Showing papers on "Vortex published in 2012"

The N-Vortex Problem: Analytical Techniques

Abstract: Introduction * N-Vortices in the Plane * Domains with Boundaries * Vortex Motion on a Sphere * Geometric Phases * Statistical Point Vortex Theories * Vortex Patch Models * Vortex Filament Models * References * Index

Cascades in Wall-Bounded Turbulence

Abstract: The kinematics and dynamics of wall-bounded turbulence are surveyed, with emphasis on the multiscale processes associated with the logarithmic layer and with its interactions with the wall. It is shown that the logarithmic law reflects a momentum cascade and that its structure agrees reasonably well with Townsend's (1961) model of a self-similar family of attached eddies, each of which contains, on average, a sweep-ejection pair, a segment of a large velocity streak, and disorganized vorticity. Those logarithmic eddies are themselves turbulent objects and can be studied in minimal simulation boxes that are much larger than those in the buffer layer. It is argued that, near the wall, the logarithmic eddies are probably the same as the vortex packets identified by experiments, but that their dynamics does not appear to be especially linked to the buffer layer. Further from the wall, they align into longer superstreaks, although the mechanism remains unclear.

Enhanced electric conductivity at ferroelectric vortex cores in BiFeO 3

Abstract: T opological defects in ferroic materials are attracting much attention both as a playground of unique physical phenomena and for potential applications in reconfigurable electronic devices. Here, we explore electronic transport at artificially created ferroelectric vortices in BiFeO3 thin films. The creation of one-dimensional conductive channels activated at voltages as low as 1 V is demonstrated. We study the electronic as well as the static and dynamic polarization structure of several topological defects using a combination of first-principles and phase-field modelling. The modelling predicts that the core structure can undergo a reversible transformation into a metastable twist structure, extending charged domain walls segments through the film thickness. The vortex core is therefore a dynamic conductor controlled by the coupled response of polarization and electron‐mobile-vacancy subsystems with external bias. This controlled creation of conductive one-dimensional channels suggests a pathway for the design and implementation of integrated oxide electronic devices based on domain patterning.

Towards Reconciling the Large-Scale Structure of Turbulent Boundary Layers in the Atmosphere and Laboratory

Abstract: A collaborative experimental effort employing the minimally perturbed atmospheric surface-layer flow over the salt playa of western Utah has enabled us to map coherence in turbulent boundary layers at very high Reynolds numbers, \({Re_{\tau}\sim\mathcal{O}(10^6)}\) . It is found that the large-scale coherence noted in the logarithmic region of laboratory-scale boundary layers are also present in the very high Reynolds number atmospheric surface layer (ASL). In the ASL these features tend to scale on outer variables (approaching the kilometre scale in the streamwise direction for the present study). The mean statistics and two-point correlation map show that the surface layer under neutrally buoyant conditions behaves similarly to the canonical boundary layer. Linear stochastic estimation of the three-dimensional correlation map indicates that the low momentum fluid in the streamwise direction is accompanied by counter-rotating roll modes across the span of the flow. Instantaneous flow fields confirm the inferences made from the linear stochastic estimations. It is further shown that vortical structures aligned in the streamwise direction are present in the surface layer, and bear attributes that resemble the hairpin vortex features found in laboratory flows. Ramp-like high shear zones that contribute significantly to the Reynolds shear-stress are also present in the ASL in a form nearly identical to that found in laboratory flows. Overall, the present findings serve to draw useful connections between the vast number of observations made in the laboratory and in the atmosphere.

Light-induced spiral mass transport in azo-polymer films under vortex-beam illumination

Abstract: When an azobenzene-containing polymer film is exposed to non-uniform illumination, a light-induced mass migration process may be induced, leading to the formation of relief patterns on the polymer-free surface. Despite many years of research effort, several aspects of this phenomenon remain poorly understood. Here we report the appearance of spiral-shaped relief patterns on the polymer film under the illumination of focused Laguerre-Gauss beams with helical wavefronts and an optical vortex at their axis. The induced spiral reliefs are sensitive to the vortex topological charge and to the wavefront handedness. These findings are unexpected because the doughnut-shaped intensity profile of Laguerre-Gauss beams contains no information about the wavefront handedness. We propose a model that explains the main features of this phenomenon through the surface-mediated interference of the longitudinal and transverse components of the optical field. These results may find applications in optical nanolithography and optical-field nanoimaging.

Control of orbital angular momentum of light with optical fibers

Abstract: We present a fiber-based method for generating vortex beams with a tunable value of orbital angular momentum from −1ℏ to +1ℏ per photon. We propose a new (to our knowledge) method to determine the modal content of the fiber and demonstrate high purity of the desired vortex state (97% after 20 m, even after bends and twists). This method has immediate utility for the multitude of applications in science and technology that exploit vortex light states.

The three-dimensional structure of momentum transfer in turbulent channels

Abstract: The quadrant analysis of the intense tangential Reynolds stress in plane turbulent channels is generalized to three-dimensional structures (Qs), with special emphasis on the logarithmic and outer layers. Wall-detached Qs are background stress fluctuations. They are small and isotropically oriented, and their contributions to the mean stress cancel. Wall-attached Qs are larger, and carry most of the mean Reynolds stresses. They form a family of roughly self-similar objects that become increasingly complex away from the wall, resembling the vortex clusters in del Alamo et al. (J. Fluid Mech., vol. 561, 2006, pp. 329–358). Individual Qs have fractal dimensions of the order of , slightly fuller than the clusters. They can be described as ‘sponges of flakes’, while vortex clusters are ‘sponges of strings’. The number of attached Qs decays away from the wall, but the fraction of the stress that they carry is independent of their sizes. A substantial fraction of the stress resides in a few large objects extending beyond the centreline, reminiscent of the very large structures of several authors. The predominant logarithmic-layer structure is a side-by-side pair of a sweep (Q4) and an ejection (Q2), with an associated cluster, and shares dimensions and stresses with the conjectured attached eddies of Townsend (J. Fluid Mech., vol. 11, 1961, pp. 97–120). Those attached eddies tend to be aligned streamwise from each other, located near the side walls between the low- and high-velocity large-scale streaks, but that organization does not extend far enough to explain the very long structures in the centre of the channel.

Possible planet-forming regions on submillimetre images

Abstract: Submillimetre images of transition discs are expected to reflect the distribution of the optically thin dust. Former observation of three transition discs LkHa330, SR21N, and HD1353444B at submillimetre wavelengths revealed images which cannot be modelled by a simple axisymmetric disc. We show that a large-scale anticyclonic vortex that develops where the viscosity has a large gradient (e.g., at the edge of the disc dead zone), might be accountable for these large-scale asymmetries. We modelled the long-term evolution of vortices being triggered by the Rossby wave instability. We found that a horseshoe-shaped (azimuthal wavenumber m=1) large-scale vortex forms by coalescing of smaller vortices within 5x10^4 yr, and can survive on the disc life-time (~5x10^6 yr), depending on the magnitude of global viscosity and the thickness of the viscosity gradient. The two-dimensional grid-based global disc simulations with local isothermal approximation and compressible-gas model have been done by the GPU version of hydrodynamic code FARGO (GFARGO). To calculate the dust continuum image at submillimetre wavelengths, we combined our hydrodynamical results with a 3D radiative transfer code. By the striking similarities of the calculated and observed submillimetre images, we suggest that the three transition discs can be modelled by a disc possessing a large-scale vortex formed near the disc dead zone edge. Since the larger dust grains (larger than mm in size) are collected in these vortices, the non-axisymmetric submillimetre images of the above transition discs might be interpreted as active planet and planetesimal forming regions situated far (> 50 AU) from the central stars.

The onset of dynamic stall revisited

Abstract: Dynamic stall on a helicopter rotor blade comprises a series of complex aerodynamic phenomena in response to the unsteady change of the blade’s angle of attack. It is accompanied by a lift overshoot and delayed massive flow separation with respect to static stall. The classical hallmark of the dynamic stall phenomenon is the dynamic stall vortex. The flow over an oscillating OA209 airfoil under dynamic stall conditions was investigated by means of unsteady surface pressure measurements and time-resolved particle image velocimetry. The characteristic features of the unsteady flow field were identified and analysed utilising different coherent structure identification methods. An Eulerian and a Lagrangian procedure were adopted to locate the axes of vortices and the edges of Lagrangian coherent structures, respectively; a proper orthogonal decomposition of the velocity field revealed the energetically dominant coherent flow patterns and their temporal evolution. Based on the complementary information obtained by these methods the dynamics and interaction of vortical structures were analysed within a single dynamic stall life cycle leading to a classification of the unsteady flow development into five successive stages: the attached flow stage; the stall development stage; stall onset; the stalled stage; and flow reattachment. The onset of dynamic stall was specified here based on a characteristic mode of the proper orthogonal decomposition of the velocity field. Variations in the flow field topology that accompany the stall onset were verified by the Lagrangian coherent structure analysis. The instantaneous effective unsteadiness was defined as a single representative parameter to describe the influence of the motion parameters. Dynamic stall onset was found to be promoted by increasing unsteadiness. The mechanism that results in the detachment of the dynamic stall vortex from the airfoil was identified as vortex-induced separation caused by strong viscous interactions. Finally, a revised criterion to discern between light and deep dynamic stall was formulated.

Unsteady force generation and vortex dynamics of pitching and plunging aerofoils

Abstract: Experimental studies of the flow topology, leading-edge vortex dynamics and unsteady force produced by pitching and plunging flat-plate aerofoils in forward flight at Reynolds numbers in the range 5000–20 000 are described. We consider the effects of varying frequency and plunge amplitude for the same effective angle-of-attack time history. The effective angle-of-attack history is a sinusoidal oscillation in the range to with mean of and amplitude of . The reduced frequency is varied in the range 0.314–1.0 and the Strouhal number range is 0.10–0.48. Results show that for constant effective angle of attack, the flow evolution is independent of Strouhal number, and as the reduced frequency is increased the leading-edge vortex (LEV) separates later in phase during the downstroke. The LEV trajectory, circulation and area are reported. It is shown that the effective angle of attack and reduced frequency determine the flow evolution, and the Strouhal number is the main parameter determining the aerodynamic force acting on the aerofoil. At low Strouhal numbers, the lift coefficient is proportional to the effective angle of attack, indicating the validity of the quasi-steady approximation. Large values of force coefficients () are measured at high Strouhal number. The measurement results are compared with linear potential flow theory and found to be in reasonable agreement. During the downstroke, when the LEV is present, better agreement is found when the wake effect is ignored for both the lift and drag coefficients.

Near-wake flow structure downwind of a wind turbine in a turbulent boundary layer

Abstract: Wind turbines operate in the surface layer of the atmospheric boundary layer, where they are subjected to strong wind shear and relatively high turbulence levels. These incoming boundary layer flow characteristics are expected to affect the structure of wind turbine wakes. The near-wake region is characterized by a complex coupled vortex system (including helicoidal tip vortices), unsteadiness and strong turbulence heterogeneity. Limited information about the spatial distribution of turbulence in the near wake, the vortex behavior and their influence on the downwind development of the far wake hinders our capability to predict wind turbine power production and fatigue loads in wind farms. This calls for a better understanding of the spatial distribution of the 3D flow and coherent turbulence structures in the near wake. Systematic wind-tunnel experiments were designed and carried out to characterize the structure of the near-wake flow downwind of a model wind turbine placed in a neutral boundary layer flow. A horizontal-axis, three-blade wind turbine model, with a rotor diameter of 13 cm and the hub height at 10.5 cm, occupied the lowest one-third of the boundary layer. High-resolution particle image velocimetry (PIV) was used to measure velocities in multiple vertical stream-wise planes (x–z) and vertical span-wise planes (y–z). In particular, we identified localized regions of strong vorticity and swirling strength, which are the signature of helicoidal tip vortices. These vortices are most pronounced at the top-tip level and persist up to a distance of two to three rotor diameters downwind. The measurements also reveal strong flow rotation and a highly non-axisymmetric distribution of the mean flow and turbulence structure in the near wake. The results provide new insight into the physical mechanisms that govern the development of the near wake of a wind turbine immersed in a neutral boundary layer. They also serve as important data for the development and validation of numerical models.

Vortex development behind a finite porous obstruction in a channel

Abstract: This experimental study describes the turbulent wake behind a two-dimensional porous obstruction, consisting of a circular array of cylinders. The cylinders extend from the channel bed through the water surface, mimicking a patch of emergent vegetation. Three patch diameters () and seven solid volume fractions () are tested. Because flow can pass through the patch, directly downstream there is a region of steady, non-zero, streamwise velocity, , called the steady wake. For the patch diameters and solid volume fractions considered here, is a function of only. The length of the steady wake () increases as decreases and can be predicted from the growth of a plane shear layer. The formation of the von-Karman vortex street is delayed until the end of the steady wake. There are two regions of elevated transverse velocity fluctuation (): directly behind the patch, associated with the wake turbulence of individual cylinders; and at the distance from the patch, associated with the formation of large-scale wake oscillation. Velocity along the centreline of the wake starts to increase only after the patch-scale vortex street is formed, and it approaches the free-stream velocity over a distance . The dimensionless length of the entire wake, , increases with patch porosity.

The wake structure behind a porous obstruction and its implications for deposition near a finite patch of emergent vegetation

Abstract: [1] This experimental study describes the mean and turbulent flow structure in the wake of a circular array of cylinders, which is a model for a patch of emergent vegetation. The patch diameter, D, and patch density, a (frontal area per volume), are varied. The flow structure is linked to a nondimensional flow blockage parameter, CDaD, which is the ratio of the patch diameter and a drag length scale (CDa)−1. CD is the cylinder drag coefficient. The velocity exiting the patch, Ue, is reduced relative to the upstream velocity, U∞, and Ue/U∞ decreases as flow blockage (CDaD) increases. A predictive model is developed for Ue/U∞. The wake behind the patch contains two peaks in turbulence intensity. The first peak occurs directly behind the patch and is related to turbulence production within the patch at the scale of individual cylinders. The second peak in turbulence intensity occurs at distance Lwdownstream from the patch and is related to the wake-scale vortices of the von Karman vortex street. The presence of the flowUe in the wake delays the formation of the von Karman vortex street until distance L1 (

An overview on heat transfer augmentation using vortex generators and nanofluids: Approaches and applications

Abstract: The subject of heat transfer enhancement has significant interest to develop the compact heat exchangers in order to obtain a high efficiency, low cost, light weight, and size as small as possible. Therefore, energy cost and environmental considerations are going on to encourage attempts to invent better performance over the existence designs. Streamwise vortices can be generated using small flow manipulators or protrusions such as wings and winglets configurations. Single-pair, single row, or two dimensional array of vortex generators (VGs) can be punched, mounted, attached or embedded in the boundary layer of flow channel. VGs generate longitudinal and transverse vortices, while longitudinal vortices are more efficient for heat transfer enhancement than transverse vortices. A dramatic augmentation in thermal performance of the thermal system can be achieved but pressure drop penalty is existed. Several parameters have been overviewed in this paper, which have pronounced effect on the convective heat transfer coefficient and pressure drop penalty. These parameters are: attack angle of VG, geometry of VG, standard and novel types of VG, spacing between the VG tips, number of pairs of VGs in the flow direction, rectangular or circular array arrangement of VGs, common-flow upper (CFU) or common-flow down (CFD) configuration of VG, pointing up (PU) or pointing down (PD) arrangement of VG with flow direction, Re number, channel aspect ratio, number of tubes of fin-tube heat exchanges (HE), circular or oval tubes of fin-tube HE, and location of VG respect to the tube of HE or from leading edge of the channel. This paper gives an overview about the early studies done in order to improve the performance of thermal systems with minimal pressure losses to derive systems with less negative impact on the environment and high level of energy economic. This study also provides an outlook for future work using nanofluids with vortex generators. This article is also summarizes the recent experimental and numerical developments on the thermal conductivity measurements of nanofluids, thermal conductivity enhancement, convection and conduction heat transfer, some applications, main problems and suggestions for future works.

Inertia and Chiral Edge Modes of a Skyrmion Magnetic Bubble

Abstract: The dynamics of a vortex in a thin-film ferromagnet resembles the motion of a charged massless particle in a uniform magnetic field. Similar dynamics is expected for other magnetic textures with a nonzero Skyrmion number. However, recent numerical simulations reveal that Skyrmion magnetic bubbles show significant deviations from this model. We show that a Skyrmion bubble possesses inertia and derive its mass from the standard theory of a thin-film ferromagnet. In addition to center-of-mass motion, other low energy modes are waves on the edge of the bubble traveling with different speeds in opposite directions.

Origins and structure of spike-type rotating stall

Abstract: In this paper we describe the structures that produce a spike-type route to rotating stall and explain the physical mechanism for their formation. The descriptions and explanations are based on numerical simulations, complemented and corroborated by experiments. It is found that spikes are caused by a loss of pressure rise capability in the rotor tip region, due to flow separation resulting from high incidence. The separation gives rise to shedding of vorticity from the leading edge and the consequent formation of vortices that span between the suction surface and the casing. As seen in the rotor frame of reference, near the casing the vortex convects toward the pressure surface of the adjacent blade. The approach of the vortex to the adjacent blade triggers a separation on that blade so the structure propagates. The above sequence of events constitutes a spike. The simulations show shed vortices over a range of tip clearances including zero. The implication is that they are not part of the tip clearance vortex, in accord with recent experimental findings. Evidence is presented for the existence of these vortex structures immediately prior to spike-type stall and, more strongly, for their causal connection with spike-type stall inception. Data from several compressors are shown to reproduce the pressure and velocity signature of the spike-type stall inception seen in the simulations.Copyright © 2012 by ASME

From the Ginzburg-Landau Model to Vortex Lattice Problems

Abstract: We introduce a “Coulombian renormalized energy” W which is a logarithmic type of interaction between points in the plane, computed by a “renormalization.” We prove various of its properties, such as the existence of minimizers, and show in particular, using results from number theory, that among lattice configurations the triangular lattice is the unique minimizer. Its minimization in general remains open.

Origins and Structure of Spike-Type Rotating Stall

Abstract: In this paper, we describe the structures that produce a spike-type route to rotating stall and explain the physical mechanism for their formation. The descriptions and explanations are based on numerical simulations, complemented and corroborated by experiments. It is found that spikes are caused by a separation at the leading edge due to high incidence. The separation gives rise to shedding of vorticity from the leading edge and the consequent formation of vortices that span between the suction surface and the casing. As seen in the rotor frame of reference, near the casing the vortex convects toward the pressure surface of the adjacent blade. The approach of the vortex to the adjacent blade triggers a separation on that blade so the structure propagates. The above sequence of events constitutes a spike. The computed structure of the spike is shown to be consistent with rotor leading edge pressure measurements from the casing of several compressors: the centre of the vortex is responsible for a pressure drop and the partially blocked passages associated with leading edge separations produce a pressure rise. The simulations show leading edge separation and shed vortices over a range of tip clearances including zero. The implication, in accord with recent experimental findings, is that they are not part of the tip clearance vortex. Although the computations always show high incidence to be the cause of the spike, the conditions that give rise to this incidence (e.g., blockage from a corner separation or the tip leakage jet from the adjacent blade) do depend on the details of the compressor.

Spatiotemporal vortex beams and angular momentum

Abstract: We present a space-time generalization of the known spatial (monochromatic) wave vortex beams carrying intrinsic orbital angular momentum (OAM) along the propagation direction. Generic spatiotemporal vortex beams are polychromatic and can carry intrinsic OAM at an arbitrary angle to the mean momentum. Applying either (i) a transverse wave-vector shift or (ii) a Lorentz boost to a monochromatic Bessel beam, we construct a family of either (i) time-diffracting or (ii) nondiffracting spatiotemporal Bessel beams, which are exact solutions of the Klein-Gordon wave equations. The proposed spatiotemporal OAM states are able to describe either photon or electron vortex states (both relativistic and nonrelativistic) and have potential applications in particle collisions, optics of moving media, quantum communications, and astrophysics.

Vortex Ring Formation in the Left Ventricle of the Heart: Analysis by 4D Flow MRI and Lagrangian Coherent Structures.

Abstract: Recent studies suggest that vortex ring formation during left ventricular (LV) rapid filling is an optimized mechanism for blood transport, and that the volume of the vortex ring is an important measure. However, due to lack of quantitative methods, the volume of the vortex ring has not previously been studied. Lagrangian Coherent Structures (LCS) is a new flow analysis method, which enables in vivo quantification of vortex ring volume. Therefore, we aimed to investigate if vortex ring volume in the human LV can be reliably quantified using LCS and magnetic resonance velocity mapping (4D PC-MR). Flow velocities were measured using 4D PC-MR in 9 healthy volunteers and 4 patients with dilated ischemic cardiomyopathy. LV LCS were computed from flow velocities and manually delineated in all subjects. Vortex volume in the healthy volunteers was 51 ± 6% of the LV volume, and 21 ± 5% in the patients. Interobserver variability was −1 ± 13% and interstudy variability was −2 ± 12%. Compared to idealized flow experiments, the vortex rings showed additional complexity and asymmetry, related to endocardial trabeculation and papillary muscles. In conclusion, LCS and 4D PC-MR enables measurement of vortex ring volume during rapid filling of the LV.

The Roles of an Expanding Wind Field and Inertial Stability in Tropical Cyclone Secondary Eyewall Formation

Abstract: The Weather and Research and Forecasting Model (WRF) is used to simulate secondary eyewall formation (SEF) in a tropical cyclone (TC) on the β plane. The simulated SEF process is accompanied by an outward expansion of kinetic energy and the TC warm core. An absolute angular momentum budget demonstrates that this outward expansion is predominantly a symmetric response to the azimuthal-mean and wavenumber-1 components of the transverse circulation. As the kinetic energy expands outward, the kinetic energy efficiency in which latent heating can be retained as local kinetic energy increases near the developing outer eyewall.The kinetic energy efficiency associated with SEF is examined further using a symmetric linearized, nonhydrostatic vortex model that is configured as a balanced vortex model. Given the symmetric tangential wind and temperature structure from WRF, which is close to a state of thermal wind balance above the boundary layer, the idealized model provides the transverse circulation assoc...

Propagation dynamics of abruptly autofocusing Airy beams with optical vortices

Abstract: We investigated the propagation dynamics of the Circular Airy Beams (CAB) with optical vortices (OVs) by numerical calculation. Comparing to the common CAB, the maximum intensity of CAB with vortices can be increased greatly at the focal plane and its focal intensity profile is doughnut-shaped when an on-axis vortex is imposed. The case for an off-axis OV and multiple OVs have been investigated as well. We demonstrate that two opposite OVs will annihilate exactly at the focal plane, with the focal intensity is highly increased.

Scanning tunneling microscopy/spectroscopy of vortices in LiFeAs

Abstract: We investigate vortices in LiFeAs using scanning tunneling microscopy/spectroscopy. Zero-field tunneling spectra show two superconducting gaps without detectable spectral weight near the Fermi energy, evidencing fully gapped multiband superconductivity. We image vortices in a wide field range from 0.1 T to 11 T by mapping the tunneling conductance at the Fermi energy. A quasihexagonal vortex lattice at low field contains domain boundaries which consist of alternating vortices with unusual coordination numbers of 5 and 7. With increasing field, the domain boundaries become ill defined, resulting in a uniformly disordered vortex matter. Tunneling spectra taken at the vortex center are characterized by a sharp peak just below the Fermi energy, apparently violating particle-hole symmetry. The image of each vortex shows energy-dependent 4-fold anisotropy which may be associated with the anisotropy of the Fermi surface. The vortex radius shrinks with decreasing temperature and becomes smaller than the coherence length estimated from the upper critical field. This is direct evidence of the Kramer-Pesch effect expected in a clean superconductor.

Flow structure on finite-span wings due to pitch-up motion

Abstract: The flow structure on low-aspect-ratio wings arising from pitch-up motion is addressed via a technique of particle image velocimetry. The objectives are to: determine the onset and evolution of the three-dimensional leading-edge vortex; provide complementary interpretations of the vortex structure in terms of streamlines, projections of spanwise and surface-normal vorticity, and surfaces of constant values of the second invariant of the velocity gradient tensor (iso- surfaces); and to characterize the effect of wing planform (rectangular versus elliptical) on this vortex structure. The pitch-up motion of the wing (plate) is from 0 to over a time span corresponding to four convective time scales, and the Reynolds number based on chord is 10 000. Volumes of constant magnitude of the second invariant of the velocity gradient tensor are interpreted in conjunction with three-dimensional streamline patterns and vorticity projections in orthogonal directions. The wing motion gives rise to ordered vortical structures along its wing surface. In contrast to development of the classical two-dimensional leading-edge vortex, the flow pattern evolves to a strongly three-dimensional form at high angle of attack. The state of the vortex system, after attainment of maximum angle of attack, has a similar form for extreme configurations of wing planform. Near the plane of symmetry, a large-scale region of predominantly spanwise vorticity dominates. Away from the plane of symmetry, the flow is dominated by two extensive regions of surface-normal vorticity, i.e. swirl patterns parallel to the wing surface. This similar state of the vortex structure is, however, preceded by different sequences of events that depend on the magnitude of the spanwise velocity within the developing vortex from the leading edge of the wing. Spanwise velocity of the order of one-half the free stream velocity, which is oriented towards the plane of symmetry of the wing, results in regions of surface-normal vorticity. In contrast, if negligible spanwise velocity occurs within the developing leading-edge vortex, onset of the regions of surface-normal vorticity occurs near the tips of the wing. These extremes of large and insignificant spanwise velocity within the leading-edge vortex are induced respectively on rectangular and elliptical planforms.