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

EFFECT OF UPSTREAM BOUNDARY LAYER ON COHERENTSTRUCTURES IN THE WAKE OF A BLUNT TRAILING EDGE PROFILED
BODY

Ross Cruikshank & Philippe Lavoie
Institute for Aerospace Studies
University of Toronto
4925 Dufferin St., Toronto, Ontario, M3H 5T6, Canadaross.cruikshank@mail.utoronto.ca & phil.lavoie@.utoronto.ca

ABSTRACTThe effect of the state of the upstream boundary layer andits thickness on the three-dimensional aspects of vortex shedding in the wake of a blunt trailing edge profiled body is investigated experimentally. Reynolds numbers based on bodythickness, d, ranging from 2 800 to 38 000 and boundary layers with displacement thicknesses up to 0.38d are considered.
Velocity field measurements of the near wake are made using
hot-wire anemometry and particle image velocimetry (PIV).
The PIV measurement plane is aligned with the trailing edge ofthe models, which allows the three-dimensional vortex shedding structures to be visualized. We assess the level of threedimensionality through the spanwise correlation of the streamwise velocity, which is shown to be sensitive to both boundary
layer transition and the thickness of the boundary layers. In allcases, the main three-dimensional features are oblique shedding and vortex dislocations. We find that, as the boundary
layer transitions, the spanwise correlation drops and we link
this to increased fluctuating vortex shedding phase drift along
the span due to greater unsteadiness in the near wake velocity
field. For the turbulent boundary cases, the fluctuating phasedrift does not change significantly with boundary layer thickness. In this range, the main mechanism affecting the spanwise
correlation is the relative strength of the vortex shedding compared to the random turbulent fluctuations in the wake.

Figure 1: Schematic of the blunt trailing edge model andcoordinate system

At relatively low Reynolds numbers, the threedimensional features can be controlled through endconditions. As the Reynolds number is increased, turbulencein the shear layers and wake begins to play a more importantrole in setting the three-dimensional structure, which cantake several forms. Over long wavelengths, the von Kármánvortices may be shed at an angle, ψ, to the span of a bluff
body, producing oblique vortex shedding. Vortex dislocations
are associated with oblique shedding above a critical angle,
wherein the vortex street assumes the pattern of a seriesof cells along the span. These cells may have different
frequencies entirely, with phase discontinuities and a complex
network of streamwise-oriented vortices connecting them(Williamson, 1992). Figure 2 shows a typical velocity fieldin the streamwise-spanwise plane of the wake to illustratethis. The coherent regions of high u† = (u − u)/u∞ roughly
correspond to the locations of the von Kármán vortex cores.
In this velocity field a dislocation exists at z ≈ −2d, where
the shedding exhibits a phase discontinuity. At z ≈ 2.5d thevortex shedding angle changes direction, but without a phase
discontinuity.
The three-dimensional structure of a wake and the spanwise correlation are closely tied to the loading experienced
by a bluff body. Firstly, the tilting of spanwise vorticity into
streamwise vorticity reduces the strength of the shed vortices,and hence, the drag. Secondly, if the vortex shedding is outof-phase across the span then the spanwise-varying induced
forces leads to a reduced net load. Therefore, understanding the three-dimensional structure of wakes is essential fora proper interpretation of how the unsteady and overall loading varies for different bluff body geometries and flow conditions. Szepessy (1994) investigated the wake of a cylinder
through the base pressure and found that the vortex shedding
spanwise phase drift was the major contributor to the spanwise
correlation at least up to the large subcritical Reynolds num-

INTRODUCTION
Wakes of bluff bodies are of interest due to how regularly they appear in engineering applications such as vehicles
and structures. Two-dimensional bluff bodies commonly exhibit vortex shedding above a critical Reynolds number, andthis leads to large periodic velocity fluctuations and unsteadyloading. The geometry of interest in the present study is ablunt trailing edge (BTE) profiled body, shown schematicallyin Figure 1. This type of body has fixed separation points
at the trailing edges. A fixed separation point removes someof the dependence of the flow field on the Reynolds number,compared to the variations exhibited for curved afterbodies.
Nevertheless, the wake of a BTE body is still sensitive to the
Reynolds number. If the incoming flow is spanwise uniform,
then at Reynolds numbers less than about 210, the vortex shedding will also be two-dimensional (Petrusma & Gai, 1996).
However, for Reynolds numbers greater than 210, the vortex
shedding develops three-dimensional features irrespective of
the initial conditions.

112th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
hot-wire measurements. The hot-wires were made in-houseon Dantec probes with 5 µm thick tungsten wire and sensing
lengths of about 1.2 mm. Hot-wire measurements were madeof the boundary layer velocity profiles at 0.5d upstream of thetrailing edge, and at various locations in the near wake by positioning the wires with a three-axis traverse system. In thecase of the c = 12.5d model, each data point was sampled at
25 kHz with a 10.5 kHz low pass filter for 120 s. With thevariable-length model, the sampling time and frequency were
120 s and 5 kHz with a 2 kHz low pass filter, respectively.
For the PIV measurements, the laser sheet was formed
from a dual-pulse Nd-YAG laser and a series of lenses to direct the beam. A Lavision Imager sCMOS camera took the images. For all of the cases with the c = 12.5d model, 3000 snapshots were taken, whereas 1000 snapshots were taken for thevariable-length model cases. The c = 12.5d cases had a field ofview of −4.5d < z < 4.5d and 0.22d < x < 5.7d with a vector
spacing 0.043d and the vector fields with the variable-length
model cases covered −5.5d < z < 2.2d and 0.22d < x < 4.9d,
for a vector spacing 0.037d. Lavision Davis 8.3.x software wasused to process all the images, using window sizes of 16x16
pixels and 50% overlap.

Figure 2: Sample velocity field in the {z, x} plane alignedwith the trailing edge at {Red = 20 500, c = 12.5d}. The
angle of the vortex shedding, ψ, is given as the dashedblack lines. For 4.5d < z < −3d, ψ = 3◦ , for 1d < z <2.5d, ψ = −11.5◦ , and for 2.5d < z < 4.5d, ψ = 16◦ .

ber regime. Unlike for a cylinder, the chord length, c, of a BTE
body can be varied independently of its thickness, d. Therefore, boundary layer thickness is decoupled from the Reynolds
number based on body thickness, Red . Rai (2018) examined
how the variability in the shedding frequency and strength for a
bluff body were linked to streamwise vortices in the boundary
layer. Vortex shedding unsteadiness is associated with threedimensionality because the shedding frequency/strength mustvary along the span for there to be a spanwise phase drift. The
aim of this study is to gain a deeper understanding of how
the two- and three-dimensional coherent structures in the wakechange with both Red and boundary layer thickness. In order
to better isolate the effect of Red and boundary layer thickness,both changes in c and u∞ are considered. Furthermore, cases
are considered where the boundary layer is either laminar or
turbulent at separation.

RESULTS AND DISCUSSION
The boundary layer profiles for all the variable-length
model cases indicate that the boundary layer is turbulent upstream of the trailing edge. The large scale two-dimensional
properties of the vortex shedding are assessed through the velocity spectra in the wake. For the variable-length model, thevelocity is measured by a hot-wire at {x, y} = {1.5d, 0.8d} andall the spectra exhibit a prominent vortex shedding peak. Using the Strouhal number, St = f d/u∞ , the spectral peak freb is found to range from ≈ 0.16 − 0.2. Figure 3
quency, St,b decreases with increasing δ ∗ /d, regardless ofshows that St
whether it is controlled through u∞ or c/d. Similar observations for a BTE body were made by Rowe et al. (2000), exceptthat they controlled the boundary layer only by using different
surface roughness trips and did not isolate the effect of c/d.
Boundary layer thickness effects the shedding period because
it is related to the time it takes for a forming vortex to be cut
off from its shear layer. According to the model of Gerrard(1966), the more diffuse the vorticity is, the longer it takes forthe vorticity from a shear layer to be sufficiently drawn acrossthe wake centerline and cut off the supply of vorticity to the
opposite forming vortex. Additionally, more diffuse boundary
layers/shear layers lead to weaker vortex shedding because theformed von Kármán vortices are less concentrated, irrespectiveof whether the boundary layer thickness is controlled throughu∞ or c/d.
With the c = 12.5d model, the boundary layer is laminarfor the Red < 10 000 cases despite the trip at the leading edge,
and between Red = 10 000 and Red = 16 000 the boundary
layer transitions before it reaches the trailing edge. The velocity spectra computed from hot-wire measurements at {x, y} =b increases with Red while the boundary{4d, 0.5d} show that Stb ≈ 0.23 at Re = 2 800 to 0.27
layer is laminar, ranging from St
at Re = 10 000. When the boundary layer transitions there isb decreases to 0.22 for thea step increase in its thickness, so St
b is higher in the turbuRed ≥ 16 000 cases. The fact that St
lent boundary layer cases for c = 12.5d than for the variablelength model cases is consistent with the more concentrated
separated shear layers when c/d is shorter. The changes inb with Red underscore that the vorticity thickness from theStseparated shear layers plays an important role in the shedding

METHODOLOGY
Experimental measurements were taken in a low
freestream turbulence intensity (< 0.1%) closed-circuit windtunnel with an octagonal cross-section nominally 1.2 m by 0.8
m. Two BTE profiled models of identical thickness (d = 25.4mm) and elliptical leading edge radius (2.5d) were used forthe experiments. The first model has a length c = 12.5d anda span of 26.8d. Datasets at 5 different u∞ were gathered, resulting in Red ranging from 2 800 to 20 500. The second model
has a span of 30.3d and consists of six independent sections,allowing the overall length to be adjusted between 31d and151d. Three flow speeds were tested for the variable-length
model, producing Red = 11 000, 22 000 and 38 000. To promote spanwise uniform and early transition to turbulence, theboundary layer is tripped on both sides of the leading edge
sections, approximately 2.5d downstream of the leading edge.
For the c = 12.5d model, the trip is a strip of zig-zag tape of
9 mm width and 0.5 mm height and for the variable-length
model, the trip is a roughness element 25 mm wide and 2 mm
high. Both models are bounded by end-plates which extend
upstream and downstream of the models.
Measurements of the flow for both models were madeusing single hot-wire anemometry, and two-component particle image velocimetry (PIV) in a {z, x} plane aligned withthe trailing edge at y = 0.5d, where the coordinate system isdefined in Figure 1. A Dantec Type 55H probe and a Dantec 56C constant temperature anemometer were used for the2

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
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Figure 3: Dependence of St( fs ) on δ ∗ /d for the variable-

Figure 4: Spanwise cross-correlation as a function of spa-

length model.

tial lag ∆z for selected cases. ρu at x = 3d in solid linesand ρφ in dashed lines.

frequency. Variations of the vorticity flux from the shear layers
among different shedding cycles due to boundary layer disturbances can lead to unsteadiness in the shedding periods andamplitudes, in line with the experiments of Rai (2018). Whenthe boundary layers transition, the levels of fluctuations in theshear layers increase. A key purpose of this study is to determine if these changes in the transitional boundary layer regime
are connected to the levels of wake three-dimensionality.
The instant shown in Figure 2 illustrates that wake threedimensionality and the overall correlation describes many
features, notably the strength of the vortex shedding, theturbulence levels, secondary vortical structures, the phasedrift/oblique shedding, and dislocation events. The overall
spanwise coherence is assessed using the cross-correlation ofu along z at constant x, defined as

the wake dynamics requires taking into account both Red andδ ∗ /d. We note that in general these values of Lρ are lower
than that measured for cylinder wakes at this Red range, which
is nominally around 1λx , where λx is the streamwise wavelength of the von Kármán vortex shedding (Bruun & Davies,
1975).

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h

i
u(x, z) − u(x, z) u(x, z + ∆z) − u(x, z + ∆z)hiρu (x, ∆z) =var u(x, z) − u(x, z)(1)
Figure 4 plots ρu (3d, ∆z) for selected cases with thec = 12.5d and variable-length model datasets. As measured inprevious studies such as Bruun & Davies (1975) and Szepessy(1994), ρu declines with increasing ∆z for all cases. For the{Red = 2 800, c = 12.5d} case, ρu is on average the highest at
any given ∆z. The drop in the correlation with increasing Red
suggests that the wake is on average less organized. For thevariable-length model cases, ρu is less sensitive to the different u∞ and c/d investigated, presumably because the boundary layer is already turbulent in all these cases. The correlation length-scale, Lρ , for the different cases was calculated
by integrating the ρu curves to either the first zero-crossing or
extrapolating them to zero.
The computed Lρ for the various test cases are summarized in Figure 5. The results for the c = 12.5d model showthat the spanwise correlation drops rapidly when the boundary
layer transitions to turbulence but stabilizes after transition for
the Red = 16 000 and 20 500 cases. This is consistent with theassociation of higher levels of turbulence in the near wake toincreased wake unsteadiness and reduced vortex shedding organization. For the variable-length model cases, Lρ generally
declines with increasing δ ∗ /d, but does not collapse among
the different Red with δ ∗ /d. While δ ∗ /d may be sufficient
to characterize the large-scale two-dimensional vortex shedb this suggests that a full picture ofding properties such as St,
E

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Figure 5: Variation of Lρ , calculated at x = 3d among thetest cases with (a) the c = 12.5d model with Red , and (b)the variable-length model with δ ∗ /d.
3

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
to cover the long wavelength range that is associated with vortex shedding.
For α that are not very well aligned with the vortex shedding direction, the velocity spatial averages calculated from⟨u‡ (xα )⟩α tend towards zero because u‡ is poorly correlated
along lines of zα . This produces low σ (α). When α is wellaligned with the vortex shedding direction, u‡ is strongly correlated along zα . For example, in Figure 2 from −1d < z < 2.5d,
the velocity field is well-correlated along the α = −11.5◦ direction. In that case averaging u‡ along zα = −11.5◦ preserves
the fluctuations associated with the vortex shedding and filters
out the small-scale fluctuations; hence, σ (−11.5◦ ) is the maximum. The best-fit shedding angle, ψ, for a given spanwise
region is defined as the α with the maximum σ (α),

A limitation of this correlation analysis is that it does nottake into account the various factors affecting the correlation,and is not reflective of the instantaneous variations in the correlation that may occur in time-varying flows like in the present
case. The instantaneous snapshots vary considerably in thelevel of spanwise correlation they exhibit, with it not uncommon for some snapshots to have a correlation above 0.8 forall ∆z. In other snapshots, the correlation drops to 0 with adistance of only 0.5λx . This wide variation in spanwise correlation at different instants in time is consistent with the occurrence of unsteady three-dimensional features. Based on aclose examination of the velocity fields in the {z, x} plane, wefind that the vortex shedding exhibits the same general typesof large-scale three-dimensional structures (i.e., dislocations
and oblique shedding) in all the investigated cases. Therefore, in Figure 5(a) and (b), the decrease in Lρ with increasing
Red and boundary layer thickness, respectively, may be reflective of 1) more dislocation events, 2) greater fluctuating phasedrift across the span from oblique shedding (i.e., steeper and/or
more frequent oblique shedding events), and/or 3) greater random small-scale fluctuations. These are important considerations in the generalization of these trends because they cannot
be expected to vary in the same way with the mean shear layer
velocity gradient and the fluctuations.
Because end-plates were used and oriented parallel to thefreestream flow, instantaneous oblique shedding events are notdriven by end-effects. Instead, phase drift in the investigatedcases can be primarily attributed to turbulence in the shear layers and near wake causing spanwise variations in the vortex
shedding. To isolate the correlation drop due to phase drift,
we employ a novel algorithm to analyze the individual PIV
snapshots to compute the shedding angle and phase across thespan.
A central idea of our shedding angle identification algorithm is that by averaging along the direction of the vonKármán vortex lines, the small-scale fluctuations can be averaged out and what is left is representative of the large-scales
directly associated with the vortex shedding. For some arbitrary angle, α, not necessarily aligned with the shedding angle,
ψ, we can define transformed coordinates aszα = z cos α − x sin αxα = z sin α + x cos α

ψ = argmax [σ (α)]

This algorithm is what was used to determine the vonKármán vortex lines which are drawn in Figures 2. Additionally, a different algorithm is used to identify the locationsof dislocations in the measured velocity fields and is able tostitch the shedding angle variations together along the span tomaintain phase continuity of the vortex shedding everywherethat it is not broken by a dislocation. The details of this aspect of the analysis are not discussed in this paper. From thecomputed spanwise variations of the shedding angles, ψ, thespanwise phase drift, ∆φz , can be calculated in all the snapshots. These quantities are directly related to each other fromgeometry through λx for a given spanwise separation ∆z as∆φz = 2π

Z
0

1
0.5λx

PSD [⟨u‡ (xα )⟩α ] d fx,α∆z tan ψ
λx(5)With this approach we can obtain statistical distributionsof ∆φz as a function of ∆z by using the information from all therecords of the ψ variations in the measured velocity fields. We
exclude phases differences across dislocations because there isno valid interpretation of ψ across a phase discontinuity in thiscontext. The distributions of ∆φz can be more efficiently summarized across all ∆z by plotting their standard deviation to
obtain a measure of the fluctuating phase drift. This is plottedfor selected cases with the c = 12.5d model and the variablelength model in Figure 6. Physically, the fluctuating phasedrift is related to the probability of measuring a given shedding phase difference at a certain separation. As ∆z increases,
the fluctuating phase drift increases because there is more opportunity for the phase to drift in between two points withgreater separation. Similar findings in the wake of a cylinder
at Red = 43 000 were reported by Szepessy (1994).
The fluctuating phase drift increases with Red as theboundary layer transitions to turbulence. This suggests thatthe increased velocity fluctuations in the shear layers as Red increases are associated with greater wake three-dimensionality,
consistent with the decline of Lρ when the boundary layer transitions. In contrast, for the variable-length model datasets, thefluctuating phase drift is not very sensitive to variations in Redor δ ∗ /d presumably because the boundary layer is turbulent inall those cases. This indicates that changes in boundary layer
thickness after the boundary layer has transitioned only havea limited effect on the large-scale coherent three-dimensional
properties of the vortex shedding for the BTE body. This suggests that the spanwise disturbances to the vortex shedding frequency and strength do not change nearly as much with Red(2)

For all α ̸= 0◦ , averaging the velocity along zα at constant xα
implies that the average is taken over varying x. Because theamplitude of the velocity fluctuations changes in the near wakewith x, we take that into account by introducing u‡ to normalize u by the local rms velocity fluctuations: u‡ = (u − u)/u′ .
Using the notation of ⟨·⟩ to denote a spatial average, and thesubscript to denote the direction angle of the spatial average,
the average of u‡ along the zα direction in a given region isexpressed as ⟨u‡ ⟩α . The power associated with the long wavelength variations in ⟨u‡ ⟩α along the xα direction for a given
region of a snapshot is represented symbolically as σ (α). It
is calculated by integrating low frequency range in the power
spectral density:

σ (α) =

(4)

(3)

where fx,α denotes the spatial frequency along the xα direction, and the integral is calculated from fx,α = 0 to 1/(0.5λx )412th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
and δ ∗ /d in the range of investigation, as compared to thechanges that happen when the boundary layer transitions.

Figure 4 plots ρφ for selected cases in dashed lines alongside the unconditional ρu with solid lines so that the relativevalues can be compared. The highest value of ρφ among thecases investigated is found for the {Red = 2 800, c = 12.5d}case, in agreement with the fluctuating phase drift curves of
Figure 6. However, clearly the spanwise phase drift does not
fully account for the drop in the spanwise correlation of the velocity with increasing ∆z. A significant reason for the decline
in ρu with ∆z is related to the random turbulent fluctuationsin the wake, which can obscure the vortex shedding signal.
Changes in the random turbulent fluctuations among the different cases may be a driving factor for why ρu declines as theboundary layer thickness is increased for the turbulent boundary layer cases.
To investigate this possibility, we can compute the component of the spanwise correlation that removes the ∆φz dependence. If as in Equation (6) we model u(x, z) as being simply
modulated along the span by the periodic von Kármán vortex
shedding, then the effect of phase drift between two points canbe accounted for in the typical correlation equation with an
added cos(∆φz ) phase term:

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h
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u(x, z) − u(x, z) u(x, z + ∆z) − u(x, z + ∆z) cos(∆φz )
h
i h

i
ρu|∆φz (x, ∆z) =std u(x, z) − u(x, z) std u(x, z) − u(x, z) cos(∆φz )(7)
We refer to ρu|∆φz as the spanwise correlation conditional on
the phase drift. If there is any phase correlation between two
points, ρu|∆φz must be higher than ρu . In the event that velocity differences between spanwise separated points are entirely
a function of ∆φz , this would be reflected by a value of 1 forρu|∆φz . Conversely, if the vortex shedding phase difference between two points did not convey useful information (i.e., if
there was no vortex shedding), ρu|∆φz would collapse onto ρu .
The variation of ρu|∆φz with ∆z for selected variablelength model datasets is provided in Figure 7. It can be seenthat ρu|∆φz declines sharply at small ∆z, similar to ρu , but
asymptotes to constant values at high ∆z in every case. The
reason for this is that at large separations, the random fluctuations in the wake tend to drive spanwise correlations to zero.
The asymptotes of ρu|∆φz are non-zero in the present cases because even at large ∆z, the wake flow is correlated via the vortex shedding. In other words, the von Kármán vortex street
gives large-scale structure to the wake at large distances. The
non-zero asymptotic values imply that if it were possible toenforce a parallel shedding condition in the turbulent boundary layer regime then there would still be a form of correlationeven at large separations.
We can interpret the magnitude of the asymptotes for eachcase as being representative of the relative strength of the vortex shedding signal to the random fluctuations. This correspondence is illustrated by comparing Figure 7 to Figure 8.
Figure 8 expresses the relative power of the vortex shedding
signal to the total velocity fluctuations measured by the hotwire at {x = 1.5d, y = 0.8d}. The power is calculated by integrating the shedding spectral peaks around the 3 dB (halfpower) bandwidth. Figure 8 shows that the relative power ofthe vortex shedding power decreases with δ ∗ /d, so it is increasingly dominated by random fluctuations as the boundary layer thickness near the trailing edge grows. This explains why ρu declines with increasing δ ∗ /d for the variablelength model cases even though the underlying large-scale
three-dimensional structure and overall phase drift does not
significant change in this range.
E

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Figure 6: Fluctuating spanwise phase drift as a functionof ∆z. (a) For the c = 12.5d cases, (b) Selected cases forthe variable-length model.

Based on the work of Szepessy (1994), we can interpretthe fluctuating phase drift in terms of a phase-based correlation coefficient. To make this interpretation, we represent
the velocity at two spanwise separated positions as sine waves
with the same frequency but phase shifted: a = cos ωt, andb = cos ωt + ∆φz . If we assume that ∆φz varies in the snapshots
independently of the shedding frequency, the phase-based correlation can be shown to be

ρφ =

1 n
∑ cos(∆φz,i )
n i=1

(6)

which is only a function of ∆φz . This is consistent with thegeneral mathematical result that the correlation of two out ofphase sine waves is simply cos(∆φz ). The value of interpretingthe vortex shedding phase drift in this way is that it allows us toisolate its effect on the actual spanwise correlation measured
from the velocity field. It removes the effect of turbulent fluctuations because the phase drift is a large-scale quantity that
depends only on the vortex shedding, whereas the measured
correlation from the velocity field is a superposition of all thepossible three-dimensional effects.

512th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
sensitivity of wake three-dimensionality to the state of the upstream boundary layer.
To examine the connection between the spanwise correlation and the shedding phase drift, an algorithm was developed
to compute the instantaneous vortex shedding angles/phasedrift along the span from the velocity field measurements. The
phase drift fluctuations were found to increase significantlywith increasing separation between points in all investigatedcases, which is consistent with the measured decline in the velocity correlation with increasing separation. This connection
between the phase drift and correlation was further explored bycomputing a phase-based correlation which is dependent only
on the spanwise phase drift. The fluctuating phase drift was
found to increase with Red in the boundary layer transitional
regime, which is consistent with the link between greater unsteadiness in the shear layers and weaker wake spanwise correlation. In contrast, varying the boundary layer thickness in the
turbulent boundary layer regime did not have an appreciable
effect on the fluctuating phase drift.
The phase-based correlation was not entirely predictive of
the velocity correlation, underscoring that another importantfactor that affects the spanwise correlation of the velocity is theturbulent fluctuations in the wake. These fluctuations can beenvisioned as essentially random disturbances to the coherent
vortex shedding signals which tend to decorrelate the velocity
field with increasing separation. When the vortex shedding isstrong relative to the turbulent fluctuations, we found that the
spanwise correlations are dominated by the large-scale vortex
shedding component, but as the vortex shedding got weaker,
the random fluctuations played a larger role. Increasing δ ∗ /dweakens the vortex shedding relative to the other velocity fluctuations in the wake, and so the spanwise correlation in the velocity field is progressively more affected by random fluctuations. These trends may have implications on possible ways to
extrapolate measured spanwise velocity correlations to higherδ ∗ /d or Red in the turbulent boundary layer regime.

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Figure 7: Spanwise correlation conditional on the phasedrift, ρu|∆φz , as a function of spatial lag ∆z for selectedcases with the variable-length model.

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Figure 8: Relative vortex shedding power to the overall

fluctuations as measured at {x, y} = {1.5d, 0.8d} for thevariable-length model.
REFERENCES
Bruun, H.H. & Davies, P.O.A.L. 1975 An experimental investigation of the unsteady pressure forces on a circular cylinder in a turbulent cross flow. J. Sound Vib. 40 (4), 535–559.
Gerrard, J. 1966 The mechanics of the formation region of vortices behind bluff bodies. J. Fluid Mech. 25 (2), 401–413.
Petrusma, M. & Gai, S. 1996 Bluff body wakes with free,
fixed, and discontinuous separation at low reynolds numbers and low aspect ratio. Exp. Fluids 20, 189–198.
Rai, M. 2018 Vortex shedding characteristics of the wake of athin flat plate with a circular trailing edge. Int. J. Heat andFluids Flow 72, 20–36.
Rowe, A., Fry, A. & Motallebi, F. 2000 Influence of boundarylayer thickness on base pressure and vortex shedding frequency. AIAA J. 39 (4), 754–756.
Szepessy, S. 1994 On the spanwise correlation of vortex shedding from a circular cylinder at high subcritical reynolds
number. Phys. Fluids 6, 2406–2416.
Williamson, C.H.K. 1992 The natural and forced formation of
spot-like vortex dislocations in the transition of a wake. J.
Fluid Mech. 243, 393–441.

CONCLUSION
The large-scale two-dimensional and three-dimensional
properties of the vortex shedding in the near wake of a blunt
trailing edge profiled body have been experimentally examined. A central question in this study was the effect of boundary layer transition and its thickness on the wake coherent
structures, which we characterize through spanwise correlations. To this end, Red was varied from 2 800 to 38 000 andthe boundary layer thickness was controlled via u∞ and model
length. In all cases the vortex shedding was found to exhibit
significant spanwise phase drift and dislocations. Because parallel end-plates were used, this phase drift is due to intrinsic
spanwise variations that develop as the flow convects over thebodies, driven by turbulence in the shear layers and near wake.
When Red was increased while the boundary layer was laminarat separation, the correlation length, Lρ (3d), dropped from approximately 0.65λx to 0.55λx . The transition to turbulence inthe boundary layer caused a more considerable drop in Lρ (3d)from about 0.55λx to 0.35λx , which is indicative of the high6