Showing papers on "Vortex published in 2005"

On the relationships between local vortex identification schemes

Abstract: We analyse the currently popular vortex identification criteria that are based on point-wise analysis of the velocity gradient tensor. A new measure of spiralling compactness of material orbits in vortices is introduced and using this measure a new local vortex identification criterion and requirements for a vortex core are proposed. The inter-relationships between the different criteria are explored analytically and in a few flow examples, using both zero and non-zero thresholds for the identification parameter. These inter-relationships provide a new interpretation of the various criteria in terms of the local flow kinematics. A canonical turbulent flow example is studied, and it is observed that all the criteria, given the proposed usage of threshold, result in remarkably similar looking vortical structures. A unified interpretation based on local flow kinematics is offered for when similarity or differences can be expected in the vortical structures educed using the different criteria.

An objective definition of a vortex

Abstract: The most widely used definitions of a vortex are not objective: they identify different structures as vortices in frames that rotate relative to each other. Yet a frame-independent vortex definition is essential for rotating flows and for flows with interacting vortices. Here we define a vortex as a set of fluid trajectories along which the strain acceleration tensor is indefinite over directions of zero strain. Physically, this objective criterion identifies vortices as material tubes in which material elements do not align with directions suggested by the strain eigenvectors. We show using examples how this vortex criterion outperforms earlier frame-dependent criteria. As a side result, we also obtain an objective criterion for hyperbolic Lagrangian structures.

Bacterial Swimming and Oxygen Transport Near Contact Lines

Abstract: Aerobic bacteria often live in thin fluid layers near solid–air–water contact lines, in which the biology of chemotaxis, metabolism, and cell–cell signaling is intimately connected to the physics of buoyancy, diffusion, and mixing. Using the geometry of a sessile drop, we demonstrate in suspensions of Bacillus subtilis the self-organized generation of a persistent hydrodynamic vortex that traps cells near the contact line. Arising from upward oxygentaxis and downward gravitational forcing, these dynamics are related to the Boycott effect in sedimentation and are explained quantitatively by a mathematical model consisting of oxygen diffusion and consumption, chemotaxis, and viscous fluid dynamics. The vortex is shown to advectively enhance uptake of oxygen into the suspension, and the wedge geometry leads to a singularity in the chemotactic dynamics near the contact line.

Numerical and experimental investigation of flow and scour around a circular pile

Abstract: The flow around a vertical circular pile exposed to a steady current is studied numerically and experimentally. The numerical model is a three-dimensional model. The model validation was achieved against new experimental data (which include two-component laser-Doppler anemometry (LDA) flow measurements and the hot-film bed shear stress measurements, and reported in the present paper) and the data of others, and a k-w turbulence model was used for closure. The model does not have a free-surface facility and therefore is applicable only to cases where the Froude number is small (Fr < 0(0.2)). The flow model was used to study the horseshoe vortex and lee-wake vortex flow processes around the pile. The influence on the horseshoe vortex of three parameters, namely the boundary-layer thickness, the Reynolds number and the bed roughness, was investigated. In the latter investigation, the steady solution of the model was chosen. A study of the influence of the unsteady solution on the previously mentioned flow processes was also carried out. The ranges of the parameters covered in the numerical simulations are: The boundary-layer-thickness-to-pile-diameter ratio is varied from 2 x 10 -2 to 10 2 , the pile Reynolds number from 10 2 to 2 × 10 6 , and the pile diameter-to-roughness ratio from 2 to about 10 3 . The amplification of the bed shear stress around the pile (including the areas under the horseshoe vortex and the lee-wake region) was obtained for various values of the previously mentioned parameters. The steady-state flow model was coupled with a morphologic model to calculate scour around a vertical circular pile exposed to a steady current in the case of non-cohesive sediment. The morphologic model includes (i) a two-dimensional bed load sediment-transport description, and (ii) a description of surface-layer sand slides for bed slopes exceeding the angle of repose. The results show that the present numerical simulation captures all the main features of the scour process. The equilibrium scour depth obtained from the simulation agrees well with the experiments for the upstream scour hole. Some discrepancy (up to 30 %) was observed, however, for the downstream scour hole. The calculations show that the amplification of the bed shear stress around the pile in the equilibrium state of the scour process is reduced considerably with respect to that experienced at the initial stage where the bed is plane.

Numerical solutions of 2‐D steady incompressible driven cavity flow at high Reynolds numbers

Abstract: SUMMARY Numerical calculations of the 2-D steady incompressible driven cavity flow are presented. The NavierStokes equations in streamfunction and vorticity formulation are solved numerically using a fine uniform grid mesh of 601 × 601. The steady driven cavity solutions are computed for Re ≤ 21,000 with a maximum absolute residuals of the governing equations that were less than 10 −10 . A new quaternary vortex at the bottom left corner and a new tertiary vortex at the top left corner of the cavity are observed in the flow field as the Reynolds number increases. Detailed results are presented and comparisons are made with benchmark solutions found in the literature.

A Self-Organized Vortex Array of Hydrodynamically Entrained Sperm Cells

Abstract: Many patterns in biological systems depend on the exchange of chemical signals between cells. We report a spatiotemporal pattern mediated by hydrodynamic interactions. At planar surfaces, spermatozoa self-organized into dynamic vortices resembling quantized rotating waves. These vortices formed an array with local hexagonal order. Introducing an order parameter that quantifies cooperativity, we found that the array appeared only above a critical sperm density. Using a model, we estimated the hydrodynamic interaction force between spermatozoa to be ∼0.03 piconewtons. Thus, large-scale coordination of cells can be regulated hydrodynamically, and chemical signals are not required.

Optical vortex coronagraph

Abstract: We describe a method to observe dim exoplanets that eliminates light from the parent star across the entire exit pupil without sacrificing light from the planet by use of a vortex mask of topological charge m=2.

Componentwise energy amplification in channel flows

Abstract: We study the linearized Navier–Stokes (LNS) equations in channel flows from an input–output point of view by analysing their spatio-temporal frequency responses. Spatially distributed and temporally varying body force fields are considered as inputs, and components of the resulting velocity fields are considered as outputs into these equations. We show how the roles of Tollmien–Schlichting (TS) waves, oblique waves, and streamwise vortices and streaks in subcritical transition can be explained as input–output resonances of the spatio-temporal frequency responses. On the one hand, we demonstrate the effectiveness of input field components, and on the other, the energy content of velocity perturbation components. We establish that wall-normal and spanwise forces have much stronger influence on the velocity field than streamwise force, and that the impact of these forces is most powerful on the streamwise velocity component. We show this using the relative scaling of the different input–output system components with the Reynolds number. We further demonstrate that for the streamwise constant perturbations, the spanwise force localized near the lower wall has, by far, the strongest effect on the evolution of the velocity field. In this paper, we analyse the dynamical properties of the Navier–Stokes (NS) equations with spatially distributed and temporally varying body force fields. These fields are considered as inputs, and different combinations of the resulting velocity fields are considered as outputs. This input–output analysis can in principle be done in any geometry and for the full nonlinear NS equations. In such generality, however, it is difficult to obtain useful results. We therefore concentrate on the geometry of channel flows, and the input–output dynamics of the linearized Navier–Stokes (LNS)

The inertio-elastic planar entry flow of low-viscosity elastic fluids in micro-fabricated geometries

Abstract: The non-Newtonian flow of dilute aqueous polyethylene oxide (PEO) solutions through micro-fabricated planar abrupt contraction-expansions is investigated. The small lengthscales and high deformation rates in the contraction throat lead to significant extensional flow effects even with dilute polymer solutions having time constants on the order of milliseconds. By considering the definition of the elasticity number, El = Wi/Re, we show that the lengthscale of the geometry is key to the generation of strong viscoelastic effects, such that the same flow behaviour cannot be reproduced using the equivalent macro-scale geometry using the same fluid. We observe significant vortex growth upstream of the contraction plane, which is accompanied by an increase of more than 200% in the dimensionless extra pressure drop across the contraction. Streak photography and video-microscopy using epifluorescent particles shows that the flow ultimately becomes unstable and three-dimensional. The moderate Reynolds numbers (0.44 ≤ Re ≤ 64) associated with these high Weissenberg number (0 ≤ Wi ≤ 548) micro-fluidic flows results in the exploration of new regions of the Re-Wi parameter space in which the effects of both elasticity and inertia can be observed. Understanding such interactions will be increasingly important in micro-fluidic applications involving complex fluids and can best be interpreted in terms of the elasticity number, El = Wi/Re, which is independent of the flow kinematics and depends only on the fluid rheology and the characteristic size of the device.

An experimental investigation of swirling jets

Abstract: The 'plug' flow emerging from a long rotating tube into a large stationary reservoir has been used in an experimental investigation of centrifugally unstable swirling jets. A moderate Reynolds number, Re = 1000, was studied extensively, and swirl numbers, S, the ratio of nozzle exit rotating speed to the mean mass axial velocity, were in the range 0-1.1. Four regimes were covered: non-swirling jets with S=0, weakly swirling jets in the range 0 S c2 , where S c1 =0.6 and S c2 = 0.88. Particular attention was paid to the dominant role of the underlying vortical flow structures and their dynamic evolution. Kelvin-Helmholtz (K-H) instability in the axial shear layer, generated by the axial velocity, leading to vortex ring formation, dominated non-swirling and weakly swirling jets

Aspects of low- and high-frequency actuation for aerodynamic flow control

Abstract: Control approaches for separated flows over aerodynamic (or bluff) bodies in which the separated flow domain scales with the characteristic length of the body are distinguished by the frequency band of the actuation input. In an approach that relies on the narrowband receptivity of the separating shear layer that is coupled to the wake (shedding) instability and scales with the characteristic advection time over the separated domain, aerodynamic performance is partially restored by a Coanda-like deflection of the forced separating shear layer toward the surface. Because the instability of the unforced shear layer may already be driven by global vortex shedding, the advection of the vortices of the forced (or controlled) layer along the surface and their ultimate shedding into the near wake can couple to wake instabilities and, therefore, may result in unsteady aerodynamic forces in the controlled flow. A different control strategy that emphasizes full or partial suppression of separation by fluidic modification of the apparent aerodynamic shape of the surface relies on controlled interaction between the actuator and the crossflow on a scale that is at least an order of magnitude smaller than the relevant global length scales.

A vortex particle method for smoke, water and explosions

Abstract: Vorticity confinement reintroduces the small scale detail lost when using efficient semi-Lagrangian schemes for simulating smoke and fire However, it only amplifies the existing vorticity, and thus can be insufficient for highly turbulent effects such as explosions or rough water We introduce a new hybrid technique that makes synergistic use of Lagrangian vortex particle methods and Eulerian grid based methods to overcome the weaknesses of both Our approach uses vorticity confinement itself to couple these two methods together We demonstrate that this approach can generate highly turbulent effects unachievable by standard grid based methods, and show applications to smoke, water and explosion simulations

Experimental study of eddy structures in a turbulent boundary layer using particle image velocimetry

Abstract: Particle image velocimetry experiments have been performed in a turbulent boundary-layer wind tunnel in order to study the coherent structures taking part in the generation and preservation of wall turbulence. The particular wind tunnel used is suitable for high-resolution experiments ($delta gt 0.3$ m) at high Reynolds numbers (up to $R_{theta} = 19,000$ in the present results). Eddy structures were identified in instantaneous velocity maps in order to determine their mean characteristics and possible relationships between these structures. In the logarithmic region, the results show that the observed eddy structures appear to organize like elongated vortices, tilted downstream, mainly at an angle of about 45° and having a cane shape. The characteristics of these vortices appear here to be universal in wall units for $R_{theta},{leq},19,000$. They seem to find their origin at a wall distance of about 25 wall units as quasi-streamwise vortices and to migrate away from the wall while tilting to form a head and a leg. Away from the wall, their radius increases and their vorticity decreases very slowly so that their circulation is nearly constant. Near the wall, the picture obtained is in fair agreement with existing models. The analysis of the results indicates a universality of the buffer-layer mechanism, even at low Reynolds number, and a sensitivity of the logarithmic region to low-Reynolds-number effects.

Parametric and internal study of the vortex tube using a CFD model

Abstract: A computational fluid dynamics (CFD) model is used to investigate the energy separation mechanism and flow phenomena within a counter-flow vortex tube. A two-dimensional axi-symmetric CFD model has been developed that exhibits the general behavior expected from a vortex tube. The model results are compared to experimental data obtained from a laboratory vortex tube operated with room temperature compressed air. The CFD model is subsequently used to investigate the internal thermal-fluid processes that are responsible for the vortex tube's temperature separation behavior. The model shows that the vortex tube flow field can be divided into three regions that correspond to: flow that will eventually leave through the hot exit (hot flow region), flow that will eventually leave through the cold exit (cold flow region), and flow that is entrained within the device (re-circulating region). The underlying physical processes are studied by calculating the heat and work transfers through control surfaces defined by the streamlines that separate these regions. It was found that the energy separation exhibited by the vortex tube can be primarily explained by a work transfer caused by a torque produced by viscous shear acting on a rotating control surface that separates the cold flow region and the hot flow region. This work transfer is from the cold region to the hot region whereas the net heat transfer flows in the opposite direction and therefore tends to reduce the temperature separation effect. A parametric study of the effect of varying the diameter and length of the vortex tube is also presented.

Vortex knots in light

Abstract: Optical vortices generically arise when optical beams are combined. Recently, we reported how several laser beams containing optical vortices could be combined to form optical vortex loops, links and knots embedded in a light beam (Leach et al 2004 Nature 432 165). Here, we describe in detail the experiments in which vortex loops form these structures. The experimental construction follows a theoretical model originally proposed by Berry and Dennis, and the beams are synthesized using a programmable spatial light modulator and imaged using a CCD camera.

Flow patterns generated by oblate medusan jellyfish: field measurements and laboratory analyses.

Abstract: Flow patterns generated by medusan swimmers such as jellyfish are known to differ according the morphology of the various animal species. Oblate medusae have been previously observed to generate vortex ring structures during the propulsive cycle. Owing to the inherent physical coupling between locomotor and feeding structures in these animals, the dynamics of vortex ring formation must be robustly tuned to facilitate effective functioning of both systems. To understand how this is achieved, we employed dye visualization techniques on scyphomedusae (Aurelia aurita) observed swimming in their natural marine habitat. The flow created during each propulsive cycle consists of a toroidal starting vortex formed during the power swimming stroke, followed by a stopping vortex of opposite rotational sense generated during the recovery stroke. These two vortices merge in a laterally oriented vortex superstructure that induces flow both toward the subumbrellar feeding surfaces and downstream. The lateral vortex motif discovered here appears to be critical to the dual function of the medusa bell as a flow source for feeding and propulsion. Furthermore, vortices in the animal wake have a greater volume and closer spacing than predicted by prevailing models of medusan swimming. These effects are shown to be advantageous for feeding and swimming performance, and are an important consequence of vortex interactions that have been previously neglected.

Secondary instability of crossflow vortices

Abstract: Crossflow-dominated swept-wing boundary layers are known to undergo a highly nonlinear transition process. In low-disturbance environments, the primary instability of these flows consists mainly of stationary streamwise vortices that modify the mean velocity field and hence the stability characteristics of the boundary layer. The result is amplitude saturation of the dominant stationary mode and strong spanwise modulation of the unsteady modes. Breakdown is not caused by the primary instability but instead by a high-frequency secondary instability of the shear layers of the distorted mean flow. The secondary instability has been observed in several previous experiments and several computational models for its behaviour exist. None of the experiments has been sufficiently detailed to allow either model validation or transition correlation. The present experiment conducted using a 45 ◦ swept wing in the low-disturbance Arizona State University Unsteady Wind Tunnel addresses the secondary instability in a detailed fashion under a variety of conditions. The results reveal that this instability is active in the breakdown of all cases investigated, and furthermore, it appears to be well-described by the computational models.

Wave capture and wave-vortex duality

Abstract: New and unexpected results are presented regarding the nonlinear interactions between a wavepacket and a vortical mean flow, with an eye towards internal wave dynamics in the atmosphere and oceans and the problem of ‘missing forces’ in atmospheric gravity-wave parametrizations. The present results centre around a prewave-breaking scenario termed ‘wave capture’, which differs significantly from the standard such scenarios associated with critical layers or mean density decay with altitude. We focus on the peculiar wave–mean interactions that accompany wave capture. Examples of these interactions are presented for layerwise-two-dimensional, layerwise-non-divergent flows in a three-dimensional Boussinesq system, in the strongstratification limit. The nature of the interactions can be summarized in the phrase ‘wave–vortex duality’, whose key points are firstly that wavepackets behave in some respects like vortex pairs, as originally shown in the pioneering work of Bretherton (1969), and secondly that a collection of interacting wavepackets and vortices satisfies a conservation theorem for the sum of wave pseudomomentum and vortex impulse, provided that the impulse is defined appropriately. It must be defined as the rotated dipole moment of the Lagrangian-mean potential vorticity (PV). This PV differs crucially from the PV evaluated from the curl of either the Lagrangian-mean or the Eulerian-mean velocity. The results are established here in the strong-stratification limit for rotating (quasi-geostrophic) as well as for non-rotating systems. The concomitant momentum budgets can be expected to be relatively complicated, and to involve far-field recoil effects in the sense discussed in B¨ & McIntyre (2003). The results underline the three-way distinction between impulse, pseudomomentum, and momentum. While momentum involves the total velocity field, impulse and pseudomomentum involve, in different ways, only the vortical part of the velocity field.

Global Stability of Vortex Solutions of the Two-Dimensional Navier-Stokes Equation

Abstract: Both experimental and numerical studies of fluid motion indicate that initially localized regions of vorticity tend to evolve into isolated vortices and that these vortices then serve as organizing centers for the flow. In this paper we prove that in two dimensions localized regions of vorticity do evolve toward a vortex. More precisely we prove that any solution of the two-dimensional Navier-Stokes equation whose initial vorticity distribution is integrable converges to an explicit self-similar solution called “Oseen’s vortex”. This implies that the Oseen vortices are dynamically stable for all values of the circulation Reynolds number, and our approach also shows that these vortices are the only solutions of the two-dimensional Navier-Stokes equation with a Dirac mass as initial vorticity. Finally, under slightly stronger assumptions on the vorticity distribution, we give precise estimates on the rate of convergence toward the vortex.

Stable vortex solitons in nonlocal self-focusing nonlinear media

Abstract: Vortices are fundamental objects which appear in many branches of physics 1. In optics, vortices are usually associated with phase singularities of diffracting optical beams, and they can be generated experimentally in different types of linear and nonlinear media 2. However, optical vortices become highly unstable in self-focusing nonlinear media due to the symmetry-breaking azimuthal instability, and they decay into several fundamental solitons 3. In spite of many theoretical ideas to stabilize optical vortices in specific nonlinear media 4, no stable optical vortices created by coherent light were readily observed in experiment 5. Thus, the important challenge remains to reveal physical mechanisms which would allow experimental observation of stable coherent vortices in realistic nonlinear media. In this Communication, we reveal that the symmetrybreaking azimuthal instability of the vortex beams can be suppressed and even eliminated completely in the media characterized by a nonlocal nonlinear response. This observation allows us to suggest a simple and realistic way to generate experimentally stable, spatially localized vortices in self-focusing nonlinear media. We study the main properties and stability of different types of vortex beams, and discuss the physical mechanism of their stabilization in spatially nonlocal nonlinear media. We notice that there exist many physical systems characterized by nonlocal nonlinear response. In particular, a nonlocal response is induced by heating and ionization, and it is known to be important in media with thermal nonlinearities such as thermal glass 6 and plasmas 7. Nonlocal response is a key feature of the orientational nonlinearities due to long-range molecular interactions in nematic liquid crystals 8. An interatomic interaction potential in Bose-Einstein condensates with dipole-dipole interactions is also known to be substantially nonlocal 9. In all such systems, nonlocal nonlinearity can be responsible for many unique features such as the familiar effect of the collapse arrest 10,11. We consider propagation of the electric-field envelope EX,Y,Z described by the paraxial wave equation,

Measurements of the flow over a low-aspect-ratio cylinder mounted on a ground plane

Abstract: The flow over a finite-height cylinder of aspect ratio 1, with one end mounted on a ground plane and the other end free, has been studied by means of surface flow visualisation, particle image velocimetry (PIV) and surface pressure measurements. The diameter-based Reynolds number was 200,000. The mean flow topology has been identified in three areas: the horseshoe vortex system, the separated flow over the free-end and the wake region. Evidence is shown for the existence of a three-horseshoe vortex system, while the mean flow over the free-end consists of an arch vortex with its bases on the forward half of the free-end. There are two tip vortices coming off the free-end. The wake region is found to be highly unsteady, with considerable variation from the mean flow.

On the evolution of the wake structure produced by a low-aspect-ratio pitching panel.

Abstract: Flow visualization is used to interrogate the wake structure produced by a rigid flat panel of aspect ratio (span/chord) 0.54 pitching in a free stream at a Strouhal number of 0.23. At such a low aspect ratio, the streamwise vorticity generated by the plate tends to dominate the formation of the wake. Nevertheless, the wake has the appearance of a three-dimensional von Karman vortex street, as observed in a wide range of other experiments, and consists of horseshoe vortices of alternating sign shed twice per flapping cycle. The legs of each horseshoe interact with the two subsequent horseshoes in an opposite-sign, then like-sign interaction in which they become entrained. A detailed vortex skeleton model is proposed for the wake formation.

Ring vortex solitons in nonlocal nonlinear media

Abstract: This study considers vortex ring solitons in nonlinear media with a spatially nonlocal self-focusing nonlinearity. Spatial nonlocality implies that the response of the medium at a particular point is not determined not only by the wave intensity at that point but also depends on the wave intensity in the vicinity.

Optical Vortices and Vortex Solitons

Abstract: Optical vortices are phase singularities nested in electromagnetic waves that constitute a fascinating source of phenomena in the physics of light and display deep similarities to their close relatives, quantized vortices in superfluids and Bose-Einstein condensates. We present a brief overview of the major advances in the study of optical vortices in different types of nonlinear media, with emphasis on the properties of {\em vortex solitons}. Self-focusing nonlinearity leads, in general, to the azimuthal instability of a vortex-carrying beam, but it can also support novel types of stable or meta-stable self-trapped beams carrying nonzero angular momentum, such as ring-like solitons, necklace beams, and soliton clusters. We describe vortex solitons created by multi-component beams, by parametrically coupled beams in quadratic nonlinear media, and in partially incoherent light, as well as discrete vortex solitons in periodic photonic lattices.

Distributed forcing of flow over a circular cylinder

Abstract: In the present study, we apply a distributed (i.e., spatially varying) forcing to flow over a circular cylinder for drag reduction. The distributed forcing is realized by a blowing and suction from the slots located at upper and lower surfaces of the cylinder. The forcing profile from each slot is sinusoidal in the spanwise direction but is steady in time. We consider two different phase differences between the upper and lower blowing/suction profiles: zero (in-phase forcing) and π (out-of-phase forcing). The Reynolds numbers considered are from 40 to 3900 covering various regimes of flow over a circular cylinder. For all the Reynolds numbers larger than 47, the present in-phase distributed forcing attenuates or annihilates the Karman vortex shedding and thus significantly reduces the mean drag and the drag and lift fluctuations. The optimal wavelength and amplitude of the in-phase forcing for maximum drag reduction are also obtained for the Reynolds number of 100. It is shown that the in-phase forcing produces the phase mismatch along the spanwise direction in the vortex shedding, weakens the strength of vortical structures in the wake, and thus reduces the drag. Unlike the in-phase forcing, the out-of-phase distributed forcing does not reduce the drag at low Reynolds numbers, but it reduces the mean drag and the drag and lift fluctuations at a high Reynolds number of 3900 by affecting the evolution of the separating shear layer, although the amount of drag reduction is smaller than that by the in-phase forcing.

Review of Unsteady Vortex Flows over Slender Delta Wings

Abstract: Nomenclature AR = aspect ratio; amplitude ratio B = probability density function of velocity c = root chord length f = frequency k = reduced frequency; axial wave number n =w ave number in angular direction P = probability p = pressure fluctuation Re =R eynolds number based on chord length S = spectral density s = local semispan T = period t = time U∞ = freestream velocity u = axial velocity v = swirl velocity x = streamwise distance xbd = breakdown location y = spanwise distance z =v ertical distance above wing surface α = angle of attack � = circulation δ = flap angle � = sweep angle ν = kinematic viscosity τ = time constant � =fi nangle ω =v orticity; radial frequency