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

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An experimental and numerical investigation of drag reduction in a turbulent boundary layer using a rigid rodlike polymer

J. S. Paschkewitz, Costas D. Dimitropoulos, Y. X. Hou, V. S. R. Somandepalli, M. G. Mungal, Eric S. G. Shaqfeh, and Parviz Moin

Phys. Fluids 17, 085101 (2005); http://dx.doi.org/10.1063/1.1993307 (17 pages) | Cited 3 times

Online Publication Date: 2 August 2005

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The drag reduction in a zero pressure gradient (ZPG) turbulent boundary layer (TBL) using a rigid rodlike polymer was experimentally and numerically investigated. Using injection of the rigid polysaccharide scleroglucan, drag reductions of approximately 10–15 % were observed, with three distinct drag reduction regimes: a non-Newtonian flow region near the injector, followed by a region of nearly constant drag reduction, and finally a region of negligible drag reduction. Decreasing the effective rotary Peclét number reduced the drag reduction effectiveness. Increasing the concentration did not improve the drag reduction, but instead shifted the spatial development of the drag reduction further downstream. A complementary direct numerical simulation of the ZPG TBL using the rigid rod constitutive equation was performed at a matching inlet Reynolds number. The simulation assumed a homogeneous concentration distribution and used estimated effective parameters for the rodlike additive. Spatial evolution of the fiber stresses is rapid and develops asynchronously with the flow structure. The simulated turbulence statistics and experimental measurements at a position 23 boundary layer thicknesses downstream compare favorably, with the primary differences due to the concentration distribution assumed in the simulation.

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47.27.nb	Boundary layer turbulence
47.27.E-	Turbulence simulation and modeling
47.50.-d	Non-Newtonian fluid flows
47.11.-j	Computational methods in fluid dynamics

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Decomposition of the spatially filtered and ensemble averaged kinetic energy, the associated fluxes and scaling trends in a rotor wake

Yi-Chih Chow, Oguz Uzol, Joseph Katz, and Charles Meneveau

Phys. Fluids 17, 085102 (2005); http://dx.doi.org/10.1063/1.1990206 (20 pages) | Cited 6 times

Online Publication Date: 4 August 2005

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Particle image velocimetry data obtained in the rotor wake of a turbomachine are used for examining elements of the ensemble averaged and spatially filtered kinetic energy. These two distinct averaging processes decompose the kinetic energy into four parts, consisting of the mean-flow resolved, mean-flow subgrid, fluctuating resolved, and fluctuating subgrid parts. Their evolution equations include energy flux terms among these parts. The results elucidate the fundamental difference between the filtered turbulence (Reynolds) production and the ensemble averaged subgrid scale (SGS) dissipation rates. Each of these terms consist of three energy fluxes, but only one of them is common to both, the flux from the mean-flow resolved to the fluctuating subgrid kinetic energy parts. The other two elements of the SGS dissipation are the fluxes from the mean-flow resolved to the mean-flow subgrid parts and the fluctuating resolved to the fluctuating subgrid parts. Likewise, the other two contributions to the turbulence production are the fluxes from the mean-flow resolved to the fluctuating resolved parts and the mean-flow subgrid to the fluctuating subgrid parts. In order to examine the decay rates of the kinetic energy parts throughout the rotor wake, a new method for determining the scaling parameters is introduced. The mean-flow resolved and subgrid parts scale with the modified velocity defect squared, but the decay rates of the turbulence parts are slower.

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47.85.Kn	Hydraulic and pneumatic machinery
47.27.wb	Turbulent wakes
47.32.-y	Vortex dynamics; rotating fluids
05.40.-a	Fluctuation phenomena, random processes, noise, and Brownian motion

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On using large-eddy simulation for the prediction of noise from cold and heated turbulent jets

Daniel J. Bodony and Sanjiva K. Lele

Phys. Fluids 17, 085103 (2005); http://dx.doi.org/10.1063/1.2001689 (20 pages) | Cited 31 times

Online Publication Date: 16 August 2005

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The results of a series of large-eddy simulations of heated and unheated jets using approximately 10⁶ grid points are presented. The computations were performed on jets at operating conditions originally investigated by Tanna in the late 1970s [H. K. Tanna, “An experimental study of jet noise Part I: Turbulent mixing noise,” J. Sound Vib., 50, 405 (1977) ]. Three acoustic Mach numbers are investigated (U_j/a_∞ = 0.5, 0.9, and 1.5) at cold (constant stagnation temperature) and heated conditions (T_j/T_∞ = 1.8, 2.7, and 2.3, respectively). The jets’ initial annular shear layers are thick relative to experimental jets and are quasi-laminar with superimposed disturbances from linear instability theory. It is observed that qualitative changes in the jets’ mean- and turbulent field structure with U_j and T_j are consistent with previous experimental data. However, the jets exhibit a faster centerline mean velocity decay rate relative to the existing data, with a corresponding 3–4 % over-prediction of the peak root-mean-square level. The acoustic pressure fluctuations in the far field are analyzed in detail. The accuracy of the overall sound pressure level predictions is found to be a strong function of the jet Mach number, with the lowest speed jets being the least accurate. At all conditions the peak acoustic frequency occurs at approximately St = fD_j/U_j = 0.25. The limited resolution of the computations is shown to impact the radiated sound by yielding effectively low-pass filtered versions of the experimental spectra, with a maximum frequency of St ≈ 1.2.

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47.27.Sd	Turbulence generated noise
47.27.wg	Turbulent jets
47.11.-j	Computational methods in fluid dynamics
47.27.nb	Boundary layer turbulence
47.40.-x	Compressible flows; shock waves
47.20.-k	Flow instabilities
47.15.-x	Laminar flows

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Experiments on the effects of aging on compliant coating drag reduction

P. R. Bandyopadhyay, C. Henoch, J. D. Hrubes, B. N. Semenov, A. I. Amirov, V. M. Kulik, A. G. Malyuga, K.-S. Choi, and M. P. Escudier

Phys. Fluids 17, 085104 (2005); http://dx.doi.org/10.1063/1.2008997 (9 pages) | Cited 4 times

Online Publication Date: 18 August 2005

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We report the experimental results from a collaborative effort between USA, Russia, and UK on the development of compliant coatings for undersea application of reduction of drag. The focus is on “shelf-life” of coatings. The coatings are based on a linear interference theory of interaction between turbulence pressure fluctuation and the viscoelastic coating. The phase shift between boundary displacement and pressure fluctuation embodies the interference effect. The natural frequency of the coating is matched to the turbulent boundary layer region of maximum Reynolds stress production. Low-molecular weight rubber-like silicone coatings have been manufactured whose properties include slow and fast damping, slow and fast aging, and varying magnitudes of elasticity, density, and thickness as well as transparency. The dynamic modulus and loss tangent vary weakly over a range of frequencies and temperature allowing compatibility with broad spectrum of turbulence. Drag measurements have been carried out over a year by the three teams in their water tunnels independently of identical coated models. We show that, with some exceptions, drag reduction generally deteriorates with the age of the coatings.

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47.85.Dh	Hydrodynamics, hydraulics, hydrostatics
47.27.nb	Boundary layer turbulence
81.40.Cd	Solid solution hardening, precipitation hardening, and dispersion hardening; aging
81.40.Jj	Elasticity and anelasticity, stress-strain relations
62.40.+i	Anelasticity, internal friction, stress relaxation, and mechanical resonances
62.20.D-	Elasticity

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Numerical simulation of the generation mechanism of axisymmetric supersonic jet screech tones

X. D. Li and J. H. Gao

Phys. Fluids 17, 085105 (2005); http://dx.doi.org/10.1063/1.2033909 (8 pages) | Cited 6 times

Online Publication Date: 23 August 2005

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In this paper an axisymmetric computational aeroacoustic procedure is developed to investigate the generation mechanism of axisymmetric supersonic jet screech tones. The axisymmetric Navier-Stokes equations and the two equations standard k-ϵ turbulence model modified by Turpin and Troyes [ “Validation of a two-equation turbulence model for axisymmetric reacting and non-reaction flows,” AIAA Paper No. 2000-3463 (2000) ] are solved in the generalized curvilinear coordinate system. A generalized wall function is applied in the nozzle exit wall region. The dispersion-relation-preserving scheme is applied for space discretization. The 2N storage low-dissipation and low-dispersion Runge-Kutta scheme is employed for time integration. Much attention is paid to far-field boundary conditions and turbulence model. The underexpanded axisymmetric supersonic jet screech tones are simulated over the Mach number from 1.05 to 1.2. Numerical results are presented and compared with the experimental data by other researchers. The simulated wavelengths of A0, A1, A2, and B modes and part of simulated amplitudes agree very well with the measurement data by Ponton and Seiner [ “The effects of nozzle exit lip thickness on plume resonance,” J. Sound Vib. 154, 531 (1992) ]. In particular, the phenomena of modes jumping have been captured correctly although the numerical procedure has to be improved to predict the amplitudes of supersonic jet screech tones more accurately. Furthermore, the phenomena of shock motions are analyzed. The predicted splitting and combination of shock cells are similar with the experimental observations of Panda [ “Shock oscillation in underexpanded screeching jets,” J. Fluid. Mech. 363, 173 (1998) ]. Finally, the receptivity process is numerically studied and analyzed. It is shown that the receptivity zone is associated with the initial thin shear layer, and the incoming and reflected sound waves.

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47.27.Sd	Turbulence generated noise
47.27.wg	Turbulent jets
47.40.Ki	Supersonic and hypersonic flows
47.10.-g	General theory in fluid dynamics
47.11.-j	Computational methods in fluid dynamics
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.20.Pc	Flow receptivity
47.40.Nm	Shock wave interactions and shock effects
47.27.nb	Boundary layer turbulence

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Flow structure in a model of aircraft trailing vortices

J. M. Faddy and D. I. Pullin

Phys. Fluids 17, 085106 (2005); http://dx.doi.org/10.1063/1.1955536 (17 pages) | Cited 3 times

Online Publication Date: 23 August 2005

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We consider a model of incompressible trailing vortices consisting of an array of counter-rotating structures in a doubly periodic domain, infinite in the vertical direction. The two-dimensional vortex array of Mallier and Maslowe is combined with an axial velocity profile chosen proportional to the initial axial vorticity to provide an initial condition for the vortex wake. This base flow is a weak solution of the steady Euler equations with three velocity components that are functions of two spatial coordinates, thus allowing its linear stability properties to be investigated. These are used to interpret several stages in the development of vortex structure observed in fully three-dimensional direct numerical simulation (DNS) at Reynolds numbers Γ/(2πν) = O(1000). For sufficiently high axial velocity, its effect can be seen, in that each vortex in the linear array first develops helical structures before undergoing a period of relaminarization. At later times the more slowly growing cooperative elliptical instabilities become apparent, but the helical structure persists and the observed vortical structures remain coherent for longer periods than in the absence of axial velocity. Using the stretched-vortex subgrid model, large-eddy simulation runs are performed at large Reynolds numbers and a mixing transition identified at about Re = 1−2×10⁴. Similar phenomena are observed in these simulations as are seen in the DNS.

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47.85.Gj	Aerodynamics
47.32.C-	Vortex dynamics
47.27.wb	Turbulent wakes
47.11.-j	Computational methods in fluid dynamics
47.20.-k	Flow instabilities

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A quasinormal scale elimination model of turbulent flows with stable stratification

Semion Sukoriansky, Boris Galperin, and Ilya Staroselsky

Phys. Fluids 17, 085107 (2005); http://dx.doi.org/10.1063/1.2009010 (28 pages) | Cited 16 times

Online Publication Date: 23 August 2005

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A new spectral model for turbulent flows with stable stratification is presented. The model is based on a quasi-Gaussian mapping of the velocity and temperature fields using the Langevin equations and employs a recursive procedure of small-scale mode elimination that results in a coupled system of differential equations for effective, horizontal and vertical, viscosities and diffusivities. With increasing stratification, the vertical viscosity and diffusivity are suppressed while their horizontal counterparts are enhanced thus explicitly accounting for the anisotropy introduced by stable stratification. The new model is used to derive various spectral characteristics of stably stratified turbulent flows. It accounts for energy accumulation in the horizontal components at the expense of the energy reduction in the vertical component. The scale elimination algorithm explicitly accounts for the combined effect of turbulence and internal waves. A modified dispersion relation for internal waves, a relationship for internal wave frequency shift, and a threshold criterion for internal wave generation in the presence of turbulent scrambling are derived. It is shown how the model can be utilized to derive parameters needed for Reynolds-averaged Navier-Stokes modeling. Implemented in the K-ϵ format, the new model produces results that agree very well with the observational data on stably stratified atmospheric boundary layers and that are difficult to obtain using traditional two-equation turbulence modeling.

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47.27.E-	Turbulence simulation and modeling
47.27.nb	Boundary layer turbulence
47.55.Hd	Stratified flows
47.20.-k	Flow instabilities
47.35.-i	Hydrodynamic waves
47.10.-g	General theory in fluid dynamics

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Linear interaction analysis applied to a mixture of two perfect gases

J. Griffond

Phys. Fluids 17, 086101 (2005); http://dx.doi.org/10.1063/1.1997982 (19 pages) | Cited 5 times

Online Publication Date: 28 July 2005

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The linear interaction analysis is applied to mixtures of two perfect gases. Differences of molar mass and constant volume specific heat between both gases are taken into account as two new wave families. Transfer functions across the shock wave from these waves to acoustic, shear or entropy waves are given. The approach is validated against numerical simulations of the interaction of concentration spots with a shock wave. The case of turbulence creation by a shock wave traveling in an inhomogeneous mixture is considered.

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47.40.Nm	Shock wave interactions and shock effects
47.11.-j	Computational methods in fluid dynamics
47.27.-i	Turbulent flows
51.30.+i	Thermodynamic properties, equations of state

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Nonaxisymmetric effects of stratified spin-up in an axisymmetric annular channel

S. A. Smirnov, D. L. Boyer, and P. G. Baines

Phys. Fluids 17, 086601 (2005); http://dx.doi.org/10.1063/1.2002999 (12 pages) | Cited 3 times

Online Publication Date: 2 August 2005

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Laboratory experiments were conducted on spin-up of a linearly stratified fluid in a rotating axisymmetric annular channel formed by two cylindrical coaxial walls and a flat bottom. Secular as well as instantaneous variation in rotation speeds was investigated for a range of Rossby numbers ε = ΔΩ/Ω ⩽ 1, where ΔΩ is the change in the rotation rate and Ω is the final rotation rate of the annulus. The experimental studies reported by Smirnov et al. [ S. A. Smirnov, P. G. Baines, D. L. Boyer, S. I. Voropayev, and A. N. Srdic-Mitrovic, “Long-time evolution of linearly stratified spin-up flows in axisymmetric geometries,” Phys. Fluids 17, 016601 (2005) ] were extended to (i) explore the density structure of the corner regions formed adjacent to the inner and outer sidewalls of the annular channel during spin-up, and to (ii) investigate the role of the boundary conditions at the vertical sidewalls in the development of nonaxisymmetric disturbances and formation of large columnar eddies at late spin-up times. The latter was achieved by introducing roughness elements in the form of vertical prisms at the inner sidewall. Observations demonstrated that isopycnals (surfaces of constant density) experience large vertical displacements near the lateral boundaries during spin-up. The density gradient reduces to near zero in the corner regions, where the fluid is stirred, and increases above/below them near the outer/inner sidewalls, respectively. The relative height of the corner regions h/H (H is the depth of the fluid layer) was found to be determined only by the relative values of the Rossby (ε) and Burger (B_u) numbers and follows the experimental dependence h/H = 0.54ε^1/2/B_u. A flow stability regime diagram is presented as a function of the Rossby and Burger numbers. Introduction of roughness elements at the inner sidewall did not alter significantly the process and time scales of stratified spin-up, large eddy formation, and subsequent relaxation to the initial state obtained with smooth sidewalls. This finding confirms that the growth of instability in the sidewall shear layers studied by Smirnov et al. does not depend on viscosity.

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47.55.Hd	Stratified flows
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.32.-y	Vortex dynamics; rotating fluids
47.20.Ft	Instability of shear flows (e.g., Kelvin-Helmholtz)

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Pore water convection within carbonaceous chondrite parent bodies: Temperature-dependent viscosity and flow structure

Keke Zhang, Xinhao Liao, and Gerald Schubert

Phys. Fluids 17, 086602 (2005); http://dx.doi.org/10.1063/1.2012047 (12 pages) | Cited 3 times

Online Publication Date: 23 August 2005

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Thermal convection of pore water within a permeable, internally heated spherical body is investigated. Account is taken of the strong temperature dependence of the viscosity of water. With application to hydrothermal circulation in carbonaceous chondrite parent bodies in mind, the variation of gravity with radius in the body is also accounted for. The critical Rayleigh number for the onset of hydrothermal convection in a spherical porous body is determined as a function of the central temperature. It is found that the basic motionless state always becomes unstable with respect to an infinitesimal disturbance characterized by spherical harmonic degree l = 2. The order of the spherical harmonics m, and hence the three-dimensional structure of the convective flow, cannot be determined by the stability analysis because of the degeneracy of the linear solution. The three-dimensional structure of the convective flow is determined by removing the degeneracy through the nonlinear effect of the temperature-dependent water viscosity. Three different convection solutions are found. However, the three-dimensional structures of these solutions are exactly the same and axisymmetric after an appropriate rotational transformation. The stability criterion is most effectively viewed as a requirement that the product of permeability and square of planetesimal radius exceed a quantity mainly dependent on central temperature. In this way, the criterion applies to planetesimals independent of the specific identification of the short-lived radionuclide responsible for early heating or its concentration. Evaluation of the criterion in this form leads to the conclusion that hydrothermal convection is likely in carbonaceous chondrite parent bodies heated sufficiently to melt the ice and raise the water temperature by tens to a hundred degrees Celsius. Weakly nonlinear convection in the planetesimals has two regions of hot upwelling water providing significant volumes of hydrothermally altered rock.

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47.27.T-	Turbulent transport processes
47.56.+r	Flows through porous media
47.35.-i	Hydrodynamic waves
47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking
66.20.-d	Viscosity of liquids; diffusive momentum transport

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A model for the formation of “optimal” vortex rings taking into account viscosity

F. B. Kaplanski and Y. A. Rudi

Phys. Fluids 17, 087101 (2005); http://dx.doi.org/10.1063/1.1996928 (7 pages) | Cited 12 times

Online Publication Date: 29 July 2005

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The evolution of a viscous vortex ring from thin to thick-cored form is considered using an improved asymptotic solution, which is obtained after impressing a spatially uniform drift on the first-order solution of the Navier–Stokes equations. The obtained class of rings can be considered as the viscous analog solution to the Norbury vortices and classified in terms of the ratio of their initial outer radius to the core radius. The model agrees with the reported theoretical and experimental results referring to the post-formation and the formation stages. By using the matching procedure suggested earlier and the obtained properties of the viscous vortex ring, it is found that when the length-to-diameter aspect ratio L/D reaches the limiting value 4.0 (“formation number”), the appropriate values of the normalized energy and circulation become around 0.3 and 2.0, respectively. An approach that enables to predict the “formation number” is proposed.

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47.32.C-	Vortex dynamics
47.10.-g	General theory in fluid dynamics

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A multiphase flow model for the unstable mixing of incompressible layered materials

Baolian Cheng, J. Glimm, D. H. Sharp, and Y. Yu

Phys. Fluids 17, 087102 (2005); http://dx.doi.org/10.1063/1.2001007 (8 pages)

Online Publication Date: 29 July 2005

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In this paper, a model for the unstable mixing of n parallel or concentric incompressible fluid layers is proposed. The approach in constructing this model is pairwise, based on a known two-incompressible-fluid mixing model. The problem complexity increases significantly in going from two to three fluids, but the increase in complexity is relatively small thereafter. We present a detailed study of the n = 3 problem, which displays all of the difficult modeling issues applicable to arbitrary n ≥ 3 while still being reasonably tractable.

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47.55.Kf	Particle-laden flows
47.20.Ma	Interfacial instabilities (e.g., Rayleigh-Taylor)
47.55.Hd	Stratified flows

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Interaction of two unequal corotating vortices

R. R. Trieling, O. U. Velasco Fuentes, and G. J. F. van Heijst

Phys. Fluids 17, 087103 (2005); http://dx.doi.org/10.1063/1.1993887 (17 pages) | Cited 11 times

Online Publication Date: 29 July 2005

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Previous high-resolution contour dynamics calculations [ Dritschel and Waugh, Phys. Fluids A 4, 1737 (1992) ] have shown that in two-dimensional inviscid flow the interaction of two unequal corotating vortices with uniform vorticity is not always associated with vortex growth and may lead to vortices smaller than the original vortices. In the present study, we investigate whether these results also hold for two-dimensional vortices with continuous vorticity distributions. Similar flow regimes are found as for uniform vorticity patches, but the variation of the flow regimes with the initial vortex radii and peak vorticities is more complicated and strongly dependent on the initial shape of the vorticity profile. It is found that the “halo” of low-value vorticity, which surrounds the cores of continuous vortices, significantly increases the critical distance at which the weaker vortex is destroyed. The halo also promotes the vortex cores to merge more efficiently, since it accounts for a substantial part of the loss of circulation into filaments. Simple transformation rules and merger criteria are derived for the inviscid interaction between two Gaussian vortices. The strong dependence of the flow regimes on the initial vorticity distribution partly explains why previous laboratory experiments in an electron plasma [ Mitchell and Driscoll, Phys. Fluids 8, 1828 (1996) ] show complete merger of two unequal vortices in a range of parameter space where contour dynamics simulations with uniform vorticity patches predict partial merger or partial straining-out of the smaller vortex. It is shown that the measured times for complete merger are in reasonable agreement with inviscid dynamics when the vortices are very similar. For more distinct vortices the weaker vortex is often observed to be destroyed on a time scale much smaller than expected from inviscid numerical simulations. An explanation for this discrepancy is given by the combined effects of vortex stripping and viscous diffusion, which leads to an enhanced erosion of the weaker vortex. These results are verified by laboratory experiments in a conventional (rotating) fluid.

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47.32.C-	Vortex dynamics
47.11.-j	Computational methods in fluid dynamics

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Imbibition of a liquid droplet on a deformable porous substrate

Daniel M. Anderson

Phys. Fluids 17, 087104 (2005); http://dx.doi.org/10.1063/1.2000247 (22 pages) | Cited 3 times

Online Publication Date: 2 August 2005

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We consider the imbibition of a liquid droplet into a deformable porous substrate. The liquid in the droplet is imbibed due to capillary suction in an initially dry and undeformed substrate. Deformation of the substrate occurs as the liquid fills the pore space. In our model, a pressure gradient in the liquid across the developing wet substrate region induces a stress gradient in the solid matrix which in turn leads to an evolving solid fraction and hence deformation. For axisymmetric droplets, we assume that the imbibition and substrate deformation at a given radial position are one-dimensional (in the vertical direction). The coupling to the droplet geometry leads to axisymmetric configurations for the deformed wet substrate. We show that the model chosen to describe the dynamics of the liquid droplet, based in this case on existing models developed for droplet spreading on rigid porous substrates, has little influence on the resultant swelling or shrinking of the substrate—these general trends can be effectively predicted by a one-dimensional imbibition and deformation model—but does strongly influence the details of the wet substrate shape. We characterize these predictions and in some cases can obtain analytical solutions for the evolution.

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47.56.+r	Flows through porous media
47.55.D-	Drops and bubbles
47.55.Kf	Particle-laden flows
68.08.Bc	Wetting

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Velocity slip in microscale cylindrical Couette flow: The Langmuir model

R. S. Myong, J. M. Reese, R. W. Barber, and D. R. Emerson

Phys. Fluids 17, 087105 (2005); http://dx.doi.org/10.1063/1.2003154 (11 pages) | Cited 18 times

Online Publication Date: 9 August 2005

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The velocity slip on the solid surfaces of microscale cylindrical Couette flow is investigated using the Langmuir adsorption model for the gas-surface molecular interaction. The accommodation coefficient in the Maxwell model, which is a free parameter based on the concept of diffusive reflection, is replaced by a physical parameter of heat adsorption in the Langmuir model. The phenomenon of velocity inversion is then clearly explained by introducing a velocity polar on the hodograph plane. It is also shown that the quantity used to determine the momentum slip in a concentric cylindrical geometry should be based upon the angular velocity, not the velocity itself. Finally, and despite their totally independent considerations of the gas-surface molecular interaction, the Maxwell and Langmuir slip models are shown to be in qualitative agreement with direct simulation Monte Carlo data in capturing the general features of the flow field.

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47.45.Gx	Slip flows and accommodation
47.85.Np	Fluidics
47.15.-x	Laminar flows
85.85.+j	Micro- and nano-electromechanical systems (MEMS/NEMS) and devices
68.43.Mn	Adsorption kinetics

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Natural convection near an isothermal wall far downstream from a source

Vadim N. Kurdyumov

Phys. Fluids 17, 087106 (2005); http://dx.doi.org/10.1063/1.2001587 (8 pages)

Online Publication Date: 11 August 2005

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Steady, two-dimensional, free convection flows near an isothermal wall are considered downstream from a heat source at large Grashof numbers for cases when the temperature of the wall is maintained the same as that of the fluid far from the wall. The analyses are given for two cases: (A) for a vertical wall and (B) for a horizontal wall, when the thermal plume spreads along the wall horizontally. The study is based on the Boussinesq boundary layer equations. The solutions have been found in the self-similar form of the second kind. The asymptotic solutions for very large and small Prandtl numbers in the case of the vertical wall, and for very large Prandtl numbers in the case of the horizontal wall are presented. It was found that in the case of the horizontal wall the self-similar solution does not exist in the specific low Prandtl-number regime, σ<0.04218.

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47.27.T-	Turbulent transport processes
47.20.-k	Flow instabilities
47.53.+n	Fractals in fluid dynamics

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Three-dimensional computation of convection of water at the center of a superconducting magnet

Syou Maki and Mitsuo Ataka

Phys. Fluids 17, 087107 (2005); http://dx.doi.org/10.1063/1.2009009 (7 pages) | Cited 1 time

Online Publication Date: 18 August 2005

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Magnetothermal convection of water (diamagnetic) contained in a shallow, cylindrical vessel heated from below and cooled from above at the center of a superconducting magnet was numerically studied. Various flow patterns appeared under the influence of the magnetic body force. The flows induced by the magnetic force whose radial component at the vessel side wall was 5.0 times gravity became axisymmetric, and the direction of the flow was opposite to that of the buoyancy-driven thermal convection. When the radial component was as large as gravity, the breaking and recovery of the axisymmetric flow pattern were aperiodically repeated. When it was 0.1 or 0.5 times gravity, the flow showed a three-spoke pattern, breaking axisymmetry. It is discussed that the conditions to obtain such a spoke pattern experimentally are application of a relatively small magnetic field, use of a shallow vessel, and observation for sufficiently long time.

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47.27.T-	Turbulent transport processes
47.65.-d	Magnetohydrodynamics and electrohydrodynamics
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.54.-r	Pattern selection; pattern formation
47.35.-i	Hydrodynamic waves

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Protocol for measuring permeability and form coefficient of porous media

José L. Lage, Paul S. Krueger, and Arunn Narasimhan

Phys. Fluids 17, 088101 (2005); http://dx.doi.org/10.1063/1.1979307 (4 pages) | Cited 4 times

Online Publication Date: 22 July 2005

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The experimental determination of permeability K and form coefficient C, two hydraulic properties necessary to characterize a porous medium, is beset with undesired secondary effects, which augment the uncertainties in their determination. This study sets forth a new measuring protocol, with derived model equations, to guide the design of experiments for accurate determination of K and C, using Darcy’s law of flow through a porous medium and Newton’s law of flow around a bluff body as constitutive equations defining K and C, respectively. The analysis shows that the model equation for measuring C requires the separation between the viscous-drag effect imposed by the porous medium and the viscous effect of the boundary walls on the measured pressure drop when defining K. Furthermore, the model equations suggest large aspect ratio channels and laminar flow with maximum Re as the best choice for measuring K and C (contrary to prevailing belief). The protocol is applicable to either individual or concurrent determination of K and C.

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47.56.+r	Flows through porous media
47.15.Cb	Laminar boundary layers
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.27.-i	Turbulent flows

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Vorticity spectra in high Reynolds number anisotropic turbulence

Scott C. Morris and John F. Foss

Phys. Fluids 17, 088102 (2005); http://dx.doi.org/10.1063/1.1989387 (4 pages) | Cited 3 times

Online Publication Date: 4 August 2005

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Assuming a turbulent flow to be homogeneous and isotropic allows for significant theoretical simplification in the description of its motions. The validity of these assumptions, first put forth by Kolmogorov [ A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluids for very large Reynolds numbers,” C. R. Acad. Sci. URSS 30, 301 (1941) ], has been the subject of considerable analytical development and extensive research as they are applied to actual flows. The present investigation describes the one-dimensional vorticity spectra of two flow fields: a single stream shear layer and the near surface region of an atmospheric boundary layer. Both flow fields exhibit a power-law region with a slope of −1 in the one-dimensional spectra of the spanwise component of vorticity in the same wave-number range for which the velocity spectra indicated the isotropic behavior. This is in strong disagreement with the isotropic prediction, which does not exhibit a power-law behavior.

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47.32.C-	Vortex dynamics
47.27.Jv	High-Reynolds-number turbulence
47.27.nb	Boundary layer turbulence

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Turbulent stress invariant analysis: Clarification of existing terminology

A. J. Simonsen and P.-Å. Krogstad

Phys. Fluids 17, 088103 (2005); http://dx.doi.org/10.1063/1.2009008 (4 pages) | Cited 10 times

Online Publication Date: 12 August 2005

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As a means of studying the structure of the turbulence, the time mean invariants, defined according to the theory of Lumley [“Computational modelling turbulent flows,” Adv. Appl. Mech. 18, 123 (1978) ] has proven to be a useful and popular tool. According to the theory there is a domain, known as the anisotropy invariant map, within which all realizable Reynolds’s stress invariants must lie. The borders of this domain describe different states of the turbulent stress tensor. It has been found that there is some confusion in the terminology used when describing these states. The confusion is related to whether the notation is used to describe the shape of the stress tensor or the eddies of the turbulence. Choi and Lumley [“The return of isotropy of homogeneous turbulence,” J. Fluid Mech. 436, 59 (2001) ] noted the same controversy in terminology, but since the confusion is still found to exist, it was thought timely to describe the fundamental relationships which relate the shape of the stress tensor and its invariants.

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47.27.Gs

Isotropic turbulence; homogeneous turbulence

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The response of compliant coating to nonstationary disturbances

Victor M. Kulik, Sergey V. Rodyakin, Sung-Bu Suh, Inwon Lee, and H. H. Chun

Phys. Fluids 17, 088104 (2005); http://dx.doi.org/10.1063/1.2011467 (4 pages) | Cited 5 times

Online Publication Date: 18 August 2005

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The amplitude and phase lag of surface deformation were determined for a compliant coating under the action of turbulent pressure fluctuations. For this purpose, pressure fluctuations were measured experimentally. The amplitude and duration of coherent wave train of pressure fluctuations were investigated using digital filtration. The transient response was calculated for stabilization of forced oscillations of the coating in approximation of local deformation. The response of coating was analyzed with considerations of its inertial properties and limited duration of coherent harmonics action of pressure fluctuations. It is shown that a compliant coating interacts only with a frequency range near the first resonance. According to the analysis, with increasing elasticity modulus of the coating material E, deformation amplitude decreases as 1/E, and dimensionless velocity of the coating surface decreases as 1/ math

. For sufficiently hard coatings, deformation amplitude becomes smaller than the thickness of the viscous sublayer, while the surface velocity remains comparable to the vertical velocity fluctuations of the flow.

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47.27.nb	Boundary layer turbulence
47.27.T-	Turbulent transport processes
47.35.-i	Hydrodynamic waves
47.32.C-	Vortex dynamics
46.35.+z	Viscoelasticity, plasticity, viscoplasticity

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Linear stability of ultrathin slipping films with insoluble surfactant

Guo-Hui Hu

Phys. Fluids 17, 088105 (2005); http://dx.doi.org/10.1063/1.2017229 (4 pages) | Cited 1 time

Online Publication Date: 18 August 2005

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To study the dewetting process of ultrathin slipping films, the stability characteristics of the surfactant-covered ultrathin films with slippage are analyzed with linear theory. A set of nonlinear equations for the film thickness and the concentration of surfactant is derived based on lubrication approximation for Newtonian viscous fluid. Results show slippage can always enhance the development of perturbations, and reduce the number density of holes when rupture occurs. A prominent characteristic of the stability is that two branches of solutions are found in the dispersion relation. This might lead to an inflexion in the growth rate curve of the most unstable modes, and a cusp point in the corresponding wave number curve for infinite slippage, which indicates that the slip has a profound effect on the linear stability of the films. The influences of the Marangoni number M, equilibrium distance l_c, and the base concentration of surfactant Γ₀ on the linear stability are also discussed for different slip lengths in the present study.

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47.45.Gx	Slip flows and accommodation
47.20.-k	Flow instabilities
47.27.T-	Turbulent transport processes
68.15.+e	Liquid thin films
68.08.Bc	Wetting
68.03.Cd	Surface tension and related phenomena

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A note on the stability of slip channel flows

Eric Lauga and Carlo Cossu

Phys. Fluids 17, 088106 (2005); http://dx.doi.org/10.1063/1.2032267 (4 pages) | Cited 12 times

Online Publication Date: 23 August 2005

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We consider the influence of slip boundary conditions on the modal and nonmodal stability of pressure-driven channel flows. In accordance with previous results by Gersting [“Hydrodynamic stability of plane porous slip flow,” Phys. Fluids 17, 2126 (1974)] but in contradiction with the recent investigation of Chu [“Instability of Navier slip flow of liquids,” C. R. Mec. 332, 895 (2004)] , we show that the slip increases significantly the value of the critical Reynolds number for linear instability. The nonmodal stability analysis, however, reveals that slip has a very weak influence on the maximum transient energy growth of perturbations at subcritical Reynolds numbers. Slip boundary conditions are therefore not likely to have a significant effect on the transition to turbulence in channel flows.

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47.45.Gx	Slip flows and accommodation
47.15.Fe	Stability of laminar flows
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.27.Cn	Transition to turbulence