a local absolute instability of the interaction. The impact on the turbulent quantities is analyzed. It is shown that a strong modification of the Reynolds stress is manifest but that this extends only a small distance from the interaction. © 2004 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
47.80.-v	Instrumentation and measurement methods in fluid dynamics
06.30.Gv	Velocity, acceleration, and rotation
47.85.L-	Flow control