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Aug 2010

Volume 22, Issue 8, Articles (08xxxx)

Issue Cover Spotlight Figure

Phys. Fluids 22, 085105 (2010); http://dx.doi.org/10.1063/1.3475816 (8 pages)

Xiaohua Wu and Parviz Moin
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On the energy of elliptical vortices

J. Vanneste and W. R. Young

Phys. Fluids 22, 081701 (2010); http://dx.doi.org/10.1063/1.3474703 (4 pages)

Online Publication Date: 9 August 2010

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Consider a two-dimensional axisymmetric vortex with circulation Γ. Suppose that this vortex is isovortically deformed into an elliptical vortex. We show that the reduction in energy is ΔE = −Γ2 ln[(q+q−1)/2]/(4π), where q2 is the ratio of the major to the minor axis of any particular elliptical vorticity contour. It is notable that ΔE is independent of the details of vorticity profile of the axisymmetric vortex and, in particular, independent of its average radius. The implications of this result for the two-dimensional inverse cascade are briefly discussed.
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47.32.-y Vortex dynamics; rotating fluids

Turbulence modulation and drag reduction by spherical particles

L. H. Zhao, H. I. Andersson, and J. J. J. Gillissen

Phys. Fluids 22, 081702 (2010); http://dx.doi.org/10.1063/1.3478308 (4 pages) | Cited 7 times

Online Publication Date: 16 August 2010

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This letter reports on the pronounced turbulence modulations and the accompanying drag reduction observed in a two-way coupled simulation of particle-laden channel flow. The present results support the view that drag reduction can be achieved not only by means of polymeric or fiber additives but also with spherical particles.
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47.27.nb Boundary layer turbulence
47.55.Kf Particle-laden flows
47.60.Dx Flows in ducts and channels
47.11.-j Computational methods in fluid dynamics
47.27.nd Channel flow

Axial and lateral particle ordering in finite Reynolds number channel flows

Katherine J. Humphry, Pandurang M. Kulkarni, David A. Weitz, Jeffrey F. Morris, and Howard A. Stone

Phys. Fluids 22, 081703 (2010); http://dx.doi.org/10.1063/1.3478311 (4 pages) | Cited 9 times

Online Publication Date: 18 August 2010

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Inertial focusing in a pressure-driven flow refers to the positioning of particles transverse to the mean flow direction that occurs as a consequence of a finite particle Reynolds number. In channels with rectangular cross-sections, and for a range of channel aspect ratios and particle confinement, experimental results are presented to show that both the location and the number of focusing positions depend on the number of particles per unit length along the channel. This axial number density is a function of both the channel cross-section and the particle volume fraction. These results are rationalized using simulations of the particle-laden flow to show the manner in which hydrodynamic interactions set the preferred locations in these confined flows. A criterion is presented for the occurrence of a stepwise transition from one to two or more trains of particles.
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47.55.Kf Particle-laden flows
47.60.Dx Flows in ducts and channels
47.11.-j Computational methods in fluid dynamics
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back to top Biofluid Mechanics

Self-similar bending in a flow: The axisymmetric case

Silas Alben

Phys. Fluids 22, 081901 (2010); http://dx.doi.org/10.1063/1.3467494 (8 pages)

Online Publication Date: 12 August 2010

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We study how sheets roll up into conical configurations when exposed to fluid flows using simulations and analysis. The simulations couple the bending of thin sheets to axisymmetric flows with vortex shedding. We find quasisteady flows with vortex ring wakes in which the radii of the rings scale with the radii of the cone bases. The cone angles scale with the dimensionless flow speed raised to the power −1/3. The drag coefficients for the cones scale with flow speed to the power −1. We find good agreement with the previously published experimental results. The scalings we have found result from a self-similar behavior of the flow at the outer edges of the cones, with length scales set by the radii of the vortex rings in the wakes.
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47.53.+n Fractals in fluid dynamics
47.32.cf Vortex reconnection and rings
47.11.-j Computational methods in fluid dynamics

Jet propulsion without inertia

Saverio E. Spagnolie and Eric Lauga

Phys. Fluids 22, 081902 (2010); http://dx.doi.org/10.1063/1.3469786 (18 pages) | Cited 4 times

Online Publication Date: 17 August 2010

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A body immersed in a highly viscous fluid can locomote by drawing in and expelling fluid through pores at its surface. We consider this mechanism of jet propulsion without inertia in the case of spheroidal bodies and derive both the swimming velocity and the hydrodynamic efficiency. Elementary examples are presented and exact axisymmetric solutions for spherical, prolate spheroidal, and oblate spheroidal body shapes are provided. In each case, entirely and partially porous (i.e., jetting) surfaces are considered and the optimal jetting flow profiles at the surface for maximizing the hydrodynamic efficiency are determined computationally. The maximal efficiency which may be achieved by a sphere using such jet propulsion is 12.5%, a significant improvement upon traditional flagella-based means of locomotion at zero Reynolds number, which corresponds to the potential flow created by a source dipole at the sphere center. Unlike other swimming mechanisms which rely on the presentation of a small cross section in the direction of motion, the efficiency of a jetting body at low Reynolds number increases as the body becomes more oblate and limits to approximately 162% in the case of a flat plate swimming along its axis of symmetry. Our results are discussed in the light of slime extrusion mechanisms occurring in many cyanobacteria.
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47.60.Kz Flows and jets through nozzles
47.11.-j Computational methods in fluid dynamics
47.56.+r Flows through porous media
back to top Micro- and Nanofluid Mechanics

Electro-osmotic flow in a wavy microchannel: Coherence between the electric potential and the wall shape function

Y. C. Shu, C. C. Chang, Y. S. Chen, and C. Y. Wang

Phys. Fluids 22, 082001 (2010); http://dx.doi.org/10.1063/1.3467035 (10 pages) | Cited 1 time

Online Publication Date: 12 August 2010

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The electro-osmotic flow through a wavy microchannel is studied under the Debye–Hückel approximation. An analytic solution by perturbation with appropriate averaging is carried out up to the second-order in terms of the small amplitude of corrugation. It is shown that the wavelength and phase difference of the corrugations can be utilized to control the flow relative to the case of flat walls. In particular, for thick electric double layers the electro-osmotic flow can be enhanced at long-wavelength corrugations because of the coherence between the electric potential and the wall shape function. Notably, these findings are not restricted to small amplitudes of corrugation. By applying the Ritz method to solve for the electro-osmotic flow, it is found that the enhancement becomes even greater (up to 30%) with increases in corrugation. Moreover, the nonlinear Poisson–Boltzmann equation is solved by finite difference to study the electro-osmotic flow in terms of the relative strength of the zeta potential. The issue of overlapped electric double layers when they are very thick is also discussed. The relative flow rate is shown to increase under the following conditions: (i) completely out-of-phase corrugations with long wavelength and large amplitude, (ii) small zeta potential, and (iii) slight overlapping of electric double layers.
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47.65.-d Magnetohydrodynamics and electrohydrodynamics
82.45.-h Electrochemistry and electrophoresis
47.60.Dx Flows in ducts and channels
47.85.L- Flow control
47.11.Bc Finite difference methods
47.61.Fg Flows in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS)

Corrugated interfaces in multiphase core-annular flow

Ho Cheung Shum (岑浩璋), Alban Sauret, Alberto Fernandez-Nieves, Howard A. Stone, and David A. Weitz

Phys. Fluids 22, 082002 (2010); http://dx.doi.org/10.1063/1.3480561 (5 pages) | Cited 3 times

Online Publication Date: 31 August 2010

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Microfluidic devices can be used to produce highly controlled and monodisperse double or multiple emulsions. The presence of inner drops inside a jet of the middle phase introduces deformations in the jet, which leads to breakup into monodisperse double emulsions. However, the ability to generate double emulsions can be compromised when the interfacial tension between the middle and outer phases is low, leading to flow with high capillary and Weber numbers. In this case, the interface between the fluids is initially deformed by the inner drops but the jet does not break into drops. Instead, the jet becomes highly corrugated, which prevents formation of controlled double emulsions. We show using numerical calculations that the corrugations are caused by the inner drops perturbing the interface and the perturbations are then advected by the flow into complex shapes.
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47.55.db Drop and bubble formation
47.60.Dx Flows in ducts and channels
47.57.Bc Foams and emulsions
82.70.Kj Emulsions and suspensions
68.03.Cd Surface tension and related phenomena
47.85.Np Fluidics
back to top Interfacial Flows

Buoyancy-induced squeezing of a deformable drop through an axisymmetric ring constriction

Thomas Ratcliffe, Alexander Z. Zinchenko, and Robert H. Davis

Phys. Fluids 22, 082101 (2010); http://dx.doi.org/10.1063/1.3464343 (19 pages) | Cited 2 times

Online Publication Date: 6 August 2010

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Axisymmetric boundary-integral (BI) simulations were made for buoyancy-induced squeezing of a deformable drop through a ring constriction. The algorithm uses the Hebeker representation for the solid-particle contribution. A high-order, near-singularity subtraction technique is essential for near-critical squeezing. The drop velocity and minimum drop-solid spacing were determined for different ring and hole sizes, viscosity ratios, and Bond numbers, where the latter is a dimensionless ratio of gravitational to interfacial forces. The drop velocity decelerates typically 100-fold or more, and the drop-solid spacing reduces to typically 0.1%–1% of the nondeformed drop radius as the drop passes through the constriction. The critical Bond number (below which trapping occurs) was determined for different conditions. For supercritical conditions, the nondimensional time required for the drop to pass through the ring increases for a fixed drop-to-hole size with increasing viscosity ratio and decreasing Bond number, but it has a nonmonotonic dependence on the ratio of the radii of the drop and ring cross section. Numerical results indicate that the square of the drop squeezing time is inversely proportional to the Bond number minus the critical Bond number for near-critical squeezing. The critical Bond number, determined from dynamic BI calculations, compares favorably to that obtained precisely from a static algorithm. The static algorithm uses the Young–Laplace equation to calculate the pendant and sessile portions of the drop interface coupled through the conditions of global pressure continuity and total drop volume conservation. Over a limited parameter space, the critical Bond number increases almost linearly with the drop-to-hole ratio and is a weak function of the ratio of the ring cross-sectional radius to the hole radius. Another dynamic phenomenon, in addition to drop squeezing, is a drop “dripping” around the outer edge of the ring constriction, and a critical Bond number maximum versus the drop-to-total ring radius ratio is caused by the transitions from squeezing to dripping for the loss of a drop steady state on a constriction. The initial stages of drop dripping are numerically simulated using a boundary-integral method for slightly supercritical Bond numbers. For very large ratios of the drop-to-hole radii, however, a sharp maximum in the critical Bond number is reached, as there is a transition from the drop passing through the inside hole to dripping over the outside edge of the ring for Bond numbers above the critical line. Drop squeezing and trapping mechanisms are also observed experimentally, and the measured critical Bond numbers and trapped drop shapes compare favorably to theoretical calculations from the Young–Laplace algorithm.
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47.55.D- Drops and bubbles
47.11.-j Computational methods in fluid dynamics
47.60.-i Flow phenomena in quasi-one-dimensional systems
02.60.Nm Integral and integrodifferential equations
47.85.Np Fluidics

Two-dimensional Stokes flow due to a pair of vortices below the free surface

Jae-Tack Jeong

Phys. Fluids 22, 082102 (2010); http://dx.doi.org/10.1063/1.3473922 (7 pages) | Cited 2 times

Online Publication Date: 17 August 2010

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A two-dimensional Stokes flow due to a pair of counter-rotating vortices of equal strength below the free surface is analyzed, and the streamline pattern and free-surface deformation are discussed. Two vortices are placed at a fixed depth and an arbitrary distance between each other. In the analysis, Stokes’ approximation is used and surface tension effects are included, but gravity is neglected. The solution is obtained by using conformal mapping and complex function theory. From the solution, typical flow patterns are seen, depending on the capillary number, Ca, and the distance between the two vortices, and some interesting results are obtained. For separation distances below a critical distance, a cusp occurs at the center of the free surface as Ca→∞, following the results of Jeong and Moffatt [“Free-surface cusps associated with flow at low Reynolds number,” J. Fluid Mech. 241, 1 (1992)] for no separation (distance of zero). However, above the critical distance, the cusp disappears and a smooth, trough-shaped interface is formed. At even greater separation distances, a pair of viscous eddies exists near the free surface beyond some critical values of Ca. As the capillary number vanishes, the solution is reduced to that of a linearized potential flow.
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47.55.dm Thermocapillary effects
47.32.-y Vortex dynamics; rotating fluids
47.55.nb Capillary and thermocapillary flows

Impact of a compound droplet on a flat surface: A model for single cell epitaxy

Savas Tasoglu, Gozde Kaynak, Andrew J. Szeri, Utkan Demirci, and Metin Muradoglu

Phys. Fluids 22, 082103 (2010); http://dx.doi.org/10.1063/1.3475527 (15 pages) | Cited 13 times

Online Publication Date: 18 August 2010

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The impact and spreading of a compound viscous droplet on a flat surface are studied computationally using a front-tracking method as a model for the single cell epitaxy. This is a technology developed to create two-dimensional and three-dimensional tissue constructs cell by cell by printing cell-encapsulating droplets precisely on a substrate using an existing ink-jet printing method. The success of cell printing mainly depends on the cell viability during the printing process, which requires a deeper understanding of the impact dynamics of encapsulated cells onto a solid surface. The present study is a first step in developing a model for deposition of cell-encapsulating droplets. The inner droplet representing the cell, the encapsulating droplet, and the ambient fluid are all assumed to be Newtonian. Simulations are performed for a range of dimensionless parameters to probe the deformation and rate of deformation of the encapsulated cell, which are both hypothesized to be related to cell damage. The deformation of the inner droplet consistently increases: as the Reynolds number increases; as the diameter ratio of the encapsulating droplet to the cell decreases; as the ratio of surface tensions of the air-solution interface to the solution-cell interface increases; as the viscosity ratio of the cell to encapsulating droplet decreases; or as the equilibrium contact angle decreases. It is observed that maximum deformation for a range of Weber numbers has (at least) one local minimum at We = 2. Thereafter, the effects of cell deformation on viability are estimated by employing a correlation based on the experimental data of compression of cells between parallel plates. These results provide insight into achieving optimal parameter ranges for maximal cell viability during cell printing.
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47.11.Df Finite volume methods
47.55.D- Drops and bubbles
47.55.nd Spreading films
68.03.Cd Surface tension and related phenomena
68.08.Bc Wetting

Accurate series solutions for gravity-driven Stokes waves

Michael C. Dallaston and Scott W. McCue

Phys. Fluids 22, 082104 (2010); http://dx.doi.org/10.1063/1.3480394 (6 pages) | Cited 1 time

Online Publication Date: 23 August 2010

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In the past, high order series expansion techniques have been used to study the nonlinear equations that govern the form of periodic Stokes waves moving steadily on the surface of an inviscid fluid. In the present study, two such series solutions are recomputed using exact arithmetic, eliminating any loss of accuracy due to accumulation of round-off error, allowing a much greater number of terms to be found with confidence. It is shown that a higher order behavior of the series generated by the solution casts doubt over arguments that rely on estimating the series’ radius of convergence. Further, the exact nature of the series is used to shed light on the unusual nature of convergence of higher order Padé approximants near the highest wave. Finally, it is concluded that, provided exact values are used in the series, these Padé approximants prove very effective in successfully predicting three turning points in both the dispersion relation and the total energy.
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47.35.Bb Gravity waves

Dynamics of the triple contact line on a nonisothermal heater at partial wetting

Vadim S. Nikolayev

Phys. Fluids 22, 082105 (2010); http://dx.doi.org/10.1063/1.3483558 (12 pages) | Cited 4 times

Online Publication Date: 30 August 2010

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The dynamics of the triple gas-liquid-solid contact line is analyzed for the case where the gas is the saturated vapor corresponding to the liquid. For partial wetting conditions, a nonstationary contact line problem where the contact line motion is caused by evaporation or condensation is treated. It is shown that the Navier slip condition alone is not sufficient to relax the hydrodynamic contact line singularity: the Marangoni term is equally important when the heat transfer is involved. The transient heat conduction inside the heater is accounted for. A multiscale problem of drop evaporation with freely moving contact line is solved in the lubrication approximation as an illustration of the proposed approach.
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47.55.dr Interactions with surfaces
47.55.pf Marangoni convection
68.03.Cd Surface tension and related phenomena
68.03.Fg Evaporation and condensation of liquids
68.08.Bc Wetting
47.45.Gx Slip flows and accommodation
back to top Viscous and Non-Newtonian Flows

The action of waving cylindrical tails with noncircular cross-section in propelling microrobots

Gábor Kósa, Moshe Shoham, and Shimon Haber

Phys. Fluids 22, 083101 (2010); http://dx.doi.org/10.1063/1.3467040 (14 pages)

Online Publication Date: 23 August 2010

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With the advent of microtechnologies, manufacturing of swimming microrobots that mimic the motion of micro-organisms has become feasible. Based upon the work of Taylor [“The action of waving cylindrical tails in propelling microscopic organisms,” Proc. R. Soc. London, Ser. A 209, 225 (1951)] , the creeping flow induced by a noncircular swimming tail waving in a plane or in spirals was investigated. Tails with rectangular, elliptic, and trapezoidal cross-sections were examined, the latter being the most commonly fabricated microtail. It was observed that for a given cross-section area and propagating wave velocity the trapezoidal cross-section yields the highest tail velocity, whereas the elliptic tail results in the lowest one. Generally, it was obtained that if the cross-section deviation from circularity is expressed by a Fourier series expansion only the symmetric second harmonic affects the propulsion of the tail provided that the wave amplitude is smaller than the cross-section mean radius and of the order of the deviation from circularity. It was also shown that for a planar wave propagating velocity, a higher swimming velocity is obtained if the wider side of the noncircular cross-section faces the waving motion. For helical tails, first order effects of noncircularity on the swimming velocity vanish.
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85.85.+j Micro- and nano-electromechanical systems (MEMS/NEMS) and devices
back to top Particulate, Multiphase, and Granular Flows

A constitutive equation for droplet distribution in unidirectional flows of dilute emulsions for low capillary numbers

Arun Ramachandran, Michael Loewenberg, and David T. Leighton, Jr.

Phys. Fluids 22, 083301 (2010); http://dx.doi.org/10.1063/1.3466577 (12 pages) | Cited 4 times

Online Publication Date: 13 August 2010

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The concentration distribution of droplets in the unidirectional flow of an emulsion for small capillary numbers (Ca) can be written as a balance between the drift flux arising from droplet deformation and the flux due to shear induced migration. The droplet drift flux is modeled using the O(Ca) theoretical results of Chan and Leal [J. Fluid Mech. 92, 131 (1979)] , while the flux due to shear-induced migration is modeled using the suspension balance approach of Nott and Brady [J. Fluid Mech. 275, 157 (1994)] , whereby particle migration is ascribed to normal stress gradients in the flowing dilute emulsion. In the limit of vanishingly small capillary numbers, the leading order contribution of the normal stresses in dilute emulsions arises from droplet-droplet interaction and thus scales as ϕ2τ, where ϕ is the droplet volume fraction and τ is the local shear stress. In our model, the normal stress calculations of Zinchenko [Prikl. Mat. Mekh. 47, 56 (1984)] are connected to our gradient diffusivity data computed from droplet trajectories [ M. Loewenberg and E. J. Hinch, J. Fluid Mech. 338, 299 (1997) ] via a reduced droplet mobility to derive the droplet flux due to shear-induced migration. As an example, the model is applied to the tube Poiseuille flow of a dilute emulsion at small Ca. It is demonstrated that the unsteady concentration distribution of droplets resulting from arbitrary time-dependent average velocity obeys a self-similar solution, provided the thickness of the droplet-depleted region near the walls is always nonzero.
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47.55.nb Capillary and thermocapillary flows
47.57.Bc Foams and emulsions
47.60.Dx Flows in ducts and channels
47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
82.70.Kj Emulsions and suspensions
47.53.+n Fractals in fluid dynamics
back to top Laminar Flows

Nature of counterflow and circulation in vortex separators

Vladimir N. Shtern and Anatoli A. Borissov

Phys. Fluids 22, 083601 (2010); http://dx.doi.org/10.1063/1.3475818 (9 pages) | Cited 1 time

Online Publication Date: 19 August 2010

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This paper focuses on the physical mechanism of elongated counterflows occurring in vortex tubes and hydrocyclones. To this end, a new solution to the Navier–Stokes equations is obtained which describes a flow pattern consisting of two through-flows and the global meridional circulation. One of the through-flows has U-shape geometry. It is shown that swirl decay due to fluid-wall friction induces both the U-shape through-flow and the circulation. The circulation does not deteriorate particle separation. The solution illustrates how the swirl-induced pressure distribution drives the counterflow and results in the paradoxical centrifugal stratification where the high-density fluid located at the periphery is hot while the low-density fluid located near the axis is cold.
Show PACS
47.10.ad Navier-Stokes equations
47.32.-y Vortex dynamics; rotating fluids
47.60.Dx Flows in ducts and channels

Vortex shedding in the wake of a step cylinder

Chris Morton and Serhiy Yarusevych

Phys. Fluids 22, 083602 (2010); http://dx.doi.org/10.1063/1.3459157 (12 pages) | Cited 3 times

Online Publication Date: 26 August 2010

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Flow past a circular cylinder with a single stepwise discontinuity in diameter was investigated numerically for the diameter ratio D/d = 2 and two Reynolds numbers, ReD = 150 and 300. The primary focus was on vortex shedding and vortex interactions occurring in the cylinder wake. In agreement with previous experimental findings, three distinct spanwise vortex cells were identified in the step-cylinder wake: a single vortex shedding cell in the wake of the small cylinder (the S-cell) and two vortex shedding cells in the wake of the large cylinder, one in the region downstream of the step (the N-cell) and the other away from the step (the L-cell). Due to the differences in vortex shedding frequencies, complex vortex connections occurred in two vortex interaction regions located between the adjacent cells. However, distinct differences in vortex splitting and vortex dislocations were identified in the two regions. The region at the boundary between the S-cell and the N-cell was relatively narrow and its spanwise extent did not fluctuate significantly. In this region, vortex dislocations manifested as half-loop connections between two S-cell vortices of opposite sign. In contrast, the region at the boundary between the N-cell and the L-cell exhibited transient behavior, with large scale vortex dislocations causing cyclic variation in the extent of N-cell vortices. Spectral analysis of velocity data showed that the presence of the N-cell was continuous through all simulations. For ReD = 300, small scale streamwise vortices forming in the wake of the large cylinder weaken the primary spanwise vortices and vortex connections, complicating vortex dynamics in the step-cylinder wake. However, no significant Reynolds number effect on the average spanwise extent of the vortex cells and the two transition regions between neighboring cells was observed. Finally, formation of N-cell vortices was shown to be linked to downwash fluctuations near the step.
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47.32.-y Vortex dynamics; rotating fluids
back to top Instability and Transition

Marginal turbulent magnetohydrodynamic flow in a square duct

Victor Shatrov and Gunter Gerbeth

Phys. Fluids 22, 084101 (2010); http://dx.doi.org/10.1063/1.3478877 (9 pages) | Cited 6 times

Online Publication Date: 23 August 2010

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Direct numerical simulations using a high-order finite-difference method were performed of the turbulent flow in a straight square duct in a transverse magnetic field. Without magnetic field the turbulence can be maintained for values of the bulk Reynolds number above approximately Re = 1077 [ M. Uhlmann et al., “Marginally turbulent flow in a square duct,” J. Fluid Mech. 588, 153 (2007) ]. In the magnetohydrodynamic case this minimal value of the bulk Reynolds number increases with the Hartmann number. The flow is laminar at Re = 3000 when the Hartmann number is larger than Ha = 12.5 and the flow is turbulent for Ha≦12.0. The secondary mean flow structure at Re = 3000 consists of eight vortices located mainly at the Hartmann walls.
Show PACS
47.27.nf Flows in pipes and nozzles
47.60.Dx Flows in ducts and channels
47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.11.Bc Finite difference methods
47.32.-y Vortex dynamics; rotating fluids
47.27.Cn Transition to turbulence

Traveling-waves consistent with turbulence-driven secondary flow in a square duct

Markus Uhlmann, Genta Kawahara, and Alfredo Pinelli

Phys. Fluids 22, 084102 (2010); http://dx.doi.org/10.1063/1.3466661 (6 pages) | Cited 5 times

Online Publication Date: 26 August 2010

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We present numerically determined traveling-wave solutions for pressure-driven flow through a straight duct with a square cross section. This family of solutions represents typical coherent structures (a staggered array of counter-rotating streamwise vortices and an associated low-speed streak) on each wall. Their streamwise average flow in the cross-sectional plane corresponds to an eight-vortex pattern much alike the secondary flow found in the turbulent regime.
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47.27.nf Flows in pipes and nozzles
47.60.Dx Flows in ducts and channels
47.27.nb Boundary layer turbulence
47.32.Ef Rotating and swirling flows
47.54.Bd Theoretical aspects
47.27.De Coherent structures
back to top Turbulent Flows

On the structure and dynamics of sheared and rotating turbulence: Anisotropy properties and geometrical scale-dependent statistics

Frank G. Jacobitz, Kai Schneider, Wouter J. T. Bos, and Marie Farge

Phys. Fluids 22, 085101 (2010); http://dx.doi.org/10.1063/1.3457167 (13 pages) | Cited 4 times

Online Publication Date: 2 August 2010

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This study is based on a series of nine direct numerical simulations of homogeneous turbulence, in which the rotation ratio f/S of Coriolis parameter to shear rate is varied. The presence of rotation stabilizes the flow, except for a narrow range of rotation ratios 0<f/S<1. The main mechanism for the flow’s destabilization is an increased turbulence production due to increased anisotropy. Reynolds stress and the dissipation rate anisotropy tensors have been evaluated and provide a reference for newly defined anisotropy measures. Wavelet-based directional energies capture the properties of velocity gradients. The intermittency of the flow in different directions is quantified with scale-dependent directional flatness. Scale-dependent helicity probability distribution functions allow one to statistically characterize the geometry of the motion at different scales. Small scales are found locally to be predominantly helical, while large scales are not since they tend to two-dimensionalization for cases with growing turbulent kinetic energy. Joint probability distribution functions show that the signs of velocity helicity and vorticity helicity are strongly correlated. This indicates that vorticity helicity tends to diminish velocity helicity.
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47.27.Gs Isotropic turbulence; homogeneous turbulence
47.27.E- Turbulence simulation and modeling
47.11.-j Computational methods in fluid dynamics
47.32.-y Vortex dynamics; rotating fluids
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Langevin and diffusion equation of turbulent fluid flow

J. J. H. Brouwers

Phys. Fluids 22, 085102 (2010); http://dx.doi.org/10.1063/1.3466658 (16 pages) | Cited 1 time

Online Publication Date: 11 August 2010

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A derivation of the Langevin and diffusion equations describing the statistics of fluid particle displacement and passive admixture in turbulent flow is presented. Use is made of perturbation expansions. The small parameter is the inverse of the Kolmogorov constant C0, which arises from Lagrangian similarity theory. The value of C0 in high Reynolds number turbulence is 5–6. To achieve sufficient accuracy, formulations are not limited to terms of leading order in C0−1 including terms next to leading order in C0−1 as well. Results of turbulence theory and statistical mechanics are invoked to arrive at the descriptions of the Langevin and diffusion equations, which are unique up to truncated terms of O(C0−2) in displacement statistics. Errors due to truncation are indicated to amount to a few percent. The coefficients of the presented Langevin and diffusion equations are specified by fixed-point averages of the Eulerian velocity field. The equations apply to general turbulent flow in which fixed-point Eulerian velocity statistics are non-Gaussian to a degree of O(C0−1). The equations provide the means to calculate and analyze turbulent dispersion of passive or almost passive admixture such as fumes, smoke, and aerosols in areas ranging from atmospheric fluid motion to flows in engineering devices.
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47.27.Gs Isotropic turbulence; homogeneous turbulence
47.11.-j Computational methods in fluid dynamics
47.10.ad Navier-Stokes equations
47.27.Jv High-Reynolds-number turbulence
47.27.nb Boundary layer turbulence
47.27.ek Direct numerical simulations

Boundary layers in rotating weakly turbulent Rayleigh–Bénard convection

Richard J. A. M. Stevens, Herman J. H. Clercx, and Detlef Lohse

Phys. Fluids 22, 085103 (2010); http://dx.doi.org/10.1063/1.3467900 (13 pages) | Cited 6 times

Online Publication Date: 13 August 2010

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The effect of rotation on the boundary layers (BLs) in a Rayleigh–Bénard system at a relatively low Rayleigh number, i.e., Ra = 4×107, is studied for different Pr by direct numerical simulations and the results are compared with laminar BL theory. In this regime, we find a smooth onset of the heat transfer enhancement as function of increasing rotation rate. We study this regime in detail and introduce a model based on the Grossmann–Lohse theory to describe the heat transfer enhancement as function of the rotation rate for this relatively low Ra number regime and weak background rotation Ro≳1. The smooth onset of heat transfer enhancement observed here is in contrast to the sharp onset observed at larger Ra≳108 by Stevens et al. [Phys. Rev. Lett. 103, 024503 (2009)] , although only a small shift in the Ra-Ro-Pr phase space is involved.
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47.27.nb Boundary layer turbulence
47.27.te Turbulent convective heat transfer
47.32.Ef Rotating and swirling flows
47.11.-j Computational methods in fluid dynamics
47.15.-x Laminar flows
47.20.Ib Instability of boundary layers; separation

High-Reynolds-number turbulent-boundary-layer wall-pressure fluctuations with dilute polymer solutions

Brian R. Elbing, Eric S. Winkel, Steven L. Ceccio, Marc Perlin, and David R. Dowling

Phys. Fluids 22, 085104 (2010); http://dx.doi.org/10.1063/1.3478982 (11 pages) | Cited 2 times

Online Publication Date: 18 August 2010

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Wall-pressure fluctuations were investigated within a high-Reynolds-number turbulent boundary layer (TBL) modified by the addition of dilute friction-drag-reducing polymer solutions. The experiment was conducted at the U.S. Navy’s Large Cavitation Channel on a 12.9 m long flat-plate test model with the surface hydraulically smooth (k+<0.2) and achieving downstream-distance-based Reynolds numbers to 220×106. The polymer (polyethylene oxide) solution was injected into the TBL through a slot in the surface. The primary flow diagnostics were skin-friction drag balances and an array of flush-mounted dynamic pressure transducers 9.8 m from the model leading edge. Parameters varied included the free-stream speed (6.7, 13.4, and 20.2 m s−1) and the injection condition (polymer molecular weight, injection concentration, and volumetric injection flux). The behavior of the pressure spectra, convection velocity, and coherence, regardless of the injection condition, were determined primarily based on the level of drag reduction. Results were divided into two regimes dependent on the level of polymer drag reduction (PDR), nominally separated at a PDR of 40%. The low-PDR regime is characterized by decreasing mean-square pressure fluctuations and increasing convection velocity with increasing drag reduction. This shows that the decrease in the pressure spectra with increasing drag reduction is due in part to the moving of the turbulent structures from the wall. Conversely, with further increases in drag reduction, the high-PDR regime has negligible variation in the mean-squared pressure fluctuations and convection velocity. The convection velocity remains constant at approximately 10% above the baseline-flow convection velocity, which suggests that the turbulent structures no longer move farther from the wall with increasing drag reduction. In light of recent numerical work, the coherence results indicate that in the low-PDR regime, the turbulent structures are being elongated in the streamwise direction and occurring at decreasing frequency. In the high-PDR regime, the rate of occurrence continues to decrease until large-scale coherent turbulent structures are potentially no longer present.
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47.27.Jv High-Reynolds-number turbulence
47.60.Dx Flows in ducts and channels
47.57.Ng Polymers and polymer solutions
47.27.nd Channel flow
47.27.nb Boundary layer turbulence
47.27.De Coherent structures

Transitional and turbulent boundary layer with heat transfer

Xiaohua Wu and Parviz Moin

Phys. Fluids 22, 085105 (2010); http://dx.doi.org/10.1063/1.3475816 (8 pages) | Cited 11 times

Online Publication Date: 26 August 2010

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We report on our direct numerical simulation of an incompressible, nominally zero-pressure-gradient flat-plate boundary layer from momentum thickness Reynolds number 80–1950. Heat transfer between the constant-temperature solid surface and the free-stream is also simulated with molecular Prandtl number Pr = 1. Skin-friction coefficient and other boundary layer parameters follow the Blasius solutions prior to the onset of turbulent spots. Throughout the entire flat-plate, the ratio of Stanton number and skin-friction St/Cf deviates from the exact Reynolds analogy value of 0.5 by less than 1.5%. Mean velocity and Reynolds stresses agree with experimental data over an extended turbulent region downstream of transition. Normalized rms wall-pressure fluctuation increases gradually with the streamwise growth of the turbulent boundary layer. Wall shear stress fluctuation, τw,rms′+, on the other hand, remains constant at approximately 0.44 over the range, 800<Reθ<1900. Turbulent Prandtl number Prt peaks at around 1.9 at the wall, and decreases monotonically toward the boundary layer edge with no near-wall secondary peak, in good agreement with previous boundary layer heat transfer experiments. In the transitional region, turbulent spots are tightly packed with numerous hairpin vortices. With the advection and merging of turbulent spots, these young isolated hairpin forests develop into the downstream turbulent region. Isosurfaces of temperature up to Reθ = 1900 are found to display well-resolved signatures of hairpin vortices, which indicates the persistence of the hairpin forests.
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47.11.-j Computational methods in fluid dynamics
47.27.nb Boundary layer turbulence
47.27.te Turbulent convective heat transfer
47.32.-y Vortex dynamics; rotating fluids

Low Reynolds number effects on rotating turbulent Poiseuille flow

O. Iida, K. Fukudome, T. Iwata, and Y. Nagano

Phys. Fluids 22, 085106 (2010); http://dx.doi.org/10.1063/1.3478980 (15 pages) | Cited 1 time

Online Publication Date: 27 August 2010

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Direct numerical simulations with a spectral method are performed to study the effects of spanwise rotation on a turbulent Poiseuille flow at very low Reynolds number. At this Reynolds number, the region of zero absolute vorticity, typically observed in the mean velocity profile of rotating Poiseuille flow, disappears in the channel center, and the mean velocity gradient becomes opposite to that of zero absolute vorticity. When zero absolute vorticity disappears, very long low-speed streaks, accompanied by the vortices aligned in the streamwise direction like a chain, dominate the flow, in which the transfer of turbulent kinetic energy into the vicinity of the wall and small-scale streamwise vortices disappear there. However, low-speed fluids are pumped up from the near-wall region, and trapped into the channel center by the larger-scale chain vortices away from the wall, which decreases the mean velocity in the channel center and shifts its peak location toward the wall.
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47.32.Ef Rotating and swirling flows
47.32.C- Vortex dynamics
47.27.nd Channel flow
47.27.nb Boundary layer turbulence
47.27.ek Direct numerical simulations
47.60.Dx Flows in ducts and channels
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Spatial characterization of vortical structures and internal waves in a stratified turbulent wake using proper orthogonal decomposition

Peter J. Diamessis, Roi Gurka, and Alex Liberzon

Phys. Fluids 22, 086601 (2010); http://dx.doi.org/10.1063/1.3478837 (15 pages) | Cited 3 times

Online Publication Date: 20 August 2010

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Proper orthogonal decomposition (POD) has been applied to two-dimensional transects of vorticity obtained from numerical simulations of the stratified turbulent wake of a towed sphere at a Reynolds number Re = (UD)/ν = 5×103 and Froude number Fr = 2U/(ND) = 4 (U and D are characteristic velocity and length scales and N is the stratification frequency). At 231 times during the interval 12<Nt<35, the streamwise and spanwise vorticity components are sampled on span-depth (yz) and stream-depth (xz) planes, respectively, at select streamwise and spanwise locations. POD appears to provide a natural decomposition of the vorticity field inside the wake core in terms of the relative influence of buoyancy on flow dynamics. The geometry of the individual eigenmodes shows a vorticity structure that is buoyancy-controlled at the lowest modes and is increasingly more actively turbulent as modal index is increased. In the wake ambient, i.e., the initially quiescent region outside the turbulent wake, the geometry of the POD modes consists of distinct internal wave rays whose angle to the horizontal is strongly dependent on modal index. Reconstruction of vorticity fields from subranges of POD modes indicates that, both inside the wake core but also in the wave-dominated ambient, each modal subrange is not only associated with a particular flow structure but also a characteristic timescale of motion. These preliminary findings suggest that POD may be a highly suitable alternative to globally defined basis functions in analyzing spatially localized internal wave fields emitted from a turbulent source that are also localized in space. In particular, it may serve as a platform toward an improved understanding of two fundamental questions associated with the nonequilibrium regime of stratified wake evolution: the structural transitions of the vorticity field within the wake core and the radiation of internal waves by the wake.
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47.32.C- Vortex dynamics
47.32.Ef Rotating and swirling flows
47.55.Hd Stratified flows
47.27.wb Turbulent wakes
47.11.-j Computational methods in fluid dynamics
47.27.ek Direct numerical simulations
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