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

PIV MEASUREMENT OF TURBULENT FLOW AND PARTICLE MOTIONOVER A ROUGH WALL
Kazumasa Matsumoto
Dept. of Civil and Earth Resources Engineering
Kyoto University
Kyoto 615-8540, Japanemail: matsumoto.kazumasa.85s@st.kyoto-u.ac.jp

Taka-aki Okamoto
Department of Civil Engineering
Meijo University
Nagoya 468-8502, Japanemail: okamotot@meijo-u.ac.jp

Michio Sanjou
Dept. of Civil and Earth Resources Engineering
Kyoto University
Kyoto 615-8540, Japanemail: michio.sanjou@water.kuciv.kyoto-u.ac.jp

ABSTRACT
To manage river environment, it is valuable to understandand evaluate the transport process of fine sediment and seeds ofplants in a natural river since it can be one of the direct causes ofdevelopment of riverine vegetation. In this study, two sets oflaboratory experiments were conducted in a flume with a bed
where hemispherical roughness elements were fixed in a
staggered array to mimic a natural river. First, to investigate thestructure of flow around the roughness elements, the velocity
distribution near the roughness layer was measured by using
particle image velocimetry (PIV). Results of PIV revealed
structure of the mean and turbulent flow field around roughness,
and also suggest that coherent motion of turbulent flows called
sweep or ejection might play a significant role in mass transport
process. Second, some particles were injected to the flow, andtheir motions near the rough bed were observed. Some
trajectories of a particle indicate that the bursting events in theroughness sublayer are responsible for particle motions aboveand between roughness elements.

a flume with a bed where hemispherical roughness elements
were fixed in a staggered array to mimic a natural river. First, toinvestigate the flow structure around roughness elements, thevelocity near the roughness layer was measured by using PIV.
Second, some spherical particles were added to the flow, andtheir motions near the rough bed were observed to investigate
influence of turbulent flows on particle transport process. Afterthese experiments, the results were compared with each other toreveal the interaction between the flow field and mechanism ofparticle transport.

2.

EXPERIMENTAL METHOD
Figure 1(a) shows a schematic view of the experimental
setup and the coordinate system. Experiments were conducted ina glass-made flume 10 m long, 0.40 m wide, and 0.50 m high.
To mimic a gravel bed, hemispherical roughness elements,
whose radius i.e. roughness k was 1.8 cm, were fixed in a
staggered array over a 7 m area of the channel bed. In this study,
two sets of experimental conditions are considered by changing
the depth of flow H, as shown in Table 1. In both cases, the bulk
mean velocity Um was set to 0.30 m/s. The Reynolds numbers
based on the mean velocity and flow depth 𝑅𝑒 ≡ 𝑈𝑚 𝐻/𝜈 were
24,000 and 36,000.
The particle image velocimetry (PIV) is one of the mosteffective ways to visualize velocity distribution (Okamoto et al.,2021). To measure two-component instantaneous velocities (i.e.
𝑢̃(𝑡) ≡ 𝑈 + 𝑢(𝑡) and 𝑣̃(𝑡) ≡ 𝑉 + 𝑣(𝑡)) by PIV, a 2.0 mm thicklaser light sheet (LLS) was generated with a 3.0 W YAG laser
source and projected into the channel. As shown in Figure 1(b),the lateral position of the LLS was at the center of the flume,
where crests and valleys of roughness elements were located. A
high-speed CCD camera (1280 pixel × 1024 pixel) at the side of
the channel was used to take illuminated flow pictures in themeasured cross-section. The size of the measurement area was
19 cm × 15 cm. The measurement area was located 3 m
downstream from the upstream edge of the rough bed region
where turbulence was fully developed.
In this study, particle motions around roughness were also
observed. Some particles were introduced to the flow and theirmotions were recorded by two video cameras (3840 × 2160
pixels) installed at the side and above the flume. The particles
were spherical, natural plant seeds with a mean diameter of 0.19
cm, specific gravity of 1.21 and settling velocity Vt of 5.2 cm/s.

1.

INTRODUCTION
Investigation of turbulent transport process of particles in an
open channel is one of the most important topics in a wide rangeof fields of engineering. When it comes to civil engineering, forexample, fine sediment and seeds of plants are conveyed by flow
and deposited to riverbed in a natural river. Aquatic vegetation
in a river channel plays an important role in determining thequality of riverine environment and the disaster risk of theirbasin. So, it is valuable to understand and evaluate the transport
process of particles in a natural river which can be one of thedirect causes of development of riverine vegetation.
The behavior of suspended particles in open channel flow is
known to be strongly affected by the coherent structure of
turbulent flows that develop near the bottom (Nino and Garcia,
1996; Cameron et al., 2020). It is well known that on a smoothwall, streaks of low momentum region induce the generation of
hairpin vortex, and then instantaneous upward and down ward
flows called ‘ejection’ and ‘sweep’ occur. Similarly, it has been
pointed out that coherent structure may be formed over a roughwall. On the other hand, there are still few studies on theinteraction between turbulence and behavior of suspended
particles in a rough-wall flow.
In this study, two laboratory experiments were conducted in1

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

(b)

Flow

x

Flow

H

z

LLS

Crest
LLS

YAG laser

Valley7.0 mHigh-speed
CCD camera

0.40 mFigure 1. Schematic views of (a) experimental setup and (b) arrangement of roughness elements.
Table 1. Experimental conditions.

(a)Um [cm/s]

H [cm]

u* [cm/s]

H/k

Re≡UmH/ν

30
30

8.0
12.0

4.0
3.6

4.4
6.7

24,00036,000Some of the particle trajectories were tracked over two sets ofconsecutive images. By combining horizontal (x-z) and vertical(x-y) trajectories obtained through the tracking procedure, sometime-series of three-dimensional positions of a particle (𝑢𝑝 (𝑡),𝑣𝑝 (𝑡) and 𝑤𝑝 (𝑡)) were calculated. In addition, PIV was also
conducted for the particle-laden flow to measure the flow
structure around ascending or descending particles.
(b)
3.

RESULTS

Mean and Turbulent Flow Structure
Results revealed structure of the flow field near the roughbed. Figure 2(a) shows the mean streamwise velocity profiles atthe crest (x/k = 1.0) and valley (x/k = 3.0) of roughness (shownin Figure 1(b)). The values of velocity at the two measurement
points are almost equal at each height except for the region near
the roughness. In the vicinity of roughness height (y/k ≈ 1), thestreamwise velocities at the crest are reduced due to the effect ofroughness, while those at the valley are relatively large. This
demonstrates that flow separates from the roughness surface justdownstream of the crest, where turbulence may be generated dueto the velocity shear.
In this study, the friction velocities 𝑢∗ were evaluated fromthe velocity profiles measured. It is known that the logarithmic
law holds for rough-surface flows as follows,〈𝑈〉 1
𝑦 − 𝑦0= ln ()+𝐵𝑢∗𝜅𝑘Figure 2. (a) Mean streamwise velocity profiles at the two
locations shown in Fig.1(b) (x/k = 1.0 and 3.0, H = 12.0cm), and (b) comparison of velocity profiles to the log law.
and 𝐵 = 8.9 and 7.4 , respectively. In both cases, the flow
velocity profiles were found to be in good agreement with thelogarithmic law in the range of 1.2 < 𝑦/𝑘 < 2.3. In this study,
this region is defined as the logarithmic layer, and the lower
layer (𝑦/𝑘 < 1.2) as the roughness sublayer. Raupach et al.,1991 defines flow field satisfying 𝑘 + > 70 as fully rough flow.
Thus, all cases in this study (𝑘 + = 720 and 650, respectively)
can be classified as this flow regime.
Figure 3 shows a contour map of time-averaged verticalvelocities 𝑉 around roughness. In this graph, the black arrows
denote time-averaged velocity vectors (𝑈, 𝑉), and the dark-grayareas and the light-gray one correspond to roughness elements(1), where 𝑦0 and 𝐵 are the position of the virtual origin and theconstant of the logarithmic law, respectively. 𝜅 is the vonKalman's constant, and in this study, 𝜅 = 0.41. The values of 𝑢∗ ,𝑦0 and 𝐵 were calculated by fitting the logarithmic law to themeasured velocity profiles. Figure 2(b) shows the velocity
distributions 〈𝑈〉(𝑦) for each case. The friction velocities for
𝐻 = 8.0 cm and 𝐻 = 12.0 cm are 𝑢∗ = 4.0 cm/s and 3.6 cm/s, respectively, and the other values are 𝑦0 = 0.86𝑘 and 0.83𝑘,

2

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

Figure 3. Contour map of mean vertical velocity 𝑉 (𝐻 =12.0 cm).

Figure 5. Contour maps of instantaneous Reynolds shear
stress – 𝑢𝑣 . Black arrows denote instantaneous velocity
vectors (𝑢̃, 𝑣̃) (𝐻 = 12.0 cm).

Figure 4. Vertical distributions of Reynolds shear stress−𝑢𝑣
̅̅̅̅ (𝐻 = 12.0 cm).
and an area behind roughness elements, respectively. Over theroughness (𝑦/𝑘 > 1.3), the values of 𝑉 are almost equal to zeroand the flow field seems homogeneous. In contrast, around andbelow the roughness height (𝑦/𝑘 < 1.3), remarkable positive
and negative values of 𝑉 are shown. At the roughness crests(𝑥/𝑘 ≈ 1,5), a pair of upward and downward flows is formed
along the wall surface, while in the cavity (3 < 𝑥/𝑘 < 4), a
downward flow intruding between roughness is observed. Thisis probably because drag force on streamwise flow by theroughness elements changes the flow direction. Although lateralvelocities were not measured in this experiment, not only thevertical flows but also lateral ones should exist in this region due
to the effect of the wall topography. Such heterogeneous velocity
field around and within roughness is called roughness sublayer(Nikora et al., 2001), where particle motions transported by flow
are expected to be significantly three-dimensional.
Such mean vertical flows are expected to partly affect thetransport of particles into and from roughness sublayer. At thesame time, since the magnitude of the wall-normal velocity issmaller than the settling velocity of particles 𝑉𝑡 , the transport
process around the rough wall seems to be strongly connected toturbulent structure as well.
Figure 4 shows vertical distributions of Reynolds shear
stress – 𝑢𝑣̅̅̅̅(𝑦) at the crest ( 𝑥/𝑘 = 1 , white circles) and thetrough (𝑥/𝑘 = 3, red squares) of the roughness. In both thepoints, the values of −𝑢𝑣
̅̅̅̅ are smallest near the water surface andFigure 6. Vertical distributions of quadrant Reynolds shear
stress 𝑅𝑆𝑖 at 𝑥/𝑘 = 3 (Valley, 𝐻 = 12.0 cm).

increase almost linearly as approaching the bottom, which is acommon tendency for an open channel flow. However, there isa significant discrepancy between the two graphs, especiallyaround the roughness (1 < 𝑦/𝑘 < 2). At the crest (𝑥/𝑘 = 1), theturbulent shear stress is steeply reduced in the vicinity of thebottom, which means production of turbulence is likely to be
restricted in this region due to drag force of the roughness
element. On the other hand, in the case of the trough (𝑥/𝑘 = 3),
the values of −𝑢𝑣
̅̅̅̅ are much larger than those in the case of thecrest. This indicates that just downstream of the crest ( 1 <𝑥/𝑘 < 3), turbulence is generated most actively in the flow since
there is a large velocity shear due to flow separation.
Next, the turbulent flow structure over the rough bed will befurther examined, which is expected to influence on the particle
transport processes. Figure 5 shows a contour map of
instantaneous Reynolds shear stress −𝑢𝑣 at a certain instance.
The black arrows in the figure denote instantaneous velocity
vectors (𝑢̃, 𝑣̃). It is well-known that the coherent motions of3

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

(b)

Figure 7. Example of the particle trajectories: (a) side view (𝑥 − 𝑦) and (b) top view (𝑥 − 𝑧) (𝐻 = 12.0 cm).
turbulent flows called ejection (𝑢 < 0, 𝑣 > 0) or sweep (𝑢 >0, 𝑣 < 0) are observed in an open channel flow with roughness
or vegetation (Bomminayuni and Stoesser, 2011). Occurrence ofsuch turbulent events can be found from the results of velocity
measurement by detecting positive values of – 𝑢𝑣 . In thiscontour, upward flow regions where the values of –uv are
positive exist apart from the rough bed ( 2 < 𝑦/𝑘 < 4 ),corresponding to ejections. At the same time, a downward flow
with high momentum, that is a sweep, occurs around and is about
to intrude into the cavity between roughness elements. Okamoto
et al., 2016 reported as to flow with submerged flexible
vegetation that the coherent motions including sweep andejection frequently penetrate into the upper part of a vegetation
patch. These observations suggest that the intermittent upwardand downward flows can be an important factor to determine
particle trajectories around and over the roughness sublayer.
To explore the mechanism of momentum transport within
and around the rough wall in more detail, a quadrant analysis
was conducted for instantaneous Reynolds stress −𝑢(𝑡)𝑣(𝑡)(Okamoto and Nezu, 2013). The quadrant Reynold stress 𝑅𝑆𝑖 isdefined as follows:
1 𝑇∫ {−𝑢(𝑡)𝑣(𝑡)}𝐼𝑖 (𝑡)𝑑𝑡
𝑇→∞ 𝑇 0𝑅𝑆𝑖 = lim

Coceal et al., 2007. Thus, it is necessary to understandrelationship between turbulent structure and transport process ofparticles over a rough wall.

Influence of Turbulence on Particle Motions
Figure 7 shows an example of the particle trajectories invertical and horizontal planes observed in this experiment. The
particle fell down outside the roughness sublayer, and repeatedsmall upward motions and downward ones several times aroundthe roughness height (1 < 𝑦/𝑘 < 1.5), which corresponds to (1)in the photos. It seems that this motion was caused by the mean
vertical flows formed along the roughness surface shown in
Figure 3 or by coherent motions of flows in the roughness
sublayer illustrated in Figure 5 and 6. After the faster motion
above the roughness height (1), the particle passed through theroughness elements with slower speed and finally stopped,
which corresponds to (2) and (3). This implies that unless any
sufficient upward force by fluid acts on a particle floating aroundthe roughness height, it falls into the cavity of roughness andbecomes easy to be trapped between roughness elements.
Moreover, it was also observed in another example of theparticle trajectories that a particle once trapped was resuspended and flew out of the rough wall. This observationsuggests that such an intermittent motion in the wall may beconnected to the momentum transport process by sweep andejection indicated in Figure 6.
Figure 8 shows a series of instantaneous velocity fields whena particle is ejected from the cavity of roughness and ascending
to the outer flow region. Here, contour and arrows show
distribution of instantaneous Reynolds stress -uv(t) and velocity
fluctuation vectors (u, v), respectively. The white circle is the
position of a particle at the moment (𝑡 = 0.30 s), and the black
dashed lines correspond to the particle trajectory before and after
the instant.
The present observation indicates the coherent structure of
turbulent flow is likely to cause particle entrainment from the(2), where 𝐼𝑖 = 1 if (𝑢, 𝑣) exists in the i-th quadrant, otherwise 𝐼𝑖 =0. Figure 6 shows the vertical profiles of quadrant Reynolds
stress 𝑅𝑆𝑖 at the valley ( 𝑥/𝑘 = 3.0 ). Around the roughness
height, contributions of the 2nd quadrant (u < 0, v > 0: ejection)and the 4th quadrant (u > 0, v < 0: sweep) to Reynolds shear
stress exceed those of the other quadrants. This implies that thecoherent structure develops and plays a significant role in massand momentum transport in this region. What is more, this graphindicates that ejection contributes to Reynolds stress more thansweep near the water surface while the 4th quadrant event ismore active around roughness. These tendencies agree withresults of numerical analysis of flow over a cubical roughness by4

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022(a) 𝑡 = 0 s (The particle exists within roughness.)(b) 𝑡 = 0.3 s (The white circle denotes the particle position.)
Figure 9. Histograms of particle step-length 𝐿 for 𝐻 =8.0 cm and 12.0 cm.
and 101. Here, the values of 𝐿 is divided by the diameter ofhemispherical roughness elements, 𝐿/𝐷, and the average values
𝛬/𝐷 were 4.5 and 2.9, respectively. The distribution of 𝐿/𝐷covers a wide range of values from one to more than ten in eachcase. This variation in the values might be attributed to theoccurrence of instantaneous upward flows, that is to sayejections. Comparing the two cases, it can be observed that the
averaged step-length is longer in the lower depth case (𝐻 =8.0 cm ) than that in the other case. This may be because
turbulence is generated more actively in the former case due tolarger friction velocity and particles are lifted up by upward flow
around roughness for a longer period of time.
In the end, a conceptual model of particle transport process
over a rough wall obtained from the results of this study is
proposed. As well as ejection, sweep may affect the particle
transport within roughness since it is the most significant eventas to momentum transport in this region, as shown in Figure 6.
Van Hout, 2013 pointed out that in open channel flow over asmooth wall, a particle on the wall gets suspended just after ahigh-speed fluid reaches the wall. This mechanism of the particle
entrainment might be applied to the rough wall flow although its
flow structure is quite different from that of a smooth wall.
However, most of the flow field in the cavity of roughness could
not be measured and still unrevealed in this experiment. Theinteraction between coherent structure and particle transport
process within the rough wall should be explored in the future
work. Just after the particle lift-up, if upward transport of lowspeed fluid occurs around over the roughness height, a particle
tends to be lifted up and transported over roughness for a long
period. Otherwise, a particle cannot ascend high enough to reachthe outer region of roughness and go back into the cavity quickly.

Figure 8. Contours of instantaneous Reynolds stress −𝑢𝑣(𝑡)with velocity fluctuation vectors (𝑢, 𝑣). The dashed blacklines denote the particle trajectory before and after each
moment (𝐻 = 8.0 cm).
rough wall. In Figure 8(a), downward flow with high momentum
occurs just above roughness and penetrates into cavity of therough wall. And 0.13 s after this moment, the particle emerged
from roughness and started to ascend into the outer flow. As
shown in Figure 6, transport of the high-momentum flow issignificant near and maybe below the roughness height (y/k ≈ 1).
So, sweep (u > 0, v < 0) seems to be a key factor to evoke particle
entrainment and lift-up from roughness sublayer into the flow.
In other words, the bursting phenomena over a rough wall may
play a significant role in determining the transport process ofparticles within and around the roughness layer.
Figure 8(b) illustrates that an instantaneous upward motionof flow with low momentum (u < 0, v > 0) is occurring in thevicinity of the ascending particle. Also, at this moment, theejections occur not only just around the particle, but also in awide area above the roughness. This implies that the particle
upward motion starting near the roughness height may occur if
the particle gets captured in the low momentum region (LMR)
above roughness and instantaneous upward flow.
To evaluate length scale of particle motions over the roughbed, step lengths of particles were calculated from the
trajectories observed in this experiment. In this study, the lengthis defined as a distance that a particle travels since it starts tomove in the streamwise direction until it stops between
roughness elements (Liu et al., 2019). Figure 9 shows histogramsof step length 𝐿 for all cases (𝐻 = 8.0 cm and 𝐻 = 12.0 cm).
The numbers of samples obtained in the experiments were 81

4.

CONCLUSIONSIn this study, the results of PIV revealed the mean andturbulent flow structure over a hemispherical rough wall.
Topography of the wall causes flow separation from theroughness surface and large velocity shear around the roughness
height. This strong shear generates turbulence and forms
coherent structure of turbulent flows, which contributes to massand momentum exchange within and around the roughness
sublayer. Moreover, observation of particle motions and theircomparison to the results of velocity measurement show that the512th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
bursting phenomena, including upward and downward flows
called ejection and sweep, can be a trigger of the suspension
process of particles within and above a rough bed.

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