12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19–22, 2022

MULTI-STRUCTURE TURBULENCE IN A BOUNDARY LAYER WITH A
UNIFORMLY SHEARED FREE STREAM

Curtis Livingston
Department of Mechanical Engineering
University of Ottawa
Ottawa, ON K1N 6N5, Canada
curtis.livingston25@gmail.com

Stavros Tavoularis
Department of Mechanical Engineering
University of Ottawa
Ottawa, ON K1N 6N5, Canada
stavros.tavoularis@uottawa.ca

ABSTRACTgeneration mechanisms; they have recently been referred to as
multi-structure turbulence (Nedić & Tavoularis, 2018).
TBL are the most intensely researched turbulent flow. In
the majority of laboratory studies, the TBL was bounded bya nominally uniform, laminar free stream, in which case the
TBL would have a canonical structure. In a few studies, TBL
were interacting with a free stream that had some weak, decaying, nearly isotropic turbulence, generated by an upstream grid(Charnay et al., 1971; Evans, 1974; Meier & Kreplin, 1980;
Hoffmann et al., 1989). Liangwei & Hoffmann (1988) investigated TBL in free streams with decaying, anisotropic turbulence, generated by bars of different diameters, and concluded
that both anisotropic and isotropic free stream turbulence hadcomparable effects on the boundary layer thickness and theskin friction. More recently, Sakai et al. (2013) examined a
TBL interacting with the wake of a cylinder in the free stream
and found that the inner layer mean flow velocity profile was
not altered by the wake, but the intensity of the turbulence decreased. The TBL studied by all these authors would havea multi-structure region, but the deviation from the canonicalstructure would have vanished as free-stream turbulence decayed. In contrast to such flows, turbulence in USF not only
does not decay downstream, but actually becomes intensified,as the result of an active turbulence production mechanism.
Although turbulence is generated by the mean shear inboth TBL and USF and there are structural similarities between outer TBL and USF (e.g., comparable Reynolds stressanisotropy levels), there are also some significant differences:a) in TBL, mean shear is produced by friction with the wall,
whereas, in USF, mean shear is imposed in the absence of awall; b) in TBL, the wall also imposes a kinematic constraint,
which is absent in USF; c) TBL are separated from the freestream by a thin interface, whereas USF are ideally unbounded
in all directions; d) the turbulence in TBL is inhomogeneous,
whereas, in USF, turbulence is ideally homogeneous on planes
normal to the flow direction; and e) in both TBL and USF,
the dominant coherent structures are horseshoe- (or hairpin)shaped vortices, grouped in packets (Adrian, 2007; Vanderwel & Tavoularis, 2011), but with the difference that the orientation of these structures is constrained by the wall in TBL

A turbulent boundary layer (TBL), generated in a watertunnel, extended to an anisotropic turbulent “free stream”, consisting of a uniformly sheared flow (USF) with a mean shearthat was in the opposite direction to that in the TBL. Measurements of the fluctuating velocity were taken with the useof hot-film anemometry, laser Doppler velocimetry and particle image velocimetry. On either side of the TBL edge, defined as the location of maximum velocity, the turbulence relaxed to its canonical structures in TBL and USF, respectively,but, in the vicinity of the edge, there was a multi-structure region (MSR), where the turbulence structure was strongly noncanonical. The dissipation parameter in the MSR was larger
than in the TBL and USF and inversely proportional to the local turbulence Reynolds number. The entire flow contained
horseshoe-shaped coherent structures, the properties of which,however, were different within the TBL, the MSR and the USF.

INTRODUCTION
Research on turbulence has, to a great extent, focussed
on canonical flows, which are geometrically simple and reproducible in the laboratory. These include, among others, gridgenerated turbulence (GT), uniformly sheared flows (USF) andtwo dimensional turbulent boundary layers (TBL). Canonicalflows themselves are a very small subset of turbulent flows,
but they retain some universal features of turbulence. The vast
majority of turbulent flows in natural and industrial systems
are non-canonical. Because of the diversity and possible complexity of strongly non-canonical flows, information collected
for one such flow is rather unlikely to apply to many others.
For this reason, a meaningful strategy for expanding our understanding of turbulence seems to be to examine flows withspecially designed, mildly non-canonical features. One such
example would be a canonical flow that is distorted by an external device or mechanism, which may eventually fade awayor be removed. Another example would be the interaction region between two canonical flows. Such flows, either in their
entirety or in limited regions, would have non-canonical structures, which are the results of more than one distinct turbulence112th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19–22, 2022
but unconstrained in USF. In view of these considerations, theinteraction region between a TBL and a uniformly sheared,
highly turbulent free stream evolving in parallel seems to bea promising environment for the study of multi-structure turbulence, which is the product of two distinct, persisting andcanonical turbulence generation mechanisms. An important
point of interest would be to examine how the coherent structures that are generated in a TBL interact with those generated in a USF in the multi-structure region between the twoflows. The only relevant previous study is the one by KislichLemyre (2003), which investigated how the large-scale structure of USF was distorted by a solid wall, which was stationaryor moving in the same or opposite direction to the flow. When
the wall moved faster than the flow, a region of low or zero
shear was detected between the wall boundary layer and thefree stream USF. Distinct coherent structures were observedon the two sides of this region, which is a region of multistructure turbulence. Unfortunately, the documentation of thisstudy has been mostly qualitative.
Turbulence theories and models require the use of a lengthscale and a time scale (or, equivalently, a velocity scale), whichcharacterise the dominant motions and by which one can scale
the various statistical properties that appear in the governing
equations. An obvious choice for a velocity scale is the squareroot of the turbulent kinetic energy per unit mass k. A suitable internal length scale is the integral length scale L, whichcharacterises the energy containing motions. The use of theintegral length scale L in the analysis is problematic, because
the definition of this scale requires consideration of spatial
variations of turbulent motions, namely, information which is
not contained in the single-point differential equations that describe local turbulent motions. Therefore, there is a need to define a length scale in terms of local variables, namely variables
that are contained in the single-point turbulence equations. Besides k and other variables, these equations contain the turbulent kinetic energy dissipation rate per unit mass ε. Althoughmechanical kinetic energy is dissipated to heat by very small“eddies”, there is consensus that the turbulent kinetic energy
dissipation rate per unit mass ε is set by the energy containing
motions. These motions set the rate by which kinetic energythat is produced at large scales is fed successively to smaller
eddies, following the energy cascade process, until it reaches
the smallest eddies, where it is dissipated. It follows that asurrogate length scale L of the energy containing eddies canbe defined by dimensional analysis, namely, by multiplying
appropriate powers of k and ε. This provides the result
L ∝ k3/2 /ε .

Figure 1.

turbulence properties evolve in a commensurate manner. Nevertheless, there is also a growing body of evidence contradicting this hypothesis in both upstream regions of canonical turbulence and in multi-structure turbulence (Vassilicos, 2015;
Nedić et al., 2017; Nedić & Tavoularis, 2018). Testing thishypothesis in the multi-structure region between a TBL anda USF and understanding the relationship among these scales
and other flow properties would be of value in explaining thelimitations and failures of current turbulence models and indeveloping improved ones.
The general goal of this research is to enlarge the available documentation on multi-structure turbulence, particularly
one that pertains to TBL. The specific goal is to document
experimentally the turbulence in a TBL that is bounded bya highly turbulent, uniformly sheared free stream that has amean shear opposite in direction to the one inside the TBL.
Extensive measurements in such flows were obtained using
hot-film anemometry, laser Doppler velocimetry and particle image velocimetry. Measurements include transverse profiles of the mean velocity, the Reynolds stresses, the integral
length scales, and the Taylor and Kolmogorov microscales
from which it was possible to calculate the local mean shear,
the turbulence anisotropies, the turbulent kinetic energy andits dissipation rate, the turbulence Reynolds number Reλ andthe dissipation parameter. Of primary interest in this work
is to characterise the behaviour of the dissipation parameterwithin the multi-structure region and its relationship to Reλand to compare the statistical properties of coherent structures
in USF, the TBL and the multi-structure region.

APPARATUS AND MEASUREMENT PROCEDURES
The experiments were performed in a recirculating watertunnel, having an enclosed test section with a width of 560
mm, a height h = 442 mm and a length of roughly 4.1 m. USF
was created by a shear generator, which was a perforated platewith linearly varying solidity, followed by a flow separator,
which was a set or parallel plates and acted as a flow straightener, as well as imposing an initial integral length scale uniformity. The examined TBL evolved along the upper wall. A
sketch of the experimental setup is shown in Fig. 1 and details
have been presented by Livingston (2020).
Vertical profiles of the mean velocity, the Reynolds
stresses and the integral length scale were obtained with a
two-component, frequency-shifted, laser Doppler velocimeter(LDV - Dantec Dynamics, Skovlunde, Denmark). The lens
used with the laser head had a focal length of 243 mm, which
produced a measurement volume in the water with approximate dimensions 0.1 × 0.1 × 2.0 mm. The flow was seededwith fused, borosilicate, hollow, glass beads (Potters Industries
LLC, Valley Forge, USA), with a density of 1,100 ± 50 kg/m3
and an average size of 10 µm. The LDV head was mounted(1)

With the introduction of L , the turbulence scaling issue
is reduced to establishing a relationship between L and L , orequivalently, to setting the value of the (dimensionless) dissipation parameter

Cε ∝

εL
L
∝
,
k3/2 L

Sketch of the flow facility and instrumentation.

(2)

where the proportionality coefficient is of order one, but has
been given different numerical values by different authors, depending on how k and ε were estimated. A cornerstone assumption of turbulence theories and models is that Cε ≈ const..
This assumption has been shown to hold approximately forextensive regions of many canonical flows, in which various

2

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19–22, 2022
conditions. The derivative (de/dt)2 was calculated by extrapolating corresponding finite differences to a zero time lag.
Velocity maps on horizontal and vertical planes were constructed with the use of a planar particle image velocimetry
system (PPIV, or simply PIV - LaVision Inc., Ypsilanti, USA).
The same particles that were used for the LDV method werealso serving as tracers for the PIV method. The frequency atwhich measurements were taken was 7.23 Hz. PIV images
were taken in two planes of measurement, the vertical centreplane (x1 , x2 ) and the horizontal plane (x1 , x3 ). For the measurements in the vertical plane, the laser was positioned underneath the test section and the laser sheet was reflected upwards
by a mirror. The camera was attached to a three-dimensional
side traverse, which allowed the light sheet to be in focus regardless of its spanwise plane position. The size and location of the images were determined from images of a fine rulerthat was inserted on the focal plane of the camera. To takemeasurements in the horizontal plane, the laser was positionedon the side of the test section, resting on wooden structureswith different heights, and a mirror reflected the light sheet
into the test section. The camera was setup on a tripod underneath the test section facing upwards. Before determining thevector fields from image pairs, the images were preprocessed.
A sliding background was subtracted from each image with ascale between 256 and 512 pixels and the particle intensities
were normalised with a scale between one and four pixels. An
algorithmic mask was applied to remove any dead pixels in thecamera photodiode array or overexposed regions in the image.
Each image was processed in an initial pass on 128 × 128 pixel
squares with a 50% overlap and in a second pass on 32 × 32
pixel squares. The local planar velocity magnitude and direction were determined from the particle displacement that corresponded to the maximum correlation between matched pairsof particle images and the time difference between the two images. Post-processing consisted of deleting values that weresignificantly different from neighbouring ones and removing
sections of the resulting vector field, where the vector density
was relatively low. Vectors that exceeded the range of expectedvelocity were also removed and replaced by interpolated values to fill-in sections of the vector field that were sparse. Theedge regions of images were discarded to prevent the final results from being influenced by edge effects.
The process of identifying vortices on PIV vector maps
was the same as the one that has been described in detail byVanderwel & Tavoularis (2011). It is based on the swirlingstrength, a scalar parameter, the value of which distinguishes
discrete vortices from a background flow with mean vorticity. A vortex was assumed to be present, when the swirlingstrength exceeded a specified threshold value. Regions of thevelocity map with sufficiently large swirling strength were fitted with an ellipse, using a minimum volume ellipse function.
The orientations of the ellipse axes were used to determine theorientation of the vortex axis. Counter-rotating vortex pairs,
which were understood to be the legs of horseshoe-shaped vortices, were identified with the use of a second algorithm.

on the side of the test section on three stacked traverses, whichallowed traversing in three mutually perpendicular directions.
Measurements were taken on the vertical centreplane of thetest section. For turbulence measurements, the streamwise U1
and vertical U2 velocity components were measured in coincident burst mode. To take measurements close to the upper
wall (within 16 mm), the beams measuring the vertical component were blocked and only the streamwise component wasmeasured. Measurements of each USF profile were made at
33 streamwise locations, at each of which 5000 samples wererecorded, typically during 140 s. For measurements near theedge of the boundary layer, 10000 samples were recorded overa time between 48 and 770 s (average of 235 s), which was atleast 100 times greater than the local integral time scale. At
the two streamwise positions of main interest, x1 /h = 5.1 and
6.5, additional one-dimensional measurements were taken that
included at least 20000 samples and on average extended forover 360 s, as well as additional two-dimensional data that included 10000 samples and took 180 s on average.
Because the data rate of the LDV system was insufficient
to measure accurately the temporal derivative of the velocity,from which one can estimate the Taylor microscale and the dissipation rate, the Taylor microscale was measured directly withthe use of a hot film probe (Dantec Dynamics, Model 55R15),
which had a 2 µm nickel film on a quartz fibre that was 70 µm
in diameter and 1.25 mm long and was of the boundary layer
type, so that the sensor could be positioned close to the wall.
The hot-film probe was inserted in the test section from the
top using waterproof parts and could be traversed in all three
directions. The hot-film signal was sampled at a rate of 800
Hz over a 35 s interval, which is at least 100 times the typical integral time scale. Ensemble averaging was performed
over 20 of these records at each location. The hot-film signal
was low-pass filtered by two double-pole, low-pass filters inseries, with the first filter cut-off frequency set to 380 Hz andthe second one set to 1.4 kHz. After the voltage signal wasrecorded and corrected for temperature differences, it was further low-pass filtered by a digital filter with a cut-off frequency
that was 2.1 times the local Kolmogorov frequency to prevent
aliasing. Attempts to calibrate the hot-film against the LDV
demonstrated the presence of a significant and non-repeatablesignal drift. This drift is attributed to changes in the thermal
resistance of the hot-film surface, as a result of deposits on
this surface, which may build up or be removed by the stream.
Drift of hot-films immersed in water is well known to users,
but there is no effective way to eliminate it or correct for it.
Thus, the hot-film measurements were unsuitable for measuring the mean velocity, the streamwise turbulent stress or the
streamwise component of the dissipation rate, from which thetotal dissipation rate can be estimated under the assumption of
local isotropy. To circumvent this problem, we devised a procedure by which we measured directly the Taylor microscalefrom the mean-free, hot-film voltage fluctuations e, even in thepresence of drift, as (Livingston, 2020)

λ ≈ U1qe2 /(de/dt)2 ,(3)

RESULTS AND DISCUSSION
1 The USF as a free stream

where the mean velocity U 1 at the same location was obtainedwith the LDV system. Equation 3 is only valid under two assumptions: first, that the velocity fluctuations are small compared to the mean local velocity and, second, that the timeinterval of samples from which the Taylor microscale was determined was sufficiently short for voltage drift to be negligible. Both assumptions were satisfied fairly well by the present

Mean velocity profiles, measured at different streamwise
locations, demonstrated that, away from the walls, the mean
shear was approximately constant (dU 1 /dx2 ≈ 0.41 s−1 , for
1.4 < x1 /h < 8), so that the “free stream“ was indeed a USF.
As the TBL on the top wall evolved streamwise, it encroachedinto the USF, altering the USF mean profile in an increas-3

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19–22, 2022
ingly larger region. The shear parameter, based on an average centreline velocity U 1c ≈ 0.13 m/s at x2 /h = 0.5, was
β = (1/U 1c )(dU 1 /dx2 ) ≈ 2.9 m−1 . Profiles of the streamwise
velocity variance at different streamwise locations demonstrated that the turbulence in the USF was approximately homogeneous on a transverse plane, with a level of inhomogeneity that was comparable to those observed in previous
USF studies in the same facility (Kislich-Lemyre, 2003; Vanderwel & Tavoularis, 2011). Moreover, the turbulence thatwas generated by the flow separator decayed in the region
x1 /h ≤ 4, but grew exponentially further downstream, following the well-established USF exponential growth law, e.g.,2
u21 /U 1c ∝ e0.1β x1 . In summary, the present results indicate thatthe free stream was a conventional USF, and so one may use
previous findings about its structure.

2

Figure 2. Streamwise evolutions of the mean velocity profiles and the physical boundary layer thickness.

Mean velocity profiles and boundary layer
thicknesses

patterns within the MSR.
An important observation is that the dissipation parameter
had significantly larger values within the MSR than outsideit, where it essentially matched values in the corresponding
canonical flows. A second important observation is that the
turbulence Reynolds number inside the MSR was lower thanoutside it. In fact, as shown in Fig. 4, across the MSR, Cε
was roughly inversely proportional to the local Reλ , whereas,in contrast, in the TBL and the USF, there was no obvious
correlation between Cε and Reλ .

Figure 2 shows vertical profiles of the mean velocity U 1 .
From fitted high-order polynomials, we determined the maximum velocity U 1max and the corresponding distance δ fromthe wall, to which we will refer as the boundary layer thickness. When plotted vs. x2 /δ , most mean velocity profiles
nearly collapsed, showing a fair degree of self-similarity of theouter boundary layer. The notable exception was the profilethat was closest to the origin (x1 /h = 1.17), which was not as
developed as the others. Moreover, the farthest away (x1 /h =6.5) profile was also slightly different from the others, which
may indicate that other influences in the test section were starting to build up. For x2 > δ , U 1 decreased approximately linearly, approaching a canonical USF. The TBL encroached into
the USF, such that U 1max ≈ const., whereas δ ∝ (x1 + 5.4h)0.8 .
Although the mean velocity profile in the inner TBL did notmatch well the canonical 1/7th power law, the growth ratesof the physical and momentum boundary layer thicknesses
were close to those in canonical TBL and so the corresponding Reynolds numbers also grew at nearly canonical rates,
namely, as Rex = x1U 1max /ν ∝ x1 and Reδ = δU 1max /ν ≈2600(x1 /h + 5.7)0.8 . The momentum integral thickness θ wascomputed by integrating the mean velocity profiles in the region 0 < x2 ≤ δ . Excluding the values at the two ends ofthe measurement range, θ /δ ≈ 0.092, which is only slightly
lower than the canonical value of 0.094. For rough purposes,
and with some reservation for the furthest downstream location, one may approximate the momentum thickness Reynolds
number as Reθ = θU 1max /ν ≈ 240(x1 /h + 5.7)0.8 , with a representative value of 1600 at x1 /h = 5.0.

34Comparisons with measurements in aboundary layer with a uniform free stream

The profiles of the mean velocity and the streamwise
Reynolds stress across a TBL on the upper wall in the present
water tunnel in the absence of USF were measured at x1 /h =5.1 with the LDV system after the shear generator and flow
separator were removed. The values of some basic properties of this TBL, together with corresponding values in
the presence of USF shown within parentheses, were as follows: U 1max = 0.14 (0.20) m/s; δ = 0.080 (0.084) m; Rex =330, 000 (470, 000); and Reθ = 1, 000 (1, 600). Differences
between the two normalised mean velocity profiles within the
TBL are within the measurement uncertainty, which was moresignificant near the wall. Neither profile could be fitted wellby the 1/7th law, but both profiles were, at least partially, fairly
close to a 1/6th law. These results show that the presence of
shear in the free stream has no measurable effect on the mean
velocity profile inside the TBL. It should be mentioned, however, that, even in the absence of USF, the free stream contained a significant level of disturbances (nearly 2%). It wasalso found that the turbulence in the inner TBL (x2 /δ ≲ 0.2)
was not affected visibly by the presence of USF, whereas,in the outer TBL (0.2 ≲ x2 /δ < 1), the local turbulence wasstronger in the presence of USF, as the result of both the overall higher turbulence level in the USF and the penetration ofcoherent structures from the USF into the TBL.

Turbulence properties

Profiles of turbulence properties at two streamwise locations are shown in Fig. 3. The Cε profile clearly shows thepresence of three regions: an essentially canonical inner halfof a TBL (to be referred to heareafter as simply TBL), for
0 ≤ x2 /δ ≲ 0.5; an essentially canonical USF, for x2 /δ ≳ 2.2
at x1 /h = 5.1 and x2 /δ ≳ 1.7 at x1 /h = 6.5; and an intermediate, non-canonical, MSR. The mean shear in the MSR was
lower than outside it and the turbulence anisotropy was lower
in the MSR as well. The turbulent shear stress profile was consistent with gradient transport. The integral length scales in theouter TBL and in the USF happened to have comparable values
and so this scale did not change measurably in the MSR. The
Taylor and Kolmogorov microscales (not shown here) exhibited nearly canonical trends outside the MSR but had distinct

5

Coherent structures

Figure 5 shows representative instantaneous velocity
maps obtained with the PIV system on the vertical centreplaneof the test section at two different elevations and two streamwise stations. These maps revealed the presence of vortices,which were interpreted as mostly cross-sections of heads ofhorseshoe-shaped coherent structures. It was hypothesised that4

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19–22, 2022

Figure 4. The dissipation parameter vs. the turbulence
Reynolds number in the multistructure region at x1 /h = 5.1(blue circles) and 6.5 (red triangles); the dashed line is a fitted
relationship of the type Cε ∝ Reλ −1 .

counter-clockwise (CCW) vortices were produced by wallgenerated mean shear, whereas clockwise (CW) vortices were
produced by free shear in the USF. Both vortex types were observed across the flow, but one may confirm qualitatively thatthe majority of vortices well inside the TBL are CCW, thosewell inside the USF are CW, and those in the multi-structure
region are mixed. These images also show flood maps of thevelocity magnitude. As shown previously for both canonical
TBL (de Silva et al., 2016) and undistorted USF (Vanderwel &Tavoularis, 2016), the flow velocity field does not change continuously across the test section, but consists of zones of nearly
uniform velocity. The vortices tend to cluster at the boundary
between such zones, in conformity with the literature.
Instantaneous velocity maps on horizontal planes at different distances from the wall (see Fig. 6) revealed the presence of many vortices, several counter-rotating pairs of which
could be matched and interpreted as cross-sections of the legsof horseshoe structures. Vortex packets were observed, straddling low-speed or high-speed streaks, which are the result ofvertical flow motion induced by the legs of a vortex. Both upright and inverted (Vanderwel & Tavoularis, 2011) horseshoe
vortices were identified in all of the horizontal planes, but theimages could not discriminate between vortices produced by
the two shear mechanisms. The density of horseshoes was
greater within the TBL than in the MSR and the USF. In all
regions, however, the densities of CW and CCW vortices were
nearly the same and the densities of upright and inverted horseshoes were also roughly the same. The latter observation conforms with the literature as far as USF is concerned (Vanderwel & Tavoularis, 2011), but seems to be a novel one for TBL.
Another piece of information that was extracted from the images was the average inclination of the horseshoes with respect
to the horizontal plane. This property was determined from the
aspect ratio of the ellipses, under the assumption that each ellipse is a cross-section of a cylindrical vortex. Our analysis
indicated that this inclination spanned a wide range, but, on
the average, was roughly 55◦ at all four elevations. This value
is somewhat larger than values reported in the TBL and USF
literature.
The distance between vortices that do not belong to thesame packet was comparable to the integral length scale. The
distance between the legs of horseshoes was roughly equal totwice the Taylor microscale. Because of the random yaw of

Figure 3. Profiles of turbulence properties at x1 /h = 5.1(blue circles) and 6.5 (red triangles); in the Cε plot, the dashedlines mark fits to measurements in a canonical TBL (Nedić
et al., 2017) and a USF (Nedić & Tavoularis, 2016).

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19–22, 2022
opposite to the direction of wall-generated shear. An intermediate, distinct, multi-structure region was identified, as having
non-canonical properties and within which the dissipation parameter was significantly larger than elsewhere and inversely
proportional to the local turbulence Reynolds number. Horseshoe vortices were the dominant coherent structures in the entire flow, but their characteristics were distinct in each of thethree flow regions.
Financial support was provided by the Natural Sciencesand Engineering Research Council of Canada.

REFERENCES
Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19 (4), 041301 (16pp).
Charnay, G., Comte-Bellot, G. & Mathieu, J. 1971 Development of a turbulent boundary layer on a flat plate. In Turbulent Shear Flows, pp. 27.1–27.10. Technical Editing andReproduction Ltd.
Evans, R. L. 1974 Free-stream turbulence effects on the turbulent boundary layer. Aeronautical Research Council Current Papers No. 1282 .
Hoffmann, J. A., Kassir, S. M. & Larwood, S. M. 1989 The
influence of free-stream turbulence on turbulent boundary
layers with mild adverse pressure gradients. Tech. Rep.
177520. NASA, Ames Research Center.
Kislich-Lemyre, B. C. 2003 The large-scale structure of uniformly sheared turbulence and its distortion by a solid wallat rest or in motion. PhD thesis, University of Ottawa.
Liangwei, Fang & Hoffmann, J.A. 1988 Effects of anisotropic
free-stream turbulence on turbulent boundary layer behavior. In Frontiers of Fluid Mechanics (ed. Shen Yuan), pp. 56– 61. Pergamon.
Livingston, C. 2020 Multi-structure turbulence in a boundary
layer with a uniformly sheared free stream. Master’s thesis,
University of Ottawa.
Meier, H. U. & Kreplin, H.-P. 1980 Influence of freestream
turbulence on boundary-layer development. AIAA J. 18 (1),
11–15.
Nedić, J. & Tavoularis, S. 2016 Energy dissipation scaling inuniformly sheared turbulence. Phys. Rev. E 93 (3).
Nedić, J. & Tavoularis, S. 2018 A case study of multi-structure
turbulence: Uniformly sheared flow distorted by a grid. Int.
J. Heat Fluid Flow 72, 233–242.
Nedić, J., Tavoularis, S. & Marusic, I. 2017 Dissipation scaling
in constant-pressure turbulent boundary layers. Phys. Rev.
Fluids 2 (3), 032601 (7pp).
Sakai, Y., Hiruta, K., Nagata, K., Suzuki, H. & Terashima, O.
2013 Effects of the cylinder wake in a freestream on statistical properties of a turbulent boundary layer. Trans. JSME
(in Japanese) 79 (799), 64–76.
de Silva, C. M., Hutchins, N. & Marusic, I. 2016 Uniform momentum zones in turbulent boundary layers. J. Fluid Mech.
786, 309–331.
Tennekes, H. 1968 Simple model for the small-scale structureof turbulence. Phys. Fluids 11 (3), 669–671.
Vanderwel, C. & Tavoularis, S. 2011 Coherent structures in
uniformly sheared turbulent flow. J. Fluid Mech. 689, 434–
464.
Vanderwel, C. & Tavoularis, S. 2016 Scalar dispersion by coherent structures in uniformly sheared flow generated in awater tunnel. J. Turbul. 17 (7), 633–650.
Vassilicos, J. C. 2015 Dissipation in turbulent flows. Annu.
Rev. Fluid Mech. 47 (1), 95–114.

Figure 5. Representative instantaneous, vertical, velocity
maps at two different elevations (top and bottom rows) andx1 /h ≈ 5.1 (left column) and 6.5 (right column); numbers on
the ordinate denote x2 /δ and numbers on the abscissa denote
x1 /h; legends (specific to each image) describe the velocity
magnitude in m/s; the physical scales of both axes are thesame; ellipses mark areas with relatively large swirl, which areinterpreted to be cross sections of mostly vortex heads; white
ellipse contours indicate clockwise rotation and black ones indicate counter-clockwise rotation.

Figure 6. Representative instantaneous, horizontal, velocity
maps showing vortex pairs in the three regions; ellipses markareas with relatively large swirl, which are interpreted to be
cross sections of mostly vortex legs; white ellipse contours
indicate clockwise rotation and black ones indicate counterclockwise rotation; hand-drawn red lines connect the axes of
selected vortex pairs, deemed to be the legs of horseshoes.

the vortices, the shortest distance between their legs would besmaller than the distance between the axes of their intersections with the horizontal plane, thus roughly validating Tennekes’ postulate that the distance between vortex legs is comparable to the Taylor microscale (Tennekes, 1968). The diameter of vortices was an order of magnitude larger than the
Kolmogorov microscale, contradicting Tennekes’ second postulate that the diameter of each vortex is comparable to the
Kolmogorov microscale.

CONCLUSIONS
A turbulent boundary layer was generated in the laboratory with a highly turbulent free stream that consisted of a
uniformly sheared flow with a mean shear direction that was

6