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

SCALAR TRANSPORT IN FLOW PAST FINITE CIRCULAR PATCHES OFTALL ROUGHNESS

D.D. Wangsawijaya1 , C. Nicolai1 , B. Ganapathisubramani1
1 Aerodynamics and Fluid Mechanics Research Group, Faculty of Engineering and Physical Sciences

University of Southampton SO17 1BJ, United Kingdom
D.D.Wangsawijaya@soton.ac.uk

ABSTRACTTE of the patch (Taddei et al., 2016; Nicolai et al., 2020). Dueto porosity, the flow may escape from the body by means oflateral, TE, and vertical bleeding, as illustrated in figure 1(a).
In this study, scalar measurements (PLIF) are conductedsimultaneously with velocity measurements (PIV), allowing us
to examine the instantaneous scalar fields as well as the velocity fields. We aim to investigate the characteristics of flow
and scalar transport in the wake and above porous patches ofas a function of patch density φ , given a point source of passive scalar upstream of the patch (figure 1a). As the scalar isreleased from the floor level, we particularly focus on the vertical scalar transport by the time-averaged (advective) and thefluctuating turbulent components of the flow, as these parameters characterise mixing on the flow downstream of the porous
patches. As a comparison, the range of φ in this study is within
the typical range observed for aquatic vegetations and urban
areas (Grimmond & Oke, 1999; Nepf, 2012). The height ofcylinders, when compared to ABL (h/δbl = 0.366), is typicalof tall buildings in the cities.

Simultaneous particle image velocimetry-planar laserinduced fluorescence (PIV-PLIF) measurements are conductedof the flow around and downstream of patches of tall cylinders
with various solidity φ ≡ Nc (d/D)2 , where Nc is the number of cylinders in a patch, d and D are the diameters of thecylinder and the patch, respectively. Results suggest that the
bleeding and scalar concentration in the wake and above thepatches are dependent upon φ . Recirculation bubble appears
at the trailing edge (TE) of the patch, limiting the flow fromconvecting downstream and forcing the flow (and the scalar)to escape vertically from the top of the patch. Above the wake,a shear layer generated by the velocity difference shields thenear-wake region. The net effect is the appearance of an elongated patch as φ decreases and a taller patch as φ increases. In
terms of scalar transport, both advective and turbulent verticalscalar transport are enhanced as φ increases. High advective
vertical scalar transport CV is concentrated around the canopy(above the canopy due to vertical bleeding and at the TE due tohigh scalar concentration), while high turbulent transport c′ v′
largely coincides with the shear layer. Joint probability density function (PDF) calculated at few selected points show that
there is an entrainment of turbulent flows from the shear layer
towards the wake of the patch below this layer, followed byscalar diffusion the the same direction and further downstreamof the patch.

EXPERIMENTAL SETUP
Simultaneous PIV-PLIF measurements are carried out inthe closed loop water flume at the University of Southampton.
The test section has the size of 6250 mm × 1200 mm (length× width), filled with water whose level is kept constant at 600
mm. A circular patch (D = 100 mm and ReD ≡ U∞ D/ν ≈4.5 × 104 , where ν = 1.0035 × 10−6 m2 s−1 is the kinematic
viscosity of water at 20◦ ) is mounted on the floor of the tunnel
at 5500 mm downstream of the test section entrance. The incoming flow is a developing turbulent boundary layer, whose
freestream velocity U∞ ≈ 0.45 ms−1 and boundary-layer thickness δbl = 82 ± 3 mm (Reτ ≡ δbl Uτ /ν ≈ 1500 and Reθ ≡θU∞ /ν ≈ 3000, where Uτ is the friction velocity, and θ isthe momentum thickness). A point source is created at 1.25D
upstream from the centre of the patch by releasing Rhodamine
6G dye solution (Peclet number PeD ≡ ReD Sc = 1.12 × 108 ,where Sc is the Schmidt number) from the ground level at aconstant flow rate (figure 1a).
Mounted on the circular patch are rigid cylinders made ofphotopolymer resin (d = 5 mm, h = 30 mm). The cylinders
are arranged in a manner pictured in figure 1(b–d), such thatφ is parametrically varied by increasing Nc while keeping D
and d constant. Table 1 and figure 1(b–e) illustrate the test
cases in this study, which comprise of 3 porous cases (C39,
C64, and C133), covering a range of 0.1 ≲ φ ≲ 0.33 (2.5 ≲aD ≲ 8.5, where a is the frontal area per unit volume, a ≡Nc d/(0.25φ D2 )), and a solid obstruction case ‘CS’ (figure 1e,

INTRODUCTION
A scenario where a developing turbulent boundary layer
impinges a canopy is commonly found in both nature and engineering applications. Example includes: flows past aquaticand terrestrial vegetations, atmospheric boundary layer (ABL)
developing over forests, urban landscapes, and wind/tidal turbines. The presence of these canopies are known to affectthe scalar, momentum, and energy transport process in theflows, which in turn can affect the ecosystem surrounding the
canopies. Here, the canopy is simplified as a group of tallcylinders of height h mounted on a circular patch (figure 1a),forming a porous body. Previous studies involved 2-D patches,
where h is equal to or taller than the flow depth, serving as
models for emergent aquatic vegetations (Nicolle & Eames,
2011; Chang & Constantinescu, 2015). A more realistic approach for vegetation canopies, urban landscapes, and windfarms is to submerge the patches in the flows (h < δbl , see figure 1a). Studies on 3-D (submerged) patches have shown thatsolidity (or solid volume fraction) of a porous body φ is critical in the determination of drag and wake characteristics at the1

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

Figure 1. (a) Illustrations of lateral, trailing edge, and vertical bleeding of a porous obstruction. Ubl is the incoming boundary-layer
velocity, whose thickness is δbl , and h is the height of the cylinders. Blue arrow shows the location of the point source (fluorescent dye
entry point). Illustration of cylindrical array test cases: (b) C39 (φ = 0.098), (c) C64 (φ = 0.160), (d) C133 (φ = 0.333), and (e) thesolid case (CS, φ = 1) in x–z plane (top view), d is cylinder diameter and D is the circular patch diameter.
Table 1.

List of cylindrical array test cases.

Cases

Nc

d/D

φ

aD

C39

39

0.05

0.098

2.483

C64

64

0.05

0.160

4.074

C133

133

0.05

0.333

8.467

CS

1

1

1

1.273

Recirculation bubbles, here shown by U < 0 (blue-shaded contours), appear to be a function of φ . In case C64 (φ = 0.16,
figure 2b), a weak bubble appears downstream of the patch; itmoves upstream towards the patch TE and becomes stronger
in case C133 (φ = 0.33, figure 2c). The “delay" in the appearance of recirculation bubble has been previously observedin both 2-D and 3-D patches (Chang & Constantinescu, 2015;
Taddei et al., 2016; Zhou & Venayagamoorthy, 2019), and also
porous plates (Castro, 1971).
Superimposed on the contours of U in figure 2 are the line
2 (solid black
contours of the Reynolds shear stress −u′ v′ /Uh/2
lines). The contours show the formation of a free shear layer(or a mixing layer) downstream of the patch, as the wake ofthe patch comes into contact with the undisturbed, faster flowin the freestream (Nicolai et al., 2020). Meanwhile, the region
below the layer and downstream of the patch TE is shieldedfrom mixing. The magnitude of −u′ v′ increases with φ , witha similar pattern observed in the variances u′ u′ and v′ v′ (notshown for brevity). The layer appears to be lifted off the patch
as φ increases for the porous patches in figure 2(a–c), which is
attributed to vertical bleeding from the interior of the patches.
Although the magnitude of the shear stress is higher, the liftoff is not observed in the solid case CS (figure 2d) as the flow
is not able to escape vertically from the patch in this case.
The time-averaged scalar field normalised by its concentration at the point source C/Cs (shown in solid gray lines infigure 2 and coloured contours in figure 3) allows further examination of the flow; with this aim, only high values of mean
concentration are shown in figure 2: the most external contour refers to a value of 1 × 10−3 . In case C39 (figure 2a),no recirculation is observed and high magnitude of C is apparent downstream of the patch as the flow bleeds from the
TE. As φ increases in case C64 (figure 2b), the region of high
C is trapped by a recirculation bubble (blue-shaded contours)
downstream of this region. At the highest φ (case C133, figure 2c), recirculation is observed at the TE and largely preventing TE bleeding from the patch as well as scalar penetration
downstream of the patch (no contour lines downstream of thepatch compared to cases C39 and C64), followed by higher
C above the patch (0 ≤ x/D ≤ 0.5, y/h > 1), which signals
a stronger vertical bleeding. The magnitude of C above thepatch is proportional to φ , which also coincides with the elevation of the shear layer (coloured contours in figure 3, cf. solid
black lines in figure 2). For porous obstructions such as these,

φ = 1).
PIV-PLIF measurements are conducted in thestreamwise–wall-normal (x–y) plane, slicing the centerline of the circular patch. The measurement domain is createdby combining successive experiments in 3 field-of-views(FOVs), extending downstream of the patch. As many as
3000 PIV image pairs are recorded for each test case intable 1 by two 4 MP CMOS cameras, while a 5.5 MP 16-bit
sCMOS camera simultaneously records PLIF images at therate of 4 Hz (boundary-layer turnover TU∞ /δbl = 1.4). The
PIV cameras are equipped with wavelength filters to filter
out the PLIF signal, and vice versa for the PLIF camera.
Image cross-correlation and post-processing of the resulting
vectors are performed using a commercial software (DaVis,
LaVision GmbH), which gives the spatial resolution of∆x+ × ∆y+ = 15 × 15 (‘+’ denotes viscous scaling). The total
size of the measurement domain is approximately 6.89D × 4h
(x × y), which is stitched from 3 FOVs of the size of 2.5D × 4h.
The complete description of the experimental setup is given
in Appendix A of Wangsawijaya et al. (2022). Further detailsof the PLIF calibration technique and image post-processing
are given by Vanderwel & Tavoularis (2014) and Lim et al.
(2022).

TIME-AVERAGED FLOW FIELDS
Figure 2 shows the coloured contours of time-averaged
streamwise velocity U for the test cases listed in table 1. Here,the origin x = 0 is at the centre of the patch, y = 0 on the floorof the tunnel, and U is normalised by Uh/2 (the incoming velocity at half-height of the cylinder, y = h/2). Both porous (figure 2a–c) and solid canopies (figure 2d) show the formation of
wake in the form of velocity deficit downstream of the patch.

2

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

Figure 2. Contours of time-averaged streamwise velocity U/Uh/2 of case: (a) C39, (b) C64, (c) C133, and (d) CS. Solid black lines
2 with the following contour levels: 0.4, 1, 1.6, ..., 4 × 10−2 . Solid gray lines (() are the Reynolds shear stress −u′ v′ /Uh/2)
are the time-averaged scalar concentration in logarithmic scale log10 (C/Cs ) with the following contour levels: –3, –2.9, ..., –2.5.
Measurement data are not available in the hatched regions.
diverges downstream of the patch. The development of c′ v′
layer is similar to that of the shear layer (shown by the line
contours of u′ v′ in figure 2), and thus related to the vertical exchange of scalar inside the shear layer. For the porous cases,
the magnitude of c′ v′ is also proportional to φ . The exception
to this is the solid case CS, which has a relatively lower c′ v′
but higher −u′ v′ compared to that of the porous cases (cf. figure 2d and 4d). Similar pattern in the development of turbulent
scalar flux and the “rooftop" shear layer has been observed invarious models of urban topography (Tomas et al., 2017; Hertwig et al., 2019; Lim et al., 2022).

TE bleeding is limited by the recirculation bubble. From theflow’s perspective, the patch appears to be ‘extended’ downstream, with the length of the extension inversely proportional
to φ (possibly akin to the length of “steady wake region" observed by Ball et al. (1996); Chen et al. (2012); Zong & Nepf
(2012)). As φ increases, the shear layer is elevated upward,
shielding the high C region above the patch and limits the vertical bleeding from the interior of the patch. The net effectis the ‘taller’ appearance of the patch. Further investigation of
the time-averaged flow fields is detailed in Wangsawijaya et al.
(2022).

It is noted that the high magnitudes of the advective andturbulent terms, CV and c′ v′ , respectively, occur in different
regions of the flow fields. High magnitude of CV is concentrated around the patch; it is observed between the patch andthe shear layer (1 < y/h ≲ 1.5, cf. figure 2b,c and 3b,c), and at
the TE of the patch up to x ≈ D (see figure 3c), where a strong
updraft (V > 0) coincides with high mean scalar concentration
C. Downstream of this region (x ≳ D), the magnitude of CV
decays dramatically, signaling less activity or transport of thescalar by the mean flow. In its place is the region of highly
positive c′ v′ (figure 4), which is persistent downstream alongwith the shear layer.

ADVECTIVE VERTICAL SCALAR TRANSPORT
Figure 3 shows the coloured contours of C/Cs , superimposed with the line contours of normalised time-averaged wallnormal velocity V /Uh/2 . For the porous patches (figure 3a–c),
the previous observation regarding the time-averaged vertical
bleeding is further confirmed by the high magnitude of V > 0
above the patch, which increases with patch density φ . For thesolid patch (case CS figure 3d), a strong updraft (V > 0) is observed in at leading edge of the patch due to flow separation
rather than vertical bleeding, followed by a downdraft (V < 0,solid gray lines in figure 3d) downstream of this region.
The strong updraft observed in the porous patches due tovertical bleeding (figure 3a–c) coincides with coincides withincreasing vertical penetration of the scalar above the patch,which increases further with φ . At the TE of the patch, highmagnitude of C at lower φ (figure 3a,b) coincides with relatively low magnitude of V . As φ increases, however, a strong
updraft appears at the TE of the patch (0.5 ≤ x/D ≲ 1, figure 3c,d), coinciding with lower magnitude of C compared tothat of figure 3(a,b). This results in a highly positive advective
scalar flux (upward transport of the mean scalar, CV > 0) in
the region surrounding the patch: above and at the TE of thepatch, with the magnitude of CV increases with φ .

We further examine the content of the turbulent flow inside the shear layer, which is also the region with high magnitude of c′ v′ , by calculating the joint probability density (PDF)of the vertical velocity and scalar fluctuations (from their
Reynolds averages), v′ and c′ , respectively. For each of theporous cases (figure 4a–c), joint PDFs are calculated at two
points marked by ‘×’. These points are selected by tracing the
maximum value of c′ v′ downstream of the patch, x/D > 0.5.
Where shear layer lift-off is clearly observed (e.g. in case C64
and C133 in figure 4b,c), the location of maximum c′ v′ above
high CV region (y > h) is selected as the first point (labelled (i)in figure 4b,c). The second point is selected at the maximum
c′ v′ , downstream of the high CV region (labelled (ii) in figure 4b,c). For the case with lowest φ (C39), where shear layer
lift-off is not visible, the first point is in the near-wake region(x/D ≈ 0.75), where high magnitude of c′ v′ is observed, approximately at the half-height of the cylinders (labelled (i) in
figure 4a). The second point (labelled (ii) in figure 2a) coincides with the shear layer (figure 2a) further downstream ofpoint (i). For the solid case CS, there is no vertical bleeding;the joint PDF is calculated at the location of maximum c′ v′

TURBULENT VERTICAL SCALAR TRANSPORT
Figure 4 shows the contours of turbulent vertical scalar
flux c′ v′ for all porous and solid cases. The contours are normalised by the source concentration Cs and the velocity at halfheight of the cylinders Uh/2 . The contours show a largely positive c′ v′ regions, i.e. the layer grows above the patch and312th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022

Figure 3. Contours of time-averaged scalar concentration in logarithmic scale log10 (C/Cs ) of case: (a) C39, (b) C64, (c) C133, and)(d) CS. Solid lines are the time-averaged wall-normal velocity V /Uh/2 with the following contour levels: 0.05, 0.075, ..., 0.2 (and –0.08, –0.07, –0.06 (). Measurement data are not available in the hatched regions.
of c′ v′ (figure 4d(i)) is highly skewed towards c′ < 0 but shows
neither preference towards v′ > 0 nor v′ < 0. In this case, thereis neither vertical bleeding nor TE bleeding as the flow is unable to escape from the interior of the patch. Instead, the flow
separates at the top and the sides of the patch. As the wakesheds from the sides of the patch, there are two possible interpretations of c′ < 0 event: either the scalar has been transported to other in-plane locations, or out of the plane. To examine these possibilities further, figure 4(d)(iii) show the joint
PDF of c′ and u′ calculated at the same location marked by ‘×’in figure 4(d). The joint PDF of c′ and u′ shows a similar pattern to that of c′ and v′ . There is no clear preference towards
u′ < 0 or u′ > 0, but there is a high probability towards c′ < 0.
This suggests that for the solid case CS, wake shedding fromthe sides of the patch is more likely to transport the scalar outof the plane.

downstream of the patch (labelled (i) in figure 4d), underneaththe shear layer (figure 2d).
Figure 4(a)(i) shows the joint PDF of c′ and v′ of caseC39 (lowest φ ) at the location marked by ‘(i)’ in figure 4(a).
This location coincides with the region with higher magnitude
of C (and thus CV , figure 2a and 3a) due to flow bleeding fromthe interior of the patch towards the TE. The joint PDF showsa relatively equally distributed probability of c′ and v′ events
across all four quadrants, with a slightly higher probability ofc′ < 0 event. However, as φ increases in case C64 and C133,
the joint PDFs shown in figures 4(b)(i) and (c)(i) are highly
skewed towards Q1 and Q3 events (c′ > 0 accompanied withv′ > 0 and c′ < 0 accompanied with v′ < 0), with higher probability of Q3 event. This location coincides with the elevatedshear layer (figure 2b,c), below the region of high CV magnitude (strong updraft and/or high scalar concentration). The
high probability of Q3 event (c′ < 0 and v′ < 0) is related tothe entrainment of turbulent flow from the shear layer, whereenhanced turbulent scalar transport occurs, towards the region
shielded below by this layer. Downstream of the high CV region, shear layer develops and diverges further (figure 2a–c).
Joint PDFs at this location for all porous cases (figure 4a(ii)–c(ii)) show the same pattern as that of point (i), although withless skewness towards Q1 and Q3. For all porous cases, mixing and entrainment of the turbulent flow towards the wake
depend on φ ; the strength of the shear layer (figure 2) and theskewness of c′ and v′ towards Q3 events grow with increasing φ . The higher probability of Q3 events (c′ < 0 rather thanc′ > 0) is related to the diffusivity of the scalar, as the scalar
is more likely to be transported to different locations (in thiscase entrained to the wake below the shear layer, v′ < 0 event).
However, we also note that the magnitude of c′ < 0 seems to
be limited to a certain value (figure 4b(i),c(i)), possibly causedby post-processing of the PLIF image, which will be examined in the future. Examination of joint PDFs of c′ and u′
at the same location inside the shear layer (figure 4b(iii) andc(iii)) shows that the probability is highly skewed towards Q2(c′ < 0, u′ > 0) and Q4 (c′ > 0, u′ < 0) events, with higher
probability of Q2 (c′ < 0 accompanied by u′ > 0), which canbe translated as the scalar diffuses further downstream of thepatch. As the shear layer diverges (figure 4b(iv) and c(iv)), theskewness towards Q2 and Q4 persists, although there is an increasing possibility of Q3 events (u′ < 0, slower flow) as thispoint is located just downstream of the recirculation regions(U < 0, figure 2b,c).
In the solid case CS, joint PDF calculated at the maxima

CONCLUSIONS
We conduct simultaneous PIV-PLIF measurements offlow around a cluster of cylinders on a circular patch, over arange of canopy density φ . Present results suggest that bothvertical and TE bleeding from the interior of the cylinders,
wake formation, shear/mixing layer development, scalar concentration, and vertical scalar transport (both advective andturbulent) are dependent upon φ . In terms of TE bleeding andwake formation downstream of the patch, recirculation bubble is shifted downstream as φ decreases, limiting the flowfrom convecting downstream. As φ increases, the recirculation bubble appears at the TE of the patch, forcing the flow to
bleed vertically from the patch; this results in the elevation of
the free shear layer developing above and downstream of thepatch. The net effect is the appearance of “taller" canopy as φincreases and “elongated" as φ decreases.
In terms of scalar transport, results suggest that both advective and turbulent vertical scalar fluxes (CV and c′ v′ , respectively) are enhanced as φ increases. High magnitude of
CV is detected around the patch, where the flow bleeds vertically from the interior of the patch towards the freestream andfrom the TE of the patch. On the other hand, the occurrence ofhigh magnitude of turbulent vertical scalar flux c′ v′ largely coincides with the shear layer. Further analysis of the joint PDF
of c′ and v′ suggests that inside the shear layer, mixing is enhanced (and more so as φ increases), there is an entrainment of
turbulent flows from this layer towards the wake region forming below this layer, followed by scalar diffusion towards the4Figure 4. (a–d) Contours of turbulent vertical scalar flux c′ v′ , normalised by CsUh/2 for all test cases shown in table 1. ‘×’ denote the location where joint PDF of c′ and v′ is calculated from each′ ′instantaneous velocity and scalar concentration fields. The joint PDFs, corresponding to locations (i, iii) and (ii, piv), are shown
p to the right of the c v contours of each test case. Plots (i) and (ii)
′
′
′
′
′
′
correspond to the vertical velocity and scalar fluctuations, v and c , normalised by their respective root mean square, v v and c c , while plots (iii) and (iv) correspond to the streamwise velocity andscalar fluctuations, u′ and c′ .

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

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022
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same direction and further downstream of the patch. For thesolid case CS, however, where there is neither vertical nor TE
bleeding, it is more likely for the scalar to be transported outof the PIV-PLIF plane.

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