Cross-Stream Vorticity Field Induced by Streamwise Vortices in Unbounded and Wall-Bounded Shear Flows

This computational study examines the unsteady cross-stream vorticity structures that form when one or more streamwise vortices are immersed in homogeneous and boundary-layer shear flows. A quasi-two-dimensional limit is considered in which the velocity and vorticity fields, while still possessing three nonzero components, have vanishing gradient in the streamwise direction. This idealization is suitable to applications such as streamwise vortices that occur along a ship hull or airplane fuselage and it can be used as an idealized representation of the quasi-streamwise vortices in the near-wall region of a turbulent boundary layer. In this quasi-two-dimensional idealization, the streamwise velocity has no effect on the cross-stream velocity associated with the vortex. However, the vortex acts to modify the cross-stream vorticity component, resulting in regions of the flow with strong deviations in streamwise velocity. This paper examines the complex structures that form as the cross-stream vorticity field is wrapped up by the vortex and the effect of these structures on the streamwise velocity field, first for vortices immersed in homogeneous shear flow and then for vortices immersed in a boundary layer along a flat wall. Received 2 January 2002 and accepted 13 August 2002 Published online 3 December 2002 RID="*" ID="*" This project was supported by the Office of Naval Research under Grant Number N00014-01-1-0015. Dr. Thomas Swain is the program manager. Communicated by T.B. Gatski     

Flow above the free end of a surface-mounted finite-height circular cylinder: A review

The wake of a surface-mounted finite-height circular cylinder and the associated vortex patterns are strongly dependent on the cylinder aspect ratio and the thickness of the boundary layer on the ground plane relative to the dimensions of the cylinder. Above a critical aspect ratio, the mean wake is characterized by streamwise tip vortex structures and Kármán vortex shedding from the sides of the cylinder. Below a critical aspect ratio, a unique mean wake structure is observed. Recent experimental studies in the literature that used phase-averaged techniques, as well as recent numerical simulations, have led to an improved physical understanding of the near-wake vortex flow patterns. However, the flow above the free end of the finite circular cylinder, and its relationship to the near wake, has not been systematically studied. The effects of aspect ratio and boundary layer thickness on the free-end flow field are also not completely understood, nor has the influence of Reynolds number on the free-end flow field been fully explored. Common features associated with the free end include separation from the leading edge, a mean recirculation zone containing a prominent cross-stream arch (or mushroom) vortex, and reattachment onto the free-surface. Other flow features that remain to be clarified include a separation bubble near the leading edge, one or two cross-stream vortices within this separation bubble, the origins of the streamwise tip or trailing vortices, and various critical points in the near-surface flow topology. This paper reviews the current understanding of the flow above the free end of a surface-mounted finite-height circular cylinder, with a focus on models of the flow field, surface oil flow visualization studies, pressure and heat flux distributions on the free-end surface, measurements of the local velocity field, and numerical simulations, found in the literature.     

Wake structures behind an oscillating bubble rising close to a vertical wall

In the present study, the wake structures behind an oscillating (zigzagging in a plane) air bubble, rising in a close vicinity of a vertical wall are experimentally investigated using a high-speed two-phase particle image velocimetry. While varying the distance between the rising bubble and the wall, the spatial and temporal variations in the spanwise and streamwise vorticity components contained in the wake vortices, in addition to the bubble trajectory, are measured in a tank filled with water. In particular, the Lagrangian streamwise vorticity fields in the bubble wake have been reconstructed and investigated in detail with different conditions. Without the wall, it is confirmed that there exist counter-rotating streamwise vortex tubes in the bubble wake, agreeing with the case of a two-dimensional zigzagging bubble, as reported in the literatures. It is also found that the hairpin vortex chain structures, initially attached to the bubble rear, evolve to detached vortex ring structures as the bubble rises in an oscillating path. While the detailed vortex structures show up quite differently from the reference case depending on the distance to the wall (e.g., actual bubble-wall collision), in general the wake behind the bubble as it moves toward and away from the wall can be summarized as: (i) transition to the detached vortex ring structures is accelerated; (ii) streamwise length of vortex tubes is shortened (evolution is interfered); (iii) counter-rotating vortex tubes approaching the wall tend to slightly bounce off and slide away (being dissipated fast) from each other on the wall; and (iv) boundary-layer like secondary flow structures are induced on the wall due to additional viscous effects. These wall-induced wake modification indicates that more fluid energy is wasted due to the wall interference, rather than being used to force the lateral movement of the bubble, which agrees with the reduced amplitude and wavelength of the oscillating bubble path on the wall. Finally, this explanation has been further confirmed by estimating the vortex-induced lateral forces acting on the bubble for each case.     

Classifying wakes produced by self-propelled fish-like swimmers using neural networks

We consider the classification of wake structures produced by self-propelled fish-like swimmers based on local measurements of flow variables. This problem is inspired by the extraordinary capability of animal swimmers in perceiving their hydrodynamic environments under dark condition. We train different neural networks to classify wake structures by using the streamwise velocity component, the crosswise velocity component, the vorticity and the combination of three flow variables, respectively. It is found that the neural networks trained using the two velocity components perform well in identifying the wake types, whereas the neural network trained using the vorticity suffers from a high rate of misclassification. When the neural network is trained using the combination of all three flow variables, a remarkably high accuracy in wake classification can be achieved. The results of this study can be helpful to the design of flow sensory systems in robotic underwater vehicles.     

Effect of velocity ratio on the streamwise vortex structures in the wake of a stack

The time-averaged velocity and streamwise vorticity fields within the wake of a stack were investigated in a low-speed wind tunnel using a seven-hole pressure probe. The experiments were conducted at a Reynolds number, based on the stack external diameter, of Re_D=2.3×10⁴. The stack, of aspect ratio AR=9, was mounted normal to a ground plane and was partially immersed in a flat-plate turbulent boundary layer, where the ratio of the boundary layer thickness to the stack height was δ/H≈0.5. The jet-to-cross-flow velocity ratio was varied from R=0 to 3, which covered the downwash, crosswind-dominated and jet-dominated flow regimes. In the downwash and crosswind-dominated flow regimes, two pairs of counter-rotating streamwise vortex structures were identified within the stack wake. The tip vortex pair located close to the free end of the stack, and the base vortex pair located close to the ground plane within the flat-plate boundary layer, were similar to those found in the wake of a finite circular cylinder, and were associated with the upwash and downwash flow fields within the stack wake, respectively. In the jet-dominated flow regime, a third pair of streamwise vortex structures was observed, referred to as the jet-wake vortex pair, which occurred within the jet-wake region above the free end of the stack. The jet-wake vortex pair had the same orientation as the base vortex pair and was associated with the jet rise. The peak vorticity and strength of the streamwise vortex structures were functions of the jet-to-cross-flow velocity ratio. For the tip vortex structures, their peak vorticity and strength reduced as the jet-to-cross-flow velocity ratio increased.     

The turbulent wake of a circular cylinder rotating about the streamwise axis

This paper presents measurements in the turbulent wake of a circular cylinder rotating with its axis normal to the free-stream velocity; in other words, the axis of rotation was parallel to the streamwise direction. All three mean velocities and six Reynolds stresses were obtained at three positions downstream of the cylinder, with and without rotation of the free-stream. Most emphasis is given to the latter results because of the better flow quality. The ratio of the circumferential velocity of the cylinder to the free-stream velocity — the swirl number — had a maximum value of 0.6. Measurements for two combinations of the free-stream and angular velocities showed the velocity deficit in the wake to be a multi-valued function of the swirl number, implying that the rotation affected the separation of the cylinder's boundary layer in a complex manner. In the turbulent wake, the rotation did not significantly alter the magnitudes of the normal stresses, but caused large changes to the shape of the profiles of the axial and cross-stream normal stresses. Eventually, the primary (cross-stream) shear stress became almost entirely positive, but there was no corresponding change to the (cross-stream) gradient of the streamwise mean velocity. Despite these alterations to the turbulence, the rotationally-activated generation terms in the Reynolds transport equations never dominated the terms that are common to the wakes of rotating and non-rotating cylinders.This work was supported by the Australian Research Council. Most of the data acquisition software was written by Mr J. J. Smith.     

Solid/free-surface juncture boundary layer and wake

 The Reynolds-averaged flow for a solid/free-surface juncture boundary layer and wake is documented. The three mean-velocity components and five of the Reynolds stresses are measured for a surface-piercing flat plate in a towing tank using a laser-Doppler velocimeter system for both boundary-layer and wake planes in regions close to the free surface. The experimental method is described, including the foil-plate model, laser-Doppler velocimeter system, conditions, and uncertainty analysis. The underlying flow data is in excellent agreement with benchmark data. Inner (near the plate and wake centerplane and below the free surface) and outer (near the free surface) regions of high streamwise vorticity of opposite sign are observed, which transport, respectively, high mean velocity and low turbulence from the outer to the inner and low mean velocity and high turbulence from the inner to the outer portions of the boundary layer and wake. For the wake, the inner region of vorticity is relatively weak. The physical mechanism for the streamwise vorticity is analyzed with regard to the Reynolds-averaged streamwise vorticity equation. The anisotropy of the crossplane normal Reynolds stresses closely correlates with the vorticity and, additionally, indicates similarity, i.e., its nature is such that it only depends on the proximity to the plate and free surface boundaries or wake centerplane symmetry plane. Free-surface effects on the Reynolds stresses are analyzed with regard to the behavior close to the free surface of the turbulent kinetic energy and the normal components of the anisotropy tensor and the anisotropy invariants. Close to the free surface, the turbulent kinetic energy is nearly constant and increases for the inner and outer portions, respectively, of the boundary layer and wake and the normal components of the anisotropy tensor and the anisotropy invariants roughly correspond to the limiting values for two-component turbulence. The similarities and differences between the present results and analysis with those from related studies are discussed. The data and analysis should have practical application with regard to the development of turbulence models for computational fluid dynamics methods for the Reynolds-averaged Navier–Stokes equations. Received: 27 May 1997/Accepted: 1 August 1997     

Planar velocity measurements of a two-dimensional compressible wake

The present study describes the application of particle image velocimetry (PIV) to investigate the compressible flow in the wake of a two-dimensional blunt base at a freestream Mach number M_X=2. The first part of the study addresses specific issues related to the application of PIV to supersonic wind tunnel flows, such as the seeding particle flow-tracing fidelity and the measurement spatial resolution. The seeding particle response is assessed through a planar oblique shock wave experiment. The measurement spatial resolution is enhanced by means of an advanced image-interrogation algorithm. In the second part, the experimental results are presented. The PIV measurements yield the spatial distribution of mean velocity and turbulence. The mean velocity distribution clearly reveals the main flow features such as expansion fans, separated shear layers, flow recirculation, reattachment, recompression and wake development. The turbulence distribution shows the growth of turbulent fluctuations in the separated shear layers up to the reattachment location. Increased velocity fluctuations are also present downstream of reattachment outside of the wake due to unsteady flow reattachment and recompression. The instantaneous velocity field is analyzed seeking coherent flow structures in the redeveloping wake. The instantaneous planar velocity and vorticity measurements return evidence of large-scale turbulent structures detected as spatially coherent vorticity fluctuations. The velocity pattern consistently shows large masses of fluid in vortical motion. The overall instantaneous wake flow is organized as a double row of counter-rotating structures. The single structures show vorticity contours of roughly elliptical shape in agreement with previous studies based on spatial correlation of planar light scattering. Peak vorticity is found to be five times higher than the mean vorticity value, suggesting that wake turbulence is dominated by the activity of large-scale structures. The unsteady behavior of the reattachment phenomenon is studied. Based on the instantaneous flow topology, the reattachment is observed to fluctuate mostly in the streamwise direction suggesting that the unsteady separation is dominated by a pumping-like motion.     

Coherent vortical and straining structures in the finite wall-mounted square cylinder wake

Topological aspects of the turbulent wake of a finite, surface-mounted, square-cross-section cylinder of h/d = 4 are addressed by decomposing the velocity field into a quasi-periodic coherent part and the unresolved incoherent fluctuations. The three-dimensional large scale structure is educed through a reconstruction of planar phase-averaged PIV measurements using the simultaneously sampled surface pressure difference on opposing sides of the obstacle as a phase reference. A topological model for the vortex structure is educed and mean streamwise wake vorticity is explained in terms of the connections between initially vertical structures shed alternately from either side of the obstacle, rather than previously proposed ‘tip’ vortex structures generated at the obstacle free-end. The coherent structure educed accounts for a significant portion of the fluctuating energy in the wake. The turbulent field is further analyzed by finding Lagrangian straining structures that form by induction of the coherent vorticity field, and these structures are related to the energy transfer from the base phase-averaged flow since they act to stretch incoherent vorticity fluctuations in their neighbourhood.     

Transition phenomena in the wake of an inclined square cylinder

The division of flow regimes in a square cylinder wake at various angles of attack (α) is studied. This study provides evidence of the existence of modes A and B instabilities in the wake of an inclined square cylinder. The critical Reynolds numbers for the inception of these instability modes were identified through the determination of discontinuities in the Strouhal number versus Reynolds number curves. The spectra and time traces of wake streamwise velocity were observed to display three distinct patterns in different flow regimes. Streamwise vortices with different wavelengths at various Reynolds numbers were visualized. A PIV technique was employed to quantitatively measure the parameters of wake vortices. The wavelengths of the streamwise vortices in the modes A and B regimes were measured by using the auto-correlation method. From the present investigation, the square cylinder wake at various angles of attack undergoes a similar transition path to that of a circular cylinder, although various quantitative parameters measured which include the critical Reynolds numbers, spanwise wavelength of secondary vortices, and the circulation and vorticity of wake vortices all show an α dependence.     

Multisensor Hot Wire Vorticity Probe Measurements of the Formation Field of Two Corotating Vortices

Experimental evidence is reported, regarding the formation of a pair of co-rotating tip vortices by a split wing configuration, consisting of two half wings at equal and opposite angles of attack. Simultaneous measurements of the three-dimensional vector fields of velocity and vorticity were conducted on a cross plane at a downstream distance corresponding to 0.3 cord lengths (near wake), using an in-house constructed 12-sensor hot wire anemometry vorticity probe. The probe consists of three closely separated orthogonal 4-wire velocity sensor arrays, measuring simultaneously the three-dimensional velocity vector at three closely spaced locations on a cross plane of the flow filed. This configuration makes possible the estimation of spatial velocity derivatives by means of a forward difference scheme of first order accuracy. Velocity measurements obtained with an X-wire are also presented for comparison. In this near wake location, the flow field is dictated by the pressure distribution established by the flow around the wings, mobilizing large masses of air and leading to the roll up of fluid sheets. Fluid streams penetrating between the wings collide, creating on the cross plane flow a stagnation point and an “impermeable” line joining the two vortex centres. Along this line fluid is directed towards the two vortices, expanding their cores and increasing their separation distance. This feeding process generates a dipole of opposite sign streamwise mean vorticity within each vortex. The rotational flow within the vortices obligates an adverse streamwise pressure gradient leading to a significant streamwise velocity deficit characterizing the vortices. The turbulent flow field is the result of temporal changes in the intensity of the vortex formation and changes in the position of the cores (wandering).     

Turbulent flow past a bubble and an ellipsoid using shadow-image and PIV techniques

An experimental investigation on flow around an oscillating bubble and solid ellipsoid with a flat bottom was conducted. A single air bubble (equivalent diameter D_e=9.12 mm) was attached to a small disk (1 mm) at the end of a needle and suspended across a vertical square channel (100 mm) by wire wherein water flowed downward at a constant flowrate. The solid ellipsoid (D_e9.1 mm) was suspended across the square channel in the same manner. The equivalent diameter-based Reynolds and Eotvos number range, 1950<Re<2250 and 11<Eo<11.5, placed the bubble in the ‘wobbly’ regime while the flow in its wake was turbulent. A constant flowrate and one bubble size was used such that flow in the wake was turbulent. Velocity measurements of the flow field around the bubble or solid were made using a one CCD camera Digital Particle Image Velocimetry (DPIV) system enhanced by Laser Induced Fluorescence (LIF). The shape of the bubble or solid was simultaneously recorded along with the velocity using a second CCD camera and an Infrared Shadow Technique (IST). In this way both the flow-field and the boundary of the bubble (solid) were measured. The velocity vector plots of flow around and in the wake of a bubble/solid, supplemented by profiles and contours of the average and root-mean-square velocities, vorticity, Reynolds stress and turbulent kinetic energy, revealed differences in the wake flow structure behind a bubble and solid. One of the significant differences was in the inherent, oscillatory motion of the bubble which not only produced vorticity in the near-wake, but as a result of apparent vorticity stretching distributed the turbulent kinetic energy associated with this flow more uniformly on its wake, in contrast to the solid.     

Flow structures and dynamics in the wakes of sliding bubbles

An experimental investigation is reported for the flow structures in the wake of an air bubble sliding under an inclined surface in quiescent water. Time-resolved particle image velocimetry (PIV) is used to study the wakes of sliding bubbles for a range of measurement planes, bubble diameters and surface inclination angles. Additionally, key aspects of the bubble’s motion are measured simultaneously using a novel method that accounts for the motion of the bubble’s interface. Thus, vortex shedding may be linked to changes in the bubble shape and path.Analysis of the measured velocity and vorticity fields reveals a wake structure consisting of a near wake that moves in close proximity to the bubble, shedding vorticity at the inversion points of the bubble path. Downstream of the bubble in the far wake, these structures evolve into asymmetrical, oppositely-oriented hairpin vortices that are generated in the near wake. These hairpin vortices bear similarities to those observed behind freely rising bubbles and near-wall bluff bodies and are found to cause significant motion of the bulk fluid. This bulk fluid motion has the potential to offer significant convective cooling of adjacent heated surfaces, such as submerged electronics components.     

Approach towards self-preservation of turbulent cylinder and screen wakes

Two-dimensional wakes generated from a circular cylinder and a 50% solidity screen have significantly different initial conditions. Accordingly, the approach towards self-preservation is quite different for the two wakes. For the cylinder wake, the normalized Reynolds stresses and spanwise vorticity decrease with increasing distance from the wake generator; the inverse occurs in the screen wake. Distributions of mean velocity, Reynolds stresses, and rms spanwise vorticity indicate that self-preservation is reached at a much smaller streamwise distance for the screen than for the cylinder wake. This result is consistent with the previously reported topological differences between these two flows.     

The transport of vorticity on rotating Bernoulli surfaces of any geometry in compressible,inviscid flow with applications to turbomachine blade rows

The transport of vorticity is analysed for a compressible, inviscid flow which is steady relative to a reference frame rotating at constant angular velocity. It is shown that Helmholtz's vorticity convection theorem does not apply to this flow but nevertheless the vortex lines are transported on a streamsurface which therefore corresponds to the familiar Bernoulli surface.Explicit, integrated results are obtained for Bernoulli surfaces of any geometry. The transport of the normal component of vorticity is obtained for the general case in closed form, whereas the transport of the streamwise component is closed in form for some cases but involves a time difference integral over the bounding streamlines.Application is made to a turbomachine blade row where the flow between two consecutive blades is examined. Explicit results are obtained for the streamwise vorticity development in the axial flow configuration in terms of the traverse time integral for a particle, taken around the blade profile. The more general mixed flow configuration is also examined where a closed result is obtained only for the incompressible case.     

Experimental investigation of the unsteady structure of a transitional plane wall jet

 A laminar wall jet undergoing transition is investigated using the particle image velocimetry (PIV) technique. The plane wall jet is issued from a rectangular channel, with the jet-exit velocity profile being parabolic. The Reynolds number, based on the exit mean velocity and the channel width, is 1450. To aid the understanding of the global flow features, laser-sheet/smoke flow visualizations are performed along streamwise, spanwise, and cross-stream directions. Surface pressure measurements are made to correlate the instantaneous vorticity distribution with the surface pressure fluctuations. The instantaneous velocity and vorticity field measurements provide the basis for understanding the formation of the inner-region vortex and the subsequent interactions between the outer-region (free-shear-layer region) and inner-region (boundary-layer region) vortical structures. Results show that under the influence of the free-shear-layer vortex, the local boundary layer becomes detached from the surface and inviscidly unstable, and a vortex is formed in the inner region. Once this vortex has formed, the free-shear-layer vortex and the inner-region vortex form a vortex couple and convect downstream. The mutual interactions between these inner- and outer-region vortical structures dominate the transition process. Farther downstream, the emergence of the three-dimensional structure in the free shear layer initiates complete breakdown of the flow. Received: 8 November 1995/Accepted: 6 November 1996     

Performance of a three-component vorticity probe in a turbulent far-wake

  A new four X-wire vorticity probe has been developed to measure all three components of the vorticity fluctuation vector simultaneously. The performance of this probe is tested in a turbulent far-wake. The measured Reynolds stresses agree with those obtained previously from simpler hot wire configurations. The variances of the lateral vorticity components agree within ±15% with those measured with a one-component vorticity probe. The variances of the streamwise vorticity component are also in reasonable agreement with those inferred from two X-wires. At high wavenumbers, the measured vorticity spectra agree with those obtained by direct numerical simulation (DNS) in the central region of a turbulent channel flow. The comparison of measured high-order moments of vorticity on the wake centerline with local isotropy also suggests the probe performs satisfactorily. Received: 31 December 1997/Accepted: 6 January 1999     

Numerical simulation of laminar flow past a circular cylinder with slip conditions

The no‐slip condition is an assumption that cannot be derived from first principles and a growing number of literatures replace the no‐slip condition with partial‐slip condition, or Navier‐slip condition. In this study, the influence of partial‐slip boundary conditions on the laminar flow properties past a circular cylinder was examined. Shallow‐water equations are solved by using the finite element method accommodating SU/PG scheme. Four Reynolds numbers (20, 40, 80, and 100) and six slip lengths were considered in the numerical simulation to investigate the effects of slip length and Reynolds number on characteristic parameters such as wall vorticity, drag coefficient, separation angle, wake length, velocity distributions on and behind the cylinder, lift coefficient, and Strouhal number. The simulation results revealed that as the slip length increases, the drag coefficient decreases since the frictional component of drag is reduced, and the shear layer developed along the cylinder surface tends to push the separation point away toward the rear stagnation point so that it has larger separation angle than that of the no‐slip condition. The length of the wake bubble zone was shortened by the combined effects of the reduced wall vorticity and wall shear stress which caused a shift of the reattachment point closer to the cylinder. The frequency of the asymmetrical vortex formation with partial slip velocity was increased due to the intrinsic inertial effect of the Navier‐slip condition. Copyright © 2011 John Wiley & Sons, Ltd.     

Effect of perforation on flow past a conic cylinder at $${\varvec{Re}}~=~100$$: wavy vortex and sign laws

In order to find the intrinsic physical mechanism of the original Kármán vortex wavily distorted across the span due to the introduction of three-dimensional (3-D) geometric disturbances, a flow past a peak-perforated conic shroud is numerically simulated at a Reynolds number of 100. Based on previous work by Meiburg and Lasheras (1988), the streamwise and vertical interactions with spanwise vortices are introduced and analyzed. Then vortex-shedding patterns in the near wake for different flow regimes are reinspected and illustrated from the view of these two interactions. Generally, in regime I, spanwise vortices are a little distorted due to the weak interaction. Then in regime II, spanwise vortices, even though curved obviously, are still shed synchronously with moderate streamwise and vertical interactions. But in regime III, violently wavy spanwise vortices in some vortex-shedding patterns, typically an \(\Omega \)-type vortex, are mainly attributed to the strong vertical interactions, while other cases, such as multiple vortex-shedding patterns in sub-regime III-D, are resulted from complex streamwise and vertical interactions. A special phenomenon, spacial distribution of streamwise and vertical components of vorticity with specific signs in the near wake, is analyzed based on two models of streamwise and vertical vortices in explaining physical reasons of top and bottom shear layers wavily varied across the span. Then these two models and above two interactions are unified. Finally two sign laws are summarized: the first sign law for streamwise and vertical components of vorticity is positive in the upper shear layer, but negative in the lower shear layer, while the second sign law for three vorticity components is always negative in the wake.     

Population,characteristics and kinematics of vortices in a confined rectangular jet with a co-flow

Vortex behavior and characteristics in a confined rectangular jet with a co-flow were examined using vortex swirling strength as a defining characteristic. On the left side of the jet, the positively (counterclockwise) rotating vortices are dominant, while negatively rotating vortices are dominant on the right side of the jet. The characteristics of vortices, such as population density, average size and strength, and deviation velocity, were calculated and analyzed in both the cross-stream direction and the streamwise direction. In the near-field of the jet, the population density, average size and strength of the dominant direction vortices show high values on both sides of the center stream with a small number of counter-rotating vortices produced in the small wake regions close to jet outlet. As the flow develops, the wake regions disappear, these count-rotating vortices also disappear, and the population of the dominant direction vortices increase and spread in the jet. The mean size and strength of the vortices decrease monotonically with streamwise coordinate. The signs of vortex deviation velocity indicate the vortices transfer low momentum to high-velocity region and high momentum to the low velocity region. The developing trends of these characteristics were also identified by tracing vortices using time-resolved particle image velocimetry data. Both the mean tracked vortex strength and size decrease with increasing downstream distance overall. At the locations of the left peak of turbulent kinetic energy, the two-point spatial cross-correlation of swirling strength with velocity fluctuation and concentration fluctuation were calculated. All the correlation fields contain one positively correlated region and one negatively correlated region although the orientations of the correlation fields varied, due to the flow transitioning from wake, to jet, to channel flow. Finally, linear stochastic estimation was used to calculate conditional structures. The large-scale structures in the velocity field revealed by linear stochastic estimation are spindle-shaped with a titling stream-wise major axis.