Mean Streamwise Vorticity Research Articles

Effects of varying Reynolds number, blowing ratio, and internal geometry on trailing edge cutback film cooling

Three-dimensional mean velocity and concentration fields have been measured for a water flow in a pressure side cutback trailing edge film cooling geometry consisting of rectangular film cooling slots separated by tapered lands. Three-component mean velocities were measured with conventional magnetic resonance velocimetry, while time-averaged concentration distributions were measured with a magnetic resonance concentration technique for flow at two Reynolds numbers (Re) differing by a factor of 2, three blowing ratios, and with and without an internal pin fin array in the coolant feed channel. The results show that the flows are essentially independent of Re for the regime tested in terms of the film cooling surface effectiveness, normalized velocity profiles, and normalized mean streamwise vorticity. Blowing ratio changes had a larger effect, with higher blowing ratios resulting in surface effectiveness improvements at downstream locations. The addition of a pin fin array within the slot feed channel made the spanwise distribution of coolant at the surface more uniform. Results are compared with transonic experiments in air at realistic density ratios described by Holloway et al. (2002a).

Alternating half-loop shedding in the turbulent wake of a finite surface-mounted square cylinder with a thin boundary layer

The configuration and energetics of the large-scale vortex structure are presented for quasi-periodic shedding in the turbulent wake of a finite (h/d = 4) square-cross-section surface-mounted cylinder protruding from a thin boundary layer (δ/h = 0.18). The three-dimensional large-scale structure is educed from phase averaged x-y and x-z planar data measured with particle image velocimetry (PIV). Simultaneous measurements of the surface pressure difference on either side of the obstacle were used to phase-align the PIV planar measurements. The topology of the educed structures resembles alternating half-loops interconnecting close to the base plate. The time averaging of this unsteady structure gives rise to mean streamwise vortices akin to those presented in the literature for similar geometries. This topological analysis offers a contrasting interpretation of the mean streamwise vorticity, which has, otherwise, been presumed to originate from structures generated at the leading edge of the free-end. The dynamical significance of the resolved large scale structures and unresolved fluctuating kinetic energy in the wake is presented, either part being responsible for roughly half the mean kinetic energy. A discussion of turbulence production in light of the base flow that supplies it with energy is put forward.

Reynolds number dependence of mean flow structure in square duct turbulence

We have performed direct numerical simulations of turbulent flows in a square duct considering a range of Reynolds numbers spanning from a marginal state up to fully developed turbulent states at low Reynolds numbers. The main motivation stems from the relatively poor knowledge about the basic physical mechanisms that are responsible for one of the most outstanding features of this class of turbulent flows: Prandtl's secondary motion of the second kind. In particular, the focus is upon the role of flow structures in its generation and characterization when increasing the Reynolds number. We present a two-fold scenario. On the one hand, buffer layer structures determine the distribution of mean streamwise vorticity. On the other hand, the shape and the quantitative character of the mean secondary flow, defined through the mean cross-stream function, are influenced by motions taking place at larger scales. It is shown that high velocity streaks are preferentially located in the corner region (e.g. less than 50 wall units apart from a sidewall), flanked by low velocity ones. These locations are determined by the positioning of quasi-streamwise vortices with a preferential sign of rotation in agreement with the above described velocity streaks' positions. This preferential arrangement of the classical buffer layer structures determines the pattern of the mean streamwise vorticity that approaches the corners with increasing Reynolds number. On the other hand, the centre of the mean secondary flow, defined as the position of the extrema of the mean cross-stream function (computed using the mean streamwise vorticity), remains at a constant location departing from the mean streamwise vorticity field for larger Reynolds numbers, i.e. it scales in outer units. This paper also presents a detailed validation of the numerical technique including a comparison of the numerical results with data obtained from a companion experiment.

Computation of turbulent flow and secondary motions in a square duct using a forced generalized lattice Boltzmann equation

Turbulent flow in a straight square duct driven by a pressure gradient exhibits remarkable flow structures such as the presence of mean streamwise vorticity or secondary flows. These secondary circulations take the form of two counter-rotating vortices near each corner of the duct. Even though their magnitudes are small compared with primary streamwise motions, they have a significant influence on flow and scalar transport and are challenging to accurately predict using computational approaches. In this paper, we employ a recently developed formulation of the generalized lattice Boltzmann equation (GLBE) with forcing term to perform large eddy simulation of fully developed turbulent flow in a square duct at a shear Reynolds number based on duct width equal to 300. Subgrid scale effects are represented by the Smagorinsky eddy viscosity model, which is modified by the van Driest damping function in the near-wall regions, in this GLBE approach, which is based on multiple relaxation times. It was found that the GLBE is able to correctly reproduce the existence of mean secondary motions and the computed detailed structure of first- and second-order statistics of main and secondary motions are in good agreement with prior direct numerical simulations based on the solution of the Navier-Stokes equations and experimental data.

Computation of a three-dimensional turbulent flow in a square duct using a cubic eddy-viscosity model

The aim of this note is an evaluation of a cubic eddy-viscosity turbulent model. The study is carried out in square duct. This configuration presents a secondary flow and a significant anisotropy between the Reynolds stress components. In order to handle wall-proximity effects in the near-wall region, damping functions are introduced. The comparison of the modified model results with DNS and LES simulations shows good agreements. In particular, the mean secondary velocity and the mean streamwise vorticity are well predicted. To cite this article: H. Gnanga et al., C. R. Mecanique 337 (2009).

Experimental study of the near field and transition region of a free jet issuing from a sharp-edged elliptic orifice plate

The mixing characteristics in the near field and transition region, the region of interest in most jet mixing applications, of an isothermal, incompressible, free jet of air issuing from a sharp-edged elliptic orifice plate of aspect ratio 2 into still air surroundings have been studied experimentally using hot-wire anemometry and a pitot-static tube. For comparison, some experiments were performed in round jets issuing from a sharp-edged orifice plate and from a contoured nozzle. All the test jets were unforced and the Reynolds number, based on the equivalent diameter of the sharp-edged elliptic orifice plate which was the same as the diameter of the sharp-edged round orifice plate or the contoured round nozzle, was 1.88 × 10 5 . The three components of the mean velocity vector, time-averaged and phase-averaged fluctuating velocity data, autocorrelation coefficients and one-dimensional spectra of the fluctuating velocities and the mean static pressure were measured. The mean streamwise vorticity, mass entrainment rates and the jet half-velocity widths have been obtained from the measured data. The results show that mixing in an elliptic jet issuing from a sharp-edged orifice plate is higher than in round jets and in elliptic jets issuing from contoured nozzles. The near field and transition region of the elliptic jet were deduced to be dominated by the axisymmetric instability mode which triggers the generation of symmetric shear layer structures. The results also show the presence of coherent structures in the near field and transition region of the jet and the effect of these coherent structures on momentum transport in the jet.

Near Field Measurements in an Equilateral Triangular Turbulent Freejet

The near-field mean flow and turbulence characteristics of a turbulent jet of air issuing from a sharp-edged equilateral triangular orifice into still air surroundings have been examined experimentally using hot-wire anemometry and a pitot-static tube. For comparison, some measurements were made in a round free air jet, also issuing from sharp-edged orifice. The Reynolds number, based on the equivalent diameter, was 1.84 x 10 5 in each jet. The three components of the mean velocity vector, the Reynolds normal and primary shear stresses, the distribution of the autocorrelation coefficients and the one-dimensional energy spectra of the fluctuating velocity signals, and the mean static pressure were measured. The mean streamwise vorticity, the half-velocity widths, mass entrainment into the jet, and the local shear in the mean streamwise velocity were obtained from the measured data

Measurements in the near flow field of an isosceles triangular turbulent free jet

The near field mean flow and turbulence characteristics of a turbulent jet of air issuing from a sharp-edged isosceles triangular orifice into still air surroundings have been examined experimentally using hot-wire anemometry and a pitot-static tube. For comparison, some measurements were made in an equilateral triangular free jet and in a round free air jet, both of which also issued from sharp-edged orifices. The Reynolds number, based on the orifice equivalent diameter, was 1.84×105 in each jet. The three components of the mean velocity vector, the Reynolds normal and primary shear stresses, the one-dimensional energy spectra of the streamwise fluctuating velocity signals and the mean static pressure were measured. The mean streamwise vorticity, the half-velocity widths, the turbulence kinetic energy and the local shear in the mean streamwise velocity were obtained from the measured data. It was found that near field mixing in the equilateral triangular jet is faster than in the isosceles triangular and round jets. The mean streamwise vorticity field was found to be dominated by counter-rotating pairs of vortices, which influenced mixing and entrainment in the isosceles triangular jet. The one-dimensional energy spectra results indicated the presence of coherent structures in the near field of all three jets and that the equilateral triangular jet was more energetic than the isosceles triangular and round jets.

Large eddy simulation (2D) of spatially developing mixing layer using vortex-in-cell for flow field and filtered probability density function for scalar field

A large eddy simulation based on filtered vorticity transport equation has been coupled with filtered probability density function transport equation for scalar field, to predict the velocity and passive scalar fields. The filtered vorticity transport has been formulated using diffusion-velocity method and then solved using the vortex method. The methodology has been tested on a spatially growing mixing layer using the two-dimensional vortex-in-cell method in conjunction with both Smagorinsky and dynamic eddy viscosity subgrid scale models for an anisotropic flow. The transport equation for filtered probability density function is solved using the Lagrangian Monte-Carlo method. The unresolved subgrid scale convective term in filtered density function transport is modelled using the gradient diffusion model. The unresolved subgrid scale mixing term is modelled using the modified Curl model. The effects of subgrid scale models on the vorticity contours, mean streamwise velocity profiles, root-mean-square velocity and vorticity fluctuations profiles and negative cross-stream correlations are discussed. Also the characteristics of the passive scalar, i.e. mean concentration profiles, root-mean-square concentration fluctuations profiles and filtered probability density function are presented and compared with previous experimental and numerical works. The sensitivity of the results to the Schmidt number, constant in mixing frequency and inflow boundary conditions are discussed. Copyright © 2005 John Wiley & Sons, Ltd.

Large eddy simulation (2D) using diffusion–velocity method and vortex‐in‐cell

AbstractA large eddy Simulation based on the diffusion‐velocity method and the discrete vortex method is presented. The vorticity‐based and eddy viscosity type subgrid scale model simulating the enstrophy transfer between the large and small scale appears as a convective term in the diffusion‐velocity formulation. The methodology has been tested on a spatially growing mixing layer using the two‐dimensional vortex‐in‐cell method and the Smagorinsky subgrid scale model. The effects on the vorticity contours, momemtum thickness, mean streamwise velocity profiles, root‐mean‐square velocity and vorticity fluctuations and negative cross‐stream correlation are discussed. Comparison is made with experiment and numerical work where diffusion is simulated using random walk. Copyright © 2004 John Wiley & Sons, Ltd.

Prediction and investigation of the turbulent flow over a rotating disk

Large-eddy simulation (LES) has been used to predict the statistically three-dimensional turbulent boundary layer (3DTBL) over a rotating disk. LES predictions for six parameter cases were compared to the experimental measurements of Littell & Eaton (1994), obtained at a momentum thickness Reynolds number of 2660. A signal-decomposition scheme was developed by modifying the method of Spalart (1988) to prescribe time-dependent boundary conditions along the radial direction, entrainment towards the disk surface was prescribed by satisfying global mass conservation. Predictions of the mean velocities and r.m.s. fluctuations are in good agreement with data, with the largest discrepancy occurring in the prediction of the wall-normal intensities. The primary and two secondary shear stresses are also in good agreement with the measurements and one-dimensional energy spectra of the velocity fluctuations agree well with established laws, i.e. a −1 slope in the buffer region and −5/3 slope near the edge of the boundary layer.Conditionally averaged velocities provide new evidence in support of the structural model of Littell & Eaton (1994) concerning the interaction of mean-flow three-dimensionality and shear-stress producing structures. Inside the buffer region under strong ejections, the conditionally averaged crossflow (radial) velocity is larger than the unconditioned mean, and the profile conditioned on strong sweeps is smaller than the mean. This is consistent with the notion that streamwise vortices having the same sign as the mean streamwise vorticity, and beneath the peak crossflow location, are mostly responsible for strong sweep events; streamwise vortices with opposite sign as the mean streamwise vorticity promote strong ejections. Comparison of two-point spatial correlations with previous measurements in two-dimensional turbulent boundary layers (2DTBLs) indicates interesting structural similarities, e.g. the correlation of wall pressure and surface-normal velocity fluctuations is an odd function of streamwise separation, being positive downstream and negative upstream. These similarities offer quantitative indirect support to the hypothesis advanced by Littell & Eaton (1994) and Johnston & Flack (1996) that structural models describing 2DTBLs may be employed as a baseline in (equilibrium) 3DTBL structural studies.

Structure of a Stronger Wall Jet Managed by a Pair of Streamwise Vortex. Behavior of Streamwise Vortex and Distortion of Mean Velocity Field.

Interaction process between a turbulent plane wall jet and a pair of streamwise vortex was investigated experimentally. Two kinds of vortex pair, i.e., common-flow up and common-flow down generated with half-delta wings mounted on the wall, were introduced into a self-preserving stronger wall jet. Measurements on the mean velocity and mean streamwise vorticity were made to examine deformation and relaxation process of the mean flow field as well as evolution of the streamwise vortex. As a strategy in the present experiment, the vortex center goes into the outer layer in the case of common-flow up and stays in the inner layer in the case of common-flow down. Consequently, streamwise vortex pair interacts strongly with the large-scale eddy governing the entire wall jet. The following remarks were recognized for the common-flow up in comparison with results of both cases ; 1) growth of vortex radius and decay of streamwise vorticity are greater, 2) recovery of the mean velocity field is much slower. The evaluation of streamwise momentum flux confirms that it is possible to manage turbulent wall jet with streamwise vortex.

Turbulent transport in the core of a trailing half-delta-wing vortex

The development of a turbulent streamwise vortex core in the wake of a half delta wing has been examined using high-resolution DPIV. The objective of this work was to gain understanding of the transport processes at work a short distance downstream of the wing trailing edge as the wake vortex developed. Experiments were conducted in the Rutgers Free Surface Water Tunnel using an in-house DPIV system. A turbulent streamwise vortex was generated by a half delta wing, with 44 cm chord length and 60° sweep angle, mounted at 30° angle of attack. Reynolds number based on chord length was 65 000. Laser sheets oriented perpendicular to the flow direction were positioned 1, 3.5, and 7 chord lengths downstream of the wing trailing edge. Instantaneous vortex centres were identified in order to track vortex meandering as well as for better quantification of turbulence levels in the vortex core. Mean and fluctuating turbulence terms in the mean streamwise vorticity transport equation along with turbulent kinetic energy dissipation and production were evaluated relative to an inertial reference frame as well as relative to a vortex-centred frame. The results of this analysis highlight the importance of this near-wake region to the downstream evolution of the trailing vortices. There is a high degree of dissipation as well as streamwise vorticity convection in the very near wake which decreases rapidly with increasing distance from the trailing edge.

Effects of velocity ratio on mixing layer three-dimensionality

Abstract Three-dimensionality in transitioning mixing layers, in the form of streamwise vortical structures, is now well established and understood. In the present investigation, the effects of velocity ratio, or more precisely of velocity difference across the layer, on the near-field generation and development of three-dimensionality in two-stream mixing layers have been investigated for the first time. Detailed time-averaged velocity measurements were obtained using a single rotatable cross-wire probe on fine cross-plane grids at four streamwise locations in the near-field region. The effects of five velocity ratios, ranging from r =0.5 to 0.9, were investigated by keeping the velocity of one stream constant while varying that of the other. The results indicate that the mixing layer three-dimensionality is strongest for the mixing layer with the lowest velocity ratio. The peak mean streamwise vorticity levels decrease with increasing velocity ratio at all the streamwise locations investigated. However, the rate of decrease is highest at the most upstream station and it decreases with increasing downstream distance. The mean streamwise vorticity contours at the first station show that their distribution is quite similar at the different velocity ratios, implying that the generating mechanism and initial disturbance fields remain unchanged with velocity ratio. However, it is conceivable that the amount of stretching in the braid regions due to the spanwise vortical structures is affected by velocity ratio. As the velocity ratio decreases (and the velocity difference across the layer increases), stronger spanwise rollers are generated which increase the amount of stretching in the braid regions and hence the streamwise vorticity is amplified. The splitter plate wake has a lasting effect on the three-dimensional structure of the mixing layers at the higher velocity ratios. The presence and effects of the wake are clearly seen in the mean velocity, mean streamwise vorticity and Reynolds stress contours.

Swirling flows in circular-to-rectangular transition ducts

Swirling flows in three circular-to-rectangular transition ducts, each of them with an aspect ratio of 2.0 at the rectangular exit, have been studied experimentally. The swirling flows were produced by swirlers whose vane angles were at 5°, 10° and 20° inclinded to the incoming flow, respectively. Flow visualization experiments were made at selected cross-sectional planes in the transition ducts. Pressure and velocity measurements were obtained on the contoured duct walls and at the rectangular exit planes, respectively. The results show that the swirling flow pattern evolves into a skewed structure at the exit plane which, in connection with the wall pressure distributions, is asymmetric with respect to the centerline of either the top and bottom walls or the side walls. Moreover, an analysis based on the mean streamwise vorticity equation with the velocity data obtained immediately downstream of the rectangular exit plane indicates that the cross-stream Reynolds stress plays an important role in transporting the streamwise vorticity of the swirling flow into the surrounding fluid.

Three-dimensional structure of straight and curved plane wakes

The formation and evolution of the three-dimensional structure of straight and mildly curved ($b/\bar{R} < 2\%$) flat plate wakes at relatively high Reynolds numbers (Reb = 28 000) have been studied through detailed measurements of the mean and fluctuating velocities. In both cases, the role of initial conditions was examined by generating wakes from untripped (laminar) and tripped (turbulent) initial boundary layers. The curved wake was affected by the angular momentum instability such that the inside half of the wake was unstable, whereas the outside half was stable. In both the straight and curved untripped wakes, large spanwise variations, in the form of ‘pinches’ and ‘crests’, were observed in the contours of mean velocity and Reynolds stresses. Well-organized, ‘spatially stationary’ streamwise vorticity was generated in the near-field region in the form of quadrupoles, to which the spanwise variations in the velocity contours were attributed. The presence of mean streamwise vorticity had a significant effect on the wake growth and defect decay rates, mainly by providing additional entrainment. In the straight wake, the mean streamwise vorticity decayed on both sides of the wake such that it had decayed completely by the far-field region. However, in the curved case, the mean streamwise vorticity on the unstable side decayed at a rate significantly lower than that on the stable side. Despite the decay of mean streamwise vorticity, the spanwise variations persisted into the far wake in both cases. The effects of curvature were also apparent in the Reynolds stress results which showed that the levels on the unstable side were increased significantly compared to those on the stable side, with the effect much stronger in the initially laminar wake. With the initial boundary layers tripped, spatially stationary streamwise vortex structures were not observed in either the straight or curved wakes and the velocity contours appeared nominally two-dimensional. This result further confirms the strong dependency of the three-dimensional structure of plane wakes on initial conditions.

Effects of streamwise vorticity injection on a plane turbulent wake

Past flow visualization investigations of plane wakes originating from laminar initial boundary layers have shown the presence of streamwise vortical structures riding among the spanwise (von Karman) vortices. Quantitative measurements of the mean streamwise vorticity were recently obtained which shed more light on their formation and subsequent evolution. Measurements made in the same wake with both initial boundary layers turbulent, however, showed that spatially stationary streamwise structures did not exist in this case, thus resulting in a distinctly different mean three-dimensional structure and streamwise evolution. In the present study, the effects of injecting streamwise vorticity on the structure and development of a wake originating from turbulent boundary layers are investigated. A corrugated extension attached to the splitter plate trailing edge produced a relatively strong array of counter-rotating pairs of streamwise vorticity which were injected into the turbulent wake. This resulted in large spanwise variations in the wake mean properties and Reynolds stress distributions. Although the mean streamwise vorticity decreased with downstream distance, the spanwise variations were found to persist into the far-field region (X/ 0 > 500) of the wake. In the near-field region (X/ 0 < 500), the wake growth was increased, and the velocity defect was reduced, both because of increased entrainment due to the injected vorticity. However, in the far-field region, the forced wake growth rate and peak Reynolds stresses were reduced significantly with respect to the undisturbed wake. This result is attributed to the effect of the relatively strong streamwise vorticity in making the spanwise structures more three dimensional and, hence, less efficient at entraining surrounding fluid.

Curved two-stream turbulent mixing layers: three-dimensional structure and streamwise evolution

The three-dimensional structure and streamwise evolution of two-stream mixing layers at high Reynolds numbers (Reδ ∼ 2.7 × 104) were studied experimentally to determine the effects of mild streamwise curvature ($\delta/ \overline{R}$ &lt; 3%). Mixing layers with velocity ratios of 0.6 and both laminar and turbulent initial boundary layers, were subjected to stabilizing and destabilizing longitudinal curvature (in the Taylor–Görtler sense). The mixing layer is affected by the angular momentum instability when the low-speed stream is on the outside of the curve, and it is stabilized when the streams are reversed so that the high-speed stream is on the outside. In both stable and unstable mixing layers, originating from laminar boundary layers, well-organized spatially stationary streamwise vorticity was generated, which produced significant spanwise variations in the mean velocity and Reynolds stress distributions. These vortical structures appear to result from the amplification of small incoming disturbances (as in the straight mixing layer), rather than through the Taylor–Görtler instability. Although the mean streamwise vorticity decayed with downstream distance in both cases, the rate of decay for the unstable case was lower. With the initial boundary layers on the splitter plate turbulent, spatially stationary streamwise vorticity was not generated in either the stable or unstable mixing layer. Linear growth was achieved for both initial conditions, but the rate of growth for the unstable case was higher than that of the stable case. Correspondingly, the far-field spanwise-averaged peak Reynolds stresses were significantly higher for the destabilized cases than for the stabilized cases, which exhibited levels comparable to, or slightly lower than, those for the straight case. A part of the Reynolds stress increase in the unstable layer is attributed to ‘extra’ production through terms in the transport equations which are activated by the angular momentum instability. Velocity spectra also indicated significant differences in the turbulence structure of the two cases, both in the near- and far-field regions.

Development of a large-aspect-ratio rectangular turbulent free jet

This paper reports the results of detailed mean flow and turbulence measurements made with hot-wire anemometry in the flowfield of a turbulent free jet of air issuing from a sharp-edged rectangular slot of aspect ratio 20 into still air surroundings. All three components of the mean velocity vector, the three Reynolds normal stresses and the two Reynolds primary shear stresses were measured. The mean streamwise vorticity and the turbulence kinetic energy have been calculated from the relevant measured data. It was found that the cross section of the jet, in the near flowfield, is dominated by counter-rotating streamwise vortices that facilitate rapid nearfield mixing. Rapid mixing is also evidenced by a short potential core length and high values of the turbulence kinetic energy and the Reynolds primary shear stresses compared with those found in an axisymmetric jet at the corresponding streamwise locations. In addition, mean streamwise velocity off-center peaks, which may be the result of the self-induction of the counter-rotating streamwise vortices, were found in the near flowfield, and the jet was found to spread monotonically in the central plane of the slot minor axis and to contract initially in the central plane of the slot major axis.

Effects of imposed spanwise perturbations on plane mixing-layer structure

The origin and evolution of spatially stationary streamwise vortical structures in plane mixing layers with laminar initial boundary layers were recently examined quantitatively (Bell &amp; Mehta 1992). When both initial boundary layers were made turbulent, such spatially-stationary streamwise structures were not measured which is indicative of the high sensitivity of these structures to initial conditions. In the present study, the effects of four different types of spanwise perturbations at the origin of the mixing layer were investigated. The wavelengths of the imposed perturbations were chosen to be comparable to the initial Kelvin-Helmholtz wavelength. For the first two perturbations, the boundary layers were otherwise left undisturbed. A serration on the splitter plate trailing edge was found to have a relatively small effect on the formation and development of the streamwise structures. The introduction of cylindrical pegs in the high-speed side boundary layer not only generated a regular array of vortex pairs, but also affected the mixing-layer growth rate and turbulence properties in the far-field region. For the other two perturbations, the initial boundary layers were tripped on the splitter plate. An array of vortex generators mounted in the high-speed boundary layer and a corrugated surface attached to the splitter plate trailing edge had essentially the same effects. Both imposed a regular array of relatively strong streamwise vortices in counter-rotating pairs upon the mixing layer. This resulted in large spanwise distortions of the mixing layer mean properties and Reynolds stresses. While the vorticity injection increased the growth rate in the near-field region as expected, the far-field growth rate was reduced by a factor of about two, together with the peak Reynolds stress levels. This result is attributed to the effect of the relatively strong streamwise vorticity in making the spanwise structures more three-dimensional and hence reducing entrainment during the pairing process. The imposed streamwise vorticity did not follow the pattern of increasing spanwise spacing seen in the ‘naturally occurring’ streamwise vorticity. The mean streamwise vorticity decayed with increasing streamwise distance in all cases, albeit at different rates.