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Dec 2009

Volume 21, Issue 12, Articles (12xxxx)

Issue Cover Spotlight Figure

Phys. Fluids 21, 123303 (2009); http://dx.doi.org/10.1063/1.3276235 (8 pages)

Florent Pignatel, Maxime Nicolas, Élisabeth Guazzelli, and David Saintillan
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Modeling of dynamic wetting far from equilibrium

Andreas Carlson, Minh Do-Quang, and Gustav Amberg

Phys. Fluids 21, 121701 (2009); http://dx.doi.org/10.1063/1.3275853 (4 pages) | Cited 6 times

Online Publication Date: 11 December 2009

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In this paper we present simulations of dynamic wetting far from equilibrium based on phase field theory. In direct simulations of recent experiments [ J. C. Bird, S. Mandre, and H. A. Stone, Phys. Rev. Lett. 100, 234501 (2008) ], we show that in order to correctly capture the dynamics of rapid wetting, it is crucial to account for nonequilibrium at the contact line, where the gas, liquid, and solid meet. A term in the boundary condition at the solid surface that naturally arises in the phase field theory is interpreted as allowing for the establishment of a local structure in the immediate vicinity of the contact line. A direct qualitative and quantitative match with experimental data of spontaneously wetting liquid droplets is shown.
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68.08.Bc Wetting
47.55.D- Drops and bubbles
47.11.-j Computational methods in fluid dynamics
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A laboratory study of low-mode internal tide scattering by finite-amplitude topography

Thomas Peacock, Matthieu J. Mercier, Henri Didelle, Samuel Viboud, and Thierry Dauxois

Phys. Fluids 21, 121702 (2009); http://dx.doi.org/10.1063/1.3267096 (4 pages) | Cited 2 times

Online Publication Date: 18 December 2009

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We present the first laboratory experimental results concerning the scattering of a low-mode internal tide by finite-amplitude Gaussian topography. Experiments performed at the Coriolis Platform in Grenoble used a recently conceived internal wave generator as a means of producing a high-quality mode-1 wave field. The evolution of the wave field in the absence and presence of a Gaussian was studied by performing spatiotemporal modal decompositions of velocity field data obtained using particle image velocimetry. The results support the belief that finite-amplitude topography produces significant reflection of the internal tide and transfer of energy from low to high modes.
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92.10.Hm Ocean waves and oscillations
92.60.hh Acoustic gravity waves, tides, and compressional waves

A spin on cavity formation during water entry of hydrophobic and hydrophilic spheres

Tadd T. Truscott and Alexandra H. Techet

Phys. Fluids 21, 121703 (2009); http://dx.doi.org/10.1063/1.3272264 (4 pages) | Cited 3 times

Online Publication Date: 31 December 2009

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Surface coating and impact velocity can dramatically affect cavity formation during water entry of spheres. Duez et al. [Nat. Phys. 3, 180 (2007) ] present a theoretical limit, dependent on impact velocity and surface static wetting angle, below which air cavities no longer form. We show that transverse spin alters the spheres surface velocity distribution to straddle this theoretical limit, resulting in cavity formation over half of the sphere and none on the other half, and yields similar results to the case of a sphere dropped without spin, at the same impact speed, when its surface is half hydrophilic and half hydrophobic.
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47.55.db Drop and bubble formation
68.08.Bc Wetting
47.32.Ef Rotating and swirling flows
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back to top Micro- and Nanofluid Mechanics

Research on the transport and deposition of nanoparticles in a rotating curved pipe

Jianzhong Lin, Peifeng Lin, and Huajun Chen

Phys. Fluids 21, 122001 (2009); http://dx.doi.org/10.1063/1.3264110 (11 pages) | Cited 2 times

Online Publication Date: 14 December 2009

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A finite-volume code and the SIMPLE scheme are used to study the transport and deposition of nanoparticles in a rotating curved pipe for different angular velocities, Dean numbers, and Schmidt numbers. The results show that when the Schmidt number is small, the nanoparticle distributions are mostly determined by the axial velocity. When the Schmidt number is many orders of magnitude larger than 1, the secondary flow will dominate the nanoparticle distribution. When the pipe corotates, the distribution of nanoparticle mass fraction is similar to that for the stationary case. There is a “hot spot” deposition region near the outside edge of bend. When the pipe counter-rotates, the Coriolis force pushes the region with high value of nanoparticle mass fraction toward inside edge of the bend. The hot spot deposition region appears inside the edge. The particle deposition over the whole edge of the bend becomes uniform as the Dean number increases. The corotation of pipe makes the particle deposition efficiency a reduction, while high counter-rotation of pipe only slightly affects the deposition efficiency. When two kinds of secondary flows are coexisting, the relative deposition efficiency is larger than that for the stationary case.
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47.60.Dx Flows in ducts and channels
47.27.nf Flows in pipes and nozzles

Dynamic contact angle effects onto the maximum drop impact spreading on solid surfaces

D. C. Vadillo, A. Soucemarianadin, C. Delattre, and D. C. D. Roux

Phys. Fluids 21, 122002 (2009); http://dx.doi.org/10.1063/1.3276259 (8 pages) | Cited 8 times

Online Publication Date: 29 December 2009

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This paper reports experimental investigations of drop impacts onto chemically treated surfaces with wettability from 5° to 160°. To follow in time the drop spreading, a high speed video camera was used, and it allows us to determine precisely the expansion of the drop and the profile of the free surface at the contact line. By changing the impact velocity, between less than 0.5 and 5 m/s, and the viscosity, from 1 to 100 mPa s, at constant surface tension, a broad range of Reynolds and Weber numbers is explored. This paper is divided into two parts. In the first part, the experimental drop evolution during spreading is directly reported and compared with previous works. Secondly, the emphasis is on the importance of the apparent dynamic contact angle for the prediction of the maximum spreading diameter. This achievement is manifested at low Reynolds numbers at which the matching between the experiment and the model is improved greatly.
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47.55.D- Drops and bubbles
68.08.Bc Wetting
68.03.Cd Surface tension and related phenomena

Hydroelectrical energy conversion in narrow confinements in the presence of transverse magnetic fields with electrokinetic effects

Farooque Munshi and Suman Chakraborty

Phys. Fluids 21, 122003 (2009); http://dx.doi.org/10.1063/1.3276291 (9 pages)

Online Publication Date: 29 December 2009

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In this work, we investigate the combined influences of externally applied axial pressure gradients and transverse magnetic fields on hydroelectrical energy conversion mechanisms in narrow fluidic confinements. This energy conversion is achieved through an exploitation of the electromagnetohydrodynamic effects as a result of electrical double layer formation and the consequent interfacial phenomena. Although no electrical field is externally applied, a reverse electrokinetic transport may be induced on account of the streaming potential field which is spontaneously developed due to the preferential migration of ionic charges with the fluid flow, as modulated by the pressure and the magnetic fields. We explore ranges of surface potentials beyond the traditional Debye–Hückel limits by employing nonlinear forms of the Poisson–Boltzmann equation for electrical potential distribution, yet adhering to a semianalytical formalism. Our studies quantitatively depict the explicit implications of the external magnetic field on the overall energy conversion efficiency through the pertinent nondimensional parameters. We also investigate the cases of low surface potentials and thin electrical double layers as special limits of the generalized considerations addressed in this work.
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47.85.Np Fluidics
47.57.jd Electrokinetic effects
47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.61.Fg Flows in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS)

Microchannel flows with superhydrophobic surfaces: Effects of Reynolds number and pattern width to channel height ratio

Y. P. Cheng, C. J. Teo, and B. C. Khoo

Phys. Fluids 21, 122004 (2009); http://dx.doi.org/10.1063/1.3281130 (12 pages) | Cited 10 times

Online Publication Date: 30 December 2009

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Superhydrophobic surfaces are widely adopted for reducing the flow resistance in microfluidic channels. The structures on the superhydrophobic surfaces may consist of longitudinal grooves, transverse grooves, posts, holes, etc. In this paper their effective slip performances are systematically studied and compared in detail through numerical simulations. The numerical results show that channel wall confinement effects have a positive influence on the effective slip length for square posts and longitudinal grooves, and a negative influence for square holes and transverse grooves. Square posts, holes, and transverse grooves all exhibit deteriorating effective slip performances at higher Reynolds numbers, while the effective slip performance of longitudinal grooves remains independent of the Reynolds number. For small pattern width to channel height ratios and at low Reynolds numbers, for low shear-free fractions, the effective slip length of square posts is equivalent of that of transverse grooves, and both geometries yield effective slip lengths which are in turn lower than those of square holes and longitudinal grooves. With increasing shear-free fractions, the effective slip length of square posts surpasses that of square holes and longitudinal grooves, but it becomes lower than that of longitudinal grooves at high Reynolds numbers or large pattern width to channel height ratios. Scaling laws for the effective slip length of superhydrophobic surfaces with square posts, square holes, and transverse grooves have previously been reported for shear-driven flows. This study extends the validity of these scaling laws to pressure-driven channel flows, even at high Reynolds numbers. The findings in this study serve as a useful guide for applications involving the reduction in flow resistance in microchannels containing superhydrophobic surfaces.
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47.60.Dx Flows in ducts and channels
47.45.Gx Slip flows and accommodation
47.11.-j Computational methods in fluid dynamics
68.08.Bc Wetting
89.20.Kk Engineering
back to top Interfacial Flows

The effect of evaporation on fingering instabilities

Jill Klentzman and Vladimir S. Ajaev

Phys. Fluids 21, 122101 (2009); http://dx.doi.org/10.1063/1.3271826 (9 pages) | Cited 2 times

Online Publication Date: 1 December 2009

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We investigate the flow of evaporating thin films of viscous liquid on inclined solid substrates under the influence of gravity. A lubrication-type approach is used to develop a three-dimensional model of the flow including physical effects such as capillarity, gravity, Marangoni stresses, disjoining pressure, and evaporation. Numerical simulations are then carried out based on the model. The effect of evaporation on the so-called fingering instability that develops along the contact line in the transverse direction of the flow is studied. It is found that evaporation acts to suppress the instability if the evaporation number, a nondimensional measure of the mass flow rate across the interface, is above a critical value. The critical value decreases as the inclination angle is decreased. For the values of evaporation number below the critical one, the fingers grow initially but then saturate at a length that depends on the evaporation conditions. It is also shown that thermocapillarity acts to enhance the instability.
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47.20.Gv Viscous and viscoelastic instabilities
68.15.+e Liquid thin films
64.70.fm Thermodynamics studies of evaporation and condensation
68.03.Cd Surface tension and related phenomena
68.03.Fg Evaporation and condensation of liquids
47.55.nb Capillary and thermocapillary flows

Numerical investigation of rising bubble wake and shape variations

Daniel Gaudlitz and Nikolaus A. Adams

Phys. Fluids 21, 122102 (2009); http://dx.doi.org/10.1063/1.3271146 (9 pages)

Online Publication Date: 3 December 2009

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The unsteady and open wake and unsteady shape changes in a bubble rising on a zigzag path are investigated by performing direct numerical simulations. For the description of phase interfaces the hybrid particle-level-set method is employed. An air bubble with a volume-equivalent diameter of dB = 5.2 mm rising in water is considered. The bubble Reynolds number is set as ReB = 598. We observe a zigzagging bubble ascent path, which is caused by periodic shedding of hairpin vortices from the bubble surface to the bubble wake. Chains of up to four hairpin vortices can be observed. A twisting of the vortex chains indicates the transition from a zigzag to a spiralling ascent path. The bubble exhibits a time-averaged ellipsoidal shape and 2,2-mode shape oscillations. The shedding of hairpin vortices is accompanied by bubble-shape deformations which can be represented by traveling surface waves. This phenomenon results in a periodic asymmetric bubble deformation and is in agreement with experimental observations.
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47.55.D- Drops and bubbles
47.35.-i Hydrodynamic waves
47.32.-y Vortex dynamics; rotating fluids
47.11.-j Computational methods in fluid dynamics

Effect of soluble surfactants on dynamic wetting of flexible substrates: A finite element study

Srinath Madasu

Phys. Fluids 21, 122103 (2009); http://dx.doi.org/10.1063/1.3274019 (10 pages) | Cited 1 time

Online Publication Date: 17 December 2009

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Dynamic wetting plays an important role in coating processes. This paper presents a finite element study of the effect of surfactants under the sorption-controlled regime on the location of the dynamic contact line for flexible solids at steady state. The bulk concentration of the surfactant is assumed to be in excess such that the bulk phase diffusion is neglected and the surface equation of state based on the Frumkin adsorption framework is used to predict the distribution of surface tension as a function of surface surfactant concentration. The finite element model solves for the fluid-structural interactions between an elastic solid and a viscous liquid along with the surfactant distribution at the liquid/vapor free surface. To predict the shape of the free surface, the model uses arbitrary Lagrangian Eulerian mesh motion in both fluid and solid phases. The variation in dynamic contact line position with respect to various parameters such as downstream pressure, Peclet number, surfactant elasticity number, Biot number, interaction parameter, and initial surface coverage are presented for the finite element model. It can be concluded that the presence of surfactant has a significant effect on the location of the dynamic contact line for flexible solids at steady state and the stability of the liquid-vapor free surface.
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47.55.dk Surfactant effects
82.70.Uv Surfactants, micellar solutions, vesicles, lamellae, amphiphilic systems, (hydrophilic and hydrophobic interactions)
68.03.Cd Surface tension and related phenomena
68.08.Bc Wetting
47.11.Fg Finite element methods
back to top Viscous and Non-Newtonian Flows

On the stick-slip flow from slit and cylindrical dies of a Phan-Thien and Tanner fluid model. I. Steady state

George Karapetsas and John Tsamopoulos

Phys. Fluids 21, 123101 (2009); http://dx.doi.org/10.1063/1.3271495 (18 pages) | Cited 1 time

Online Publication Date: 8 December 2009

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The steady planar and cylindrical stick-slip flows for a viscoelastic fluid are computed using the Phan-Thien and Tanner (PTT) constitutive model. The mixed finite element method is used in combination with the elastic-viscous stress-splitting technique and the streamline upwind Petrov–Galerkin discretization for the constitutive equation. This combination of methods when applied to the PTT constitutive model allows us to compute steady state solutions up to high Weissenberg numbers; practically without an upper limit. Equally important, the global Jacobian matrix is generated in order to be able to perform a linear stability analysis of the computed steady state. The dependence of the steady solutions on all the problem parameters is examined. In the limit of a Newtonian fluid, the expansion coefficients near the singularity are computed with comparable accuracy to those from previous analytical and numerical studies, which include the singular finite element method. In the case of a viscoelastic liquid, it is shown that the computed solutions converge quadratically with mesh refinement even at the exit plane of the die and also locally very close to the singularity. The form of the converged solution near the singularity is examined as well as its dependence on various rheological parameters. It is shown that the singularity at the die exit is a logarithmic one and always integrable. Under such conditions our calculations can be extended to determine the linear stability of the herein computed steady states.
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47.50.Cd Modeling
47.45.Gx Slip flows and accommodation
47.11.Fg Finite element methods
02.70.Dh Finite-element and Galerkin methods
02.60.Cb Numerical simulation; solution of equations
02.10.Yn Matrix theory
47.57.Qk Rheological aspects
back to top Particulate, Multiphase, and Granular Flows

Gravity induced sedimentation of slender fibers

K. Gustavsson and A.-K. Tornberg

Phys. Fluids 21, 123301 (2009); http://dx.doi.org/10.1063/1.3273091 (15 pages) | Cited 1 time

Online Publication Date: 14 December 2009

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Gravity induced sedimentation of slender, rigid fibers in a highly viscous fluid is investigated by large scale numerical simulations. The fiber suspension is considered on a microscopic level and the flow is described by the Stokes equations in a three dimensional periodic domain. Numerical simulations are performed to study in great detail the complex dynamics of a cluster of fibers. A repeating cycle is identified. It consists of two main phases: a densification phase, where the cluster densifies and grows, and a coarsening phase, during which the cluster becomes smaller and less dense. The dynamics of these phases and their relation to fluctuations in the sedimentation velocity are analyzed. Data from the simulations are also used to investigate how average fiber orientations and sedimentation velocities are influenced by the microstructure in the suspension. The dynamical behavior of the fiber suspension is very sensitive to small random differences in the initial configuration and a number of realizations of each numerical experiment are performed. Ensemble averages of the sedimentation velocity and fiber orientation are presented for different values of the effective concentration of fibers and the results are compared to experimental data. The numerical code is parallelized using the Message Passing Instructions (MPI) library and numerical simulations with up 800 fibers can be run for very long times which is crucial to reach steady levels of the averaged quantities. The influence of the periodic boundary conditions on the process is also carefully investigated.
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47.57.E- Suspensions
47.11.-j Computational methods in fluid dynamics

Experimental study of the bouncing trajectory of a particle along a rotating wall

A. Le Quiniou, F. Rioual, P. Héritier, and Y. Lapusta

Phys. Fluids 21, 123302 (2009); http://dx.doi.org/10.1063/1.3273364 (8 pages)

Online Publication Date: 17 December 2009

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We intend to present a new experimental setup that allows the study of the trajectory of a solid spherical particle bouncing at a high velocity along a rotating plate. Using different surface treatments for the plate, we can explore the phase space for the mechanical parameters of the problem (normal restitution coefficient en and dynamic friction coefficient μ). An accurate statistical analysis of the trajectory (radial and angular velocities) has been conducted based on an image analysis procedure. Experiments show a regime of successive bounces, followed by a regime of permanent contact of the particle along the vane and a transition from a rolling with a sliding regime to a rolling without sliding regime triggered by the friction particle/wall. A simple model using two mechanical parameters (normal coefficient of restitution en and friction coefficient μ), as proposed recently [ A. Le Quiniou and F. Rioual, “Flow of a particle along a rotating wall,” Europhys. Lett. 82, 34001 (2008) ], is sufficient to reproduce quantitatively all the features of the trajectory. The friction coefficient has to be determined independently using a mechanical protocol of impact of a single particle on a fixed wall—following Foerster et al. [“Measurements of the collision properties of small spheres,” Phys. Fluids 6, 1108 (1994) ]—in particular, an outcome of this study is that the initial spin of the particle appears to have no effect on the features of the impact as long as the relative velocities at the contact are considered.
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47.55.-t Multiphase and stratified flows
46.70.De Beams, plates, and shells
02.50.-r Probability theory, stochastic processes, and statistics
46.55.+d Tribology and mechanical contacts
47.32.Ef Rotating and swirling flows

Falling jets of particles in viscous fluids

Florent Pignatel, Maxime Nicolas, Élisabeth Guazzelli, and David Saintillan

Phys. Fluids 21, 123303 (2009); http://dx.doi.org/10.1063/1.3276235 (8 pages) | Cited 2 times

Online Publication Date: 18 December 2009

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multimedia

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We have investigated the time evolution of a jet of non-Brownian particles falling under the action of gravity in a viscous liquid at low Reynolds number. Different regimes have been observed depending on volume fraction and particle-to-jet diameter ratio. In particular, the jet has been found to be unstable and to develop varicose modulation of its diameter at low volume fractions. The dominant wavelength and saturated amplitude have been measured and are observed to decrease with increasing volume fraction. A simple numerical simulation using point particles is able to capture the major features of the instability.
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47.11.-j Computational methods in fluid dynamics
47.60.Kz Flows and jets through nozzles
47.20.-k Flow instabilities
47.15.Uv Laminar jets

Structure and dynamics of dilute suspensions of finite-Reynolds-number settling fibers

Mansoo Shin, Donald L. Koch, and Ganesh Subramanian

Phys. Fluids 21, 123304 (2009); http://dx.doi.org/10.1063/1.3274612 (25 pages) | Cited 3 times

Online Publication Date: 23 December 2009

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Many-fiber simulations and a linear stability analysis are used to explore the structure and dynamics that arise in a dilute suspension of sedimenting slender fibers with finite particle Reynolds numbers. Dynamic simulations based on a slender-body treatment of the fibers coupled with a pseudospectral solution of the Navier–Stokes equations reveal an inhomogeneous structure dominated by the largest wavelength that fits in the periodic simulation cell. This structure becomes weaker with increasing fiber Reynolds number and fiber concentration. A linear stability analysis shows that the stability of the homogeneous state of the suspension is determined by the direction of the horizontal migration of a fiber in a weak shear field with vertical streamlines produced by a perturbation to the fiber number density. The lift force on a settling fiber, in a plane transverse to gravity, has two contributions. The first contribution results from a broken symmetry in the presence of shear at finite Reynolds number, and involves the coupled effects of the shear and translational inertial terms. The second contribution is related to the sedimentation-driven drift of an inclined fiber, and is present even in the Stokes limit. Both contributions act to push fibers toward downward flowing, high density regions, and the net transverse drift is therefore of a destabilizing nature. The drift calculation and its implications for the instability of a homogeneous suspension are explored up to a Reynolds number of 10.6. The structure factor, fluid velocity fluctuations, and deviations of the fiber orientation away from the horizontal plane are found to generally decrease with increasing Reynolds number as a result of the increasing dominance of the inertial torque acting to rotate settling fibers toward the horizontal plane.
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47.57.ef Sedimentation and migration
47.55.-t Multiphase and stratified flows
47.11.-j Computational methods in fluid dynamics
47.10.ad Navier-Stokes equations
47.15.Fe Stability of laminar flows
47.20.-k Flow instabilities
back to top Laminar Flows

Laminar dispersion at high Péclet numbers in finite-length channels: Effects of the near-wall velocity profile and connection with the generalized Leveque problem

M. Giona, A. Adrover, S. Cerbelli, and F. Garofalo

Phys. Fluids 21, 123601 (2009); http://dx.doi.org/10.1063/1.3263704 (20 pages) | Cited 3 times

Online Publication Date: 3 December 2009

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This article develops the theory of laminar dispersion in finite-length channel flows at high Péclet numbers, completing the classical Taylor–Aris theory which applies for long-term, long-distance properties. It is shown, by means of scaling analysis and invariant reformulation of the moment equations, that solute dispersion in finite length channels is characterized by the occurrence of a new regime, referred to as the convection-dominated transport. In this regime, the properties of the dispersion boundary layer and the values of the scaling exponents controlling the dependence of the moment hierarchy on the Péclet number are determined by the local near-wall behavior of the axial velocity. Specifically, different scaling laws in the behavior of the moment hierarchy occur, depending whether the cross-sectional boundary is smooth or nonsmooth (e.g., presenting corner points or cusps). This phenomenon marks the difference between the dispersion boundary layer and the thermal boundary layer in the classical Leveque problem. Analytical and numerical results are presented for typical channel cross sections in the Stokes regime.
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47.60.Dx Flows in ducts and channels
47.27.te Turbulent convective heat transfer
47.15.Cb Laminar boundary layers
47.15.-x Laminar flows

Energy harvesting through flow-induced oscillations of a foil

Zhangli Peng and Qiang Zhu

Phys. Fluids 21, 123602 (2009); http://dx.doi.org/10.1063/1.3275852 (9 pages) | Cited 4 times

Online Publication Date: 22 December 2009

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By using a Navier–Stokes model, we examine a novel flow energy harvesting device consisting of a flapping foil mounted on a damper (representing the power generator) and a rotational spring. Self-induced and self-sustained flapping motions, including a heaving motion h(t) and a pitching motion α(t), are excited by an incoming flow and power extraction is achieved from the heaving response. Depending upon the configuration of the system and the mechanical parameters (e.g., the location of the pitching axis and the stiffness of the rotational spring), four different responses are recorded: (i) the foil remains stable in its initial position (α = 0 and h = 0); (ii) periodic pitching (around α = 0) and heaving motions are excited; (iii) the foil undergoes irregular motions characterized by switching between oscillations around two pitching angles; and (iv) the foil rotates to a position with an angle to the incoming flow and oscillates around it. The existence of response (ii) suggests the feasibility of controllable and stable flow energy extraction by this device. Through numerical simulations with a Navier–Stokes model we have determined combinations of geometric and mechanical parameters to achieve this response. The corresponding energy harvesting capacity and efficiency are predicted.
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47.10.ad Navier-Stokes equations
84.60.-h Direct energy conversion and storage
back to top Turbulent Flows

Spectrally condensed turbulence in thin layers

H. Xia, M. Shats, and G. Falkovich

Phys. Fluids 21, 125101 (2009); http://dx.doi.org/10.1063/1.3275861 (10 pages) | Cited 5 times

Online Publication Date: 18 December 2009

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We present experimental results on the properties of bounded turbulence in thin fluid layers. In contrast with the theory of two-dimensional (2D) turbulence, the effects of the bottom friction and of the spectral condensation of the turbulence energy are important in our experiment. Here we investigate how these two factors affect statistical moments of turbulent fluctuations. The inverse energy cascade in a bounded turbulent quasi-2D flow leads to the formation of a large coherent vortex (condensate) fed by turbulence. This vortex, depending on its strength, can substantially affect the turbulence statistics, even at small scales. Up to the intermediate strength of the condensate, the velocity moments similar to those in isotropic 2D turbulence are recovered by subtracting the coherent component from the velocity fields. A strong condensate leaves a footprint on the underlying turbulence; it generates stronger non-Gaussianity and reduces the efficiency of the inverse energy cascade. Remarkably, the energy flux in the cascade derived from the third-order structure function using the Kolmogorov flux relation gives physically meaningful values in a broad range of experimental parameters regardless of the condensate strength. This result has important implications for the analysis of the atmospheric wind data in upper troposphere and lower stratosphere.
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47.27.-i Turbulent flows
47.32.-y Vortex dynamics; rotating fluids

The competition between quadratic and integral invariants in inviscid truncated two-dimensional and quasigeostrophic shallow-water turbulence

S. Fox and P. A. Davidson

Phys. Fluids 21, 125102 (2009); http://dx.doi.org/10.1063/1.3276294 (10 pages)

Online Publication Date: 29 December 2009

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We investigate the behavior of spectrally truncated simulations of inviscid two-dimensional and quasigeostrophic shallow-water (QGSW) turbulence. Under the assumption that the only conserved quantities are the energy and enstrophy (the total energy and the potential enstrophy in the case of QGSW turbulence), it is possible to use arguments from statistical mechanics to predict an absolute equilibrium form for the (total) energy spectrum E(k) = ak/(k2+b), where a and b are constants. However, other robust integral invariants exist in these systems. In strictly two-dimensional turbulence the low-wavenumber spectrum has the expansion E ∼ Jk−1+Lk+Ik3+O(k5), where J, L, and I are various integral moments of the two-point vorticity correlation function 〈ωω′〉. J and L are invariants, while I is generally time dependent. In the case of QGSW turbulence, the equivalent expansion for the total energy spectrum is Et ∼ LkR2k−1+mathkR2k+mathkR2k3+mathkR2k5+O(k7), where kR is the Rossby deformation wavenumber and math, math, and math are related to further integral moments of the two-point vorticity correlation function. In this system it is found that math and math are additional invariants. There must, therefore, be competition at the low-wavenumber end of the spectrum between the developing equilibrium spectrum and the region controlled by the integral invariants. We find that while the equilibrium spectrum comes to dominate an increasing range of wavenumbers, it is always blocked from the region k→0 by the presence of the integral invariants. Furthermore, the rate at which the region occupied by the equilibrium spectrum expands is almost independent of the form of both the equilibrium and low-wavenumber spectra. This can be interpreted as the inverse energy cascade, which carries the equilibrium spectrum to low k, being insensitive to the very high and very low k form of the spectrum.
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47.27.-i Turbulent flows
47.32.-y Vortex dynamics; rotating fluids

The number of degrees of freedom of three-dimensional Navier–Stokes turbulence

Chuong V. Tran

Phys. Fluids 21, 125103 (2009); http://dx.doi.org/10.1063/1.3276295 (7 pages) | Cited 3 times

Online Publication Date: 29 December 2009

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In Kolmogorov’s phenomenological theory of turbulence, the energy spectrum in the inertial range scales with the wave number k as k−5/3 and extends up to a dissipation wave number kν, which is given in terms of the energy dissipation rate ϵ and viscosity ν by kν∝(ϵ/ν3)1/4. This result leads to Landau’s heuristic estimate for the number of degrees of freedom that scales as Re9/4, where Re is the Reynolds number. Here we consider the possibility of establishing a quantitative basis for these results from first principles. In particular, we examine the extent to which they can be derived from the three-dimensional Navier–Stokes system, making use of Kolmogorov’s hypothesis of finite and viscosity-independent energy dissipation only. It is found that the Taylor microscale wave number kT (a close cousin of kν) can be expressed in the form kT ≤ CU/ν = (CU/‖u‖)1/2(ϵ/ν3)1/4. Here U and ‖u‖ are a “microscale” velocity and the root mean square velocity, respectively, and C ≤ 1 is a dynamical parameter. This result can be seen to be in line with Kolmogorov’s prediction for kν. Furthermore, it is shown that the minimum number of greatest Lyapunov exponents whose sum becomes negative does not exceed Re9/4, where Re is defined in terms of an average energy dissipation rate, the system length scale, and ν. This result is in a remarkable agreement with the Landau estimate, up to a presumably slight discrepancy between the conventional and the present energy dissipation rates used in the definition of Re.
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47.10.ad Navier-Stokes equations
47.27.-i Turbulent flows

Buoyant formation number of a starting buoyant jet

Ruo-Qian Wang, Adrian Wing-Keung Law, E. Eric Adams, and Oliver B. Fringer

Phys. Fluids 21, 125104 (2009); http://dx.doi.org/10.1063/1.3275849 (9 pages) | Cited 3 times

Online Publication Date: 29 December 2009

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Understanding the influence of buoyancy on the formation number is important for analyzing the development of a starting buoyant jet and the interactions between its vortex ring and trailing stem. Numerical simulations with a large-eddy simulation model are performed to reproduce the starting buoyant jet in conditions ranging from pure jet to lazy plume. From the results, an improved method to determine the formation number is proposed based on the occurrence of a step jump in the vortex ring circulation. A comparison of the numerical results with the experimental data for a starting pure jet is first performed. The widely accepted formation number (≈4.0) is obtained, which implies that the method is satisfactory. The effect of buoyancy on the formation number is then investigated for two turbulent discharge conditions of Re = 2000 and 2500 and with a wide range of buoyancy flux. Best-fit results are obtained that correlate the formation number with the Richardson number. Finally, a slug model that incorporates buoyancy is developed to allow prediction of the “buoyant formation number” for the starting buoyant jet using a limiting value of 0.33 for the dimensionless energy, which is the same value for a pure jet.
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47.11.-j Computational methods in fluid dynamics
47.60.Kz Flows and jets through nozzles
47.32.-y Vortex dynamics; rotating fluids
47.27.wg Turbulent jets
47.27.-i Turbulent flows

Reynolds number effect on the wake of two staggered cylinders

Y. Zhou, S. X. Feng, Md. Mahbub Alam, and H. L. Bai

Phys. Fluids 21, 125105 (2009); http://dx.doi.org/10.1063/1.3275846 (14 pages) | Cited 1 time

Online Publication Date: 29 December 2009

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This work aims to investigate, based on the measured/reported Strouhal number (St) and the flow structure, the Reynolds number (Re) effect on the wake of two identical cylinders with a diameter of d over P∗ = P/d = 1.2–4.0 and α = 0°–90°, where P is the center-to-center spacing between the two cylinders and α is the angle of incident flow with respect to the line through the two cylinder centers. The Re range examined is from 1.5×103 to 2.0×104. Two hotwires were used to measure St simultaneously behind each of the two cylinders. The St-Re relationship is classified into four distinct types, i.e., types 1–4. Each is linked to distinct initial conditions, viz., interactions between the four shear layers around the cylinders. Type 1 occurs at small P∗, not exceeding 1.25. The two cylinders act like a single body, producing a single St across the wake throughout the range of Re examined. On the other hand, type 2 occurs at small α (<10°). Although single valued, the St in type 2 displays a sudden jump with increasing Re due to a switch in the shear layer, separated from the upstream cylinder, from overshooting to reattachment on the downstream cylinder (type 2A) or from reattachment to coshedding vortices (type 2B), depending on P∗. Type 3 is in the region of intermediate P∗ [(1.2–1.5)–2.2] and α (10°–75°). Two distinct St occur at low Re. The lower and the higher ranges of St are associated with the downstream and upstream cylinders, respectively. With increasing Re, the higher St collapses to the lower, which is attributed to a change in the inner shear layer, separated from the upstream cylinder, from squeezing through the gap between cylinders to reattachment on the downstream cylinder. Type 4 occurs at large P∗ (>1.2–2.2) and again exhibits at low Re two St, above and below the Strouhal number St0 in the wake of an isolated cylinder, both changing suddenly or progressively to St0 with increasing Re, which results from a change in the inner shear layer, separated from the upstream cylinder, from reattachment on the downstream cylinder to forming vortices between the cylinders. These types of Re-St relationships are also connected to the flow structure modes reported in literature. The dependence of the St and St-Re relationships on P∗ and α is provided, which may be used for the prediction of St in related problems.
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47.27.wb Turbulent wakes
47.32.-y Vortex dynamics; rotating fluids

Characteristics of coherent vortical structures in turbulent flows over progressive surface waves

Di Yang and Lian Shen

Phys. Fluids 21, 125106 (2009); http://dx.doi.org/10.1063/1.3275851 (23 pages) | Cited 5 times

Online Publication Date: 29 December 2009

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Vortical structures in turbulence over progressive surface waves are studied using the data from direct numerical simulation of a stress-driven turbulent Couette flow above a waving surface. Instantaneous flow field and its evolution, vorticity statistics, and conditionally averaged flow field with various sampling methods are examined. Unique vortical structures are identified, which are found to be strongly dependent on the wave motion. For a slow wave (with a small value of wave age c/u∗ = 2; here c is the phase speed of the wave and u∗ is the friction velocity), the vortical structures are characterized by reversed horseshoe vortices and quasistreamwise vortices. The former is concentrated above the wave trough and is associated with sweep events there; the latter has high intensity over the windward face of the wave and is associated with ejection events. Relative to the waveform, the coherent vortical structures propagate in the downstream direction. Vortex turning and vortex stretching play an important role in the vortex transformation and evolution processes. For an intermediate wave (c/u∗ = 14) and a fast wave (c/u∗ = 25), the dominant vortical structure is bent quasistreamwise vortices, which are predominantly horizontal but have a distinctive downward bending in their upstream ends near the wave trough. The vortices are found to propagate in the upstream direction with respect to the waveform. The above-wave coherent vortices identified in this study are found to play an important role in the turbulent transport process.
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47.11.-j Computational methods in fluid dynamics
47.27.-i Turbulent flows
47.32.-y Vortex dynamics; rotating fluids
47.35.-i Hydrodynamic waves

Turbulent flow and organized motions over a two-dimensional rough wall

Lukas Vesely, Christian Haigermoser, Davide Greco, and Michele Onorato

Phys. Fluids 21, 125107 (2009); http://dx.doi.org/10.1063/1.3276905 (19 pages)

Online Publication Date: 29 December 2009

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Particle image velocimetry measurements at relatively low Reynolds number in a turbulent boundary layer over a two-dimensional roughened surface are presented and compared to those for a smooth wall. The main goal of the study was to give a contribution to the understanding of the behavior of the turbulent organized motions, when the influence of the wall roughness on the turbulent structures may be expected to be noticeable, i.e., for relatively high roughness and relatively low Reynolds number. In addition, the flow behavior with respect to the wall similarity hypothesis in the case of moderately large values of the roughness height k and moderately low Reynolds number was tested. The behavior of the turbulent coherent motions appears to be similar for the two flows in the outer layer. Quantitative differences, observed mainly in the roughness sublayer, are enlightened comparing spatial velocity correlations and vortex population density and strength in the wall-normal-streamwise plane and in planes parallel to the wall. Mean flows expressed in velocity defect law, inner scaled streamwise Reynolds normal stress, and Reynolds shear stresses profiles show excellent agreement in the outer layer between the rough wall and the smooth surface. Wall normal Reynolds normal stress profiles, instead, show some small discrepancy, but within the measurement uncertainty.
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47.27.nb Boundary layer turbulence
47.80.Cb Velocity measurements
47.32.-y Vortex dynamics; rotating fluids

Influence of gravity on collisions of monodispersed droplets in homogeneous isotropic turbulence

Ryo Onishi, Keiko Takahashi, and Satoru Komori

Phys. Fluids 21, 125108 (2009); http://dx.doi.org/10.1063/1.3276906 (8 pages) | Cited 4 times

Online Publication Date: 30 December 2009

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This paper studies the gravity influence on collisions of monodispersed droplets in homogeneous isotropic turbulence by means of direct numerical simulations (DNSs). The DNS results show that, in certain Stokes and Reynolds regimes, collision frequencies are significantly reduced in the presence of gravity. Those decreases are mainly attributable to the decrease in the droplet relative velocity, since the change in radial distribution function—often referred to preferential concentration—is small. Further analysis of the results reveals that droplet sedimentation due to gravity shortens the droplet-fluid interaction time, consequently weakening the relative motions between droplets. These observations lead to an analytical model that can be used to estimate the velocity fluctuations of sedimenting particles under gravity. Utilizing this model, we constructed a further analytical model for estimating the gravitational influence on collisions. Given flow and particle parameters, the model calculates the ratio of collision frequencies with and without the effect of gravity. Past studies simply noted that the gravitational influence is negligible when the droplet sedimenting velocity is much smaller than the flow velocity fluctuations. Our analytical model further suggests that the gravitational influence on collisions of monodispersed cloud droplets with non-negligible sedimentation rates stays negligibly small even in high Reynolds number flows, such as those typically found in convective clouds.
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47.55.D- Drops and bubbles
02.60.Cb Numerical simulation; solution of equations
47.11.Kb Spectral methods
47.27.ek Direct numerical simulations
47.27.Gs Isotropic turbulence; homogeneous turbulence
47.55.Kf Particle-laden flows
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