flow patterns and turbulence structures in a scour hole downstream of a submerged weir

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Flow patterns and turbulence structures in a scour hole

downstream of a submerged weir

Dawei Guan1; Bruce W. Melville, M. ASCE2; and Heide Friedrich3

Abstract:

Scouring downstream of submerged weirs is a common problem resulting from the interaction of the

three-dimensional turbulent flow field around the structures and the mobile channel bed. This paper

presents the distributions of flow patterns, bed shear stresses and turbulence structures in the approach

flow and the scour hole downstream of a submerged weir. The experiments were conducted under the

clear water scour condition for an equilibrium scour hole. The experimental results show that the flow

structures are considerably changed by the presence of the structure. A large recirculation zone and a

flow reattachment region are formed downstream of the submerged weir. Strongly paired cellular

secondary flows are observed in the scour hole. The turbulence structures ahead of the recirculation

zone govern the dimensions of the scour hole.

CE database subject headings: submerged weir, scour, flow pattern, bed shear stress, turbulence,

secondary flows

1PhD student, Dept. of Civil and Environmental Engineering, The University of Auckland, Private bag 92019,

Auckland 1142, New Zealand. E-mail: [email protected]

2Professor, Dept. of Civil and Environmental Engineering, The University of Auckland, Private bag 92019,

Auckland 1142, New Zealand. E-mail: b.melville@auckland. ac.nz

3Lecturer, Dept. of Civil and Environmental Engineering, The University of Auckland, Private bag 92019,

Auckland 1142, New Zealand. E-mail: [email protected]

Journal of Hydraulic Engineering. Submitted August 9, 2012; accepted July 16, 2013; posted ahead of print October 3, 2013. doi:10.1061/(ASCE)HY.1943-7900.0000803

Copyright 2013 by the American Society of Civil Engineers

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Introduction

Submerged weirs (or dams) are low head hydraulic structures constructed in the channel of a

waterway for the purpose of limiting excessive channel bed degradation, raising the upstream water

level and reducing the flow velocity. The flow depth on the weir crest is deep enough for barges to get

through, even during dry seasons. Thus once built, such weirs will improve river navigation

conditions. In sloping, straight channels, several consecutive submerged weirs can be constructed if

necessary. The effect of a submerged weir is to suddenly change the channel bed elevation. This

sudden change of bed elevation at a submerged weir not only influences the flow pattern but also

results in local scour downstream of the structures.

For practical purposes, the most important scour parameters are the scour hole dimensions (i.e.

maximum scour depth ds and length ls) at the equilibrium phase. Therefore, maximum scour depth

and length have been widely studied, providing a selection of empirical equations (Bormann and

Julien 1991; D'Agostino and Ferro 2004; Marion et al. 2004; Chen et al. 2005; Marion et al. 2006) to

be applied to the design of submerged weirs. However, there are only a few studies on the flow

structure in the scour hole downstream of submerged weirs. Ben Meftah and Mossa (2006) studied

flow turbulence in an equilibrium scour hole downstream of one weir in a sequence of weirs. Bhuiyan

et al. (2007) were the first investigators to detect the three-dimensional turbulence structure

downstream of a W-weir in a meandering channel.

In order to precisely predict the scouring downstream of submerged weirs, it is important to develop a

good understanding of the turbulence flow structures around such hydraulic structures. The present

study aims to obtain information on flow patterns, boundary shear stresses, turbulence intensities and

Reynolds shear stresses in the scour zone. The experiments were confined to the clear water scour

condition and the scour hole downstream of one single submerged weir at the equilibrium phase.

Experiments

Experimental set-up



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The experimental work was conducted in a 12 m-long, 0.38 m-deep and 0.44 m-wide glass sided,

tilting flume (Figure 1) in the Hydraulic Laboratory of The University of Auckland. At the upstream

end of the flume, the water is fed into a mixing chamber and enters the flume through a honeycomb

flow straightener, which effectively eliminates any rotational flow component induced in the return

pipelines, so that uniform flow is obtained. At the downstream end, sediment from the scour hole is

trapped in a separated hopper-like sump, from where pumps return the flow to the inlet end of the

flume.

Figure 1

The sediment used in the experiments was coarse sand, with median diameter d50= 0.85 mm and

relative submerged particle density Δ=1.65. The sediment size distribution was near uniform, with a

standard deviation σg=1.3. The weir used in the experiments was a 10 mm-thick rectangular plastic

plate, with the same width as the flume. In the experiments, the weir was inserted into the bed with a

40mm protrusion from the initial flat bed and located 4.5 m from the outlet of the flume. During the

test the approach flow depth y and tail water depth yt were maintained at 150 mm.

The upstream flow was fully developed in the experiment. The average approach flow velocity U0 for

this experiment was estimated from the vertical distribution of approach flow velocities on the

centreline of the flume in front of the weir, when the uniform flow was achieved as shown in Figure 2.

The approach average flow velocity U0 = 0.296 m/s was determined as the velocity at 0.368y (Yalin

1992). The average approach flow shear velocity, smu /014.0* , was estimated from the

logarithmic form of the velocity profile (Figure 2); the average approach flow critical shear velocity

cu* = 0.021 m/s was determined using the Shields diagram for the respective particle size (Melville

1997). Thus, the ratio of bed shear to critical shear velocity for the approach flow ( 67.0** cuu )

was calculated. The corresponding Reynolds number ( UyRe ) and Froude number

( gyUFr ) were 44,400 and 0.24, respectively.

Figure 2



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Bed profile and velocity measurement

Theoretically, for clear water scour the equilibrium of the scour process should be defined as the

condition when the dimensions of the scour hole do not grow with time. However, even in small scale

laboratory experiments, it may take several days or weeks to attain equilibrium conditions (Melville

and Chiew 1999). Thus it is important to conduct continuing bed profile measurements to understand

the scour process and ensure the scour equilibrium phase is obtained. The three-dimensional scour

geometry downstream of the weir was measured throughout the experiment using Seatek’s Multiple

Transducer Arrays (MTAs) as a function of time. The instrument is an ultrasonic ranging system,

comprising 32 transducers, which can detect the distance from the sensors to reflective objects. The

measuring accuracy of the system is approximately ± 1 mm. The detailed description of this device

can be found in Friedrich et al. (2005). During the test, only 27 transducers were employed, among

which 2 transducers were used for water surface measurements, with a 125 mm interval. The

transducers were mounted in a rectangular grid (see Figure 3) on a carriage that can be moved along

the top rail of the flume. The system was operated at 5Hz and allowed measurement of the whole

scour region in about 1 minute. Taking into account the detection of suspended sediment particles, the

outliers of the raw bed profile data were filtered in the data postprocessing. The procedure of the

programme was to use 3σ as the threshold for the outlier detection (well known as the 3-σ rule),

where σ is the standard deviation derived from the original data set. The filtered data were then

analysed by spline interpolation procedures. The final resolution of each processed bed profile is 10

mm × 10 mm.

Figure 3

At the start of the experiment, the sediment bed was levelled with a scraper after setting the weir. The

flume was then filled to the desired water depth. The filling process took place slowly to avoid

disturbance around the weir before the actual experiment. Water temperature was measured in order

to set the initial experimental parameters for the MTAs. After starting both pumps with the required

settings, the water depth and the slope of the flume were adjusted, to get uniform flow for the



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approach flow upstream of the weir, whilst the flow depth downstream of the weir was controlled by

adjusting the location of an overflow pipe in the sump. When uniform flow was obtained, bed profiles

and water surface were measured with 27 MTAs sensors as a function of time. The scour process

lasted around 23 days until the scour hole reached equilibrium. The time evolution of maximum scour

depth and final scour geometry are shown in Figures 4 and 5. As shown in Figure 4, the temporal

development of the scour hole experiences three stages. The maximum scour depth ds develops very

quickly during the first day, then progresses at a decreasing rate over the following 19 days, as it

approaches the equilibrium stage. During the final stage, the values of ds fluctuated around an average

value of 151 mm, which is taken as the maximum scour depth at the equilibrium phase (dse) in this

study.

Figures 4 and 5

After the scour hole reached equilibrium, the flow field was measured using a three component

downward facing Nortek Vectrino+ acoustic velocimeter. The probe measures the velocities 50mm

beneath the acoustic transmitter, which must be submerged, and consequently velocities within the

first 55 mm depth beneath the water surface were not measured. Measurements were taken along the

centreline longitudinal section and on three other transverse cross sections. The velocimeter was used

with a sampling rate of 200 Hz. The sampling volume was cylindrical, having 6 mm diameter and an

adjustable height varying from 1 to 7 mm. As suggested by Dey et al. (2011), the sampling height was

set as 1 to 2.5 mm in the near bed zone to avoid interfering with sediment particles; a 4 mm sampling

height was used in the upper flow zone of the centreline longitudinal section, and 7 mm for the three

other transverse cross sections. The closest measuring location to the bed was always 5 mm from the

bed surface. At each measurement point, 2 min samples were collected. Throughout the experiments,

the signal-to-noise (SNR) ratio for each beam was maintained above 15. After the experiments were

completed, the output data from the velocimeter were filtered using WinADV software (Wahl 2000).

The filter was set to remove spikes (using the phase-space threshold method of Goring and Nikora

(2002)) and data with low correlation (Minimum COR < 70). Although the best configurations for the

velocimeter were carefully chosen during the experiments, the results for some locations at 8.5 to 10



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cm above the bed in the centreline longitudinal section still had relatively high noise and low

correlations. These locations are called velocimeter weak spots or “velocity holes”, which are mainly

caused by the return signal interference from the boundary (Martin et al. 2002). After filtering, around

55% of data for these weak spots were of good quality and therefore retained. For all other

measurement points, more than 80% of the data were retained after filtering. The velocity power

spectrum for the filtered data points was examined with Kolmogorov’s “-5/3” law, conforming that

the data presented in this paper are of high quality.

Results and Discussion

2D velocity distribution

Figure 6

Figure 6 shows the distribution of time-averaged velocity vectors on the centreline longitudinal

section. The velocity vectors are determined from the average values of the stream-wise and vertical

velocity components. It can be seen that the upstream flow is quite uniform even at the equilibrium

stage. When this uniform flow approaches the submerged weir, the flow pattern is altered by the

sudden change of bed elevation. The approach flow is accelerated at the crest of the weir and a weak

back flow is created immediately upstream of the weir. At the upstream base of the weir, a small

scour hole (around 20 mm depth) was observed, which was produced by weak vortices, generated by

the interaction of the approach flow and the associated back flow. Downstream of the weir, a large

recirculation zone developed (see Figure 6). Immediately downstream of the weir, vortices can be

clearly observed, indicated by a recirculating movement of sediment close to the weir. For other parts

of this zone, the occasionally random movement of sediment particles is seen at the equilibrium phase

of scouring. At the rear of the recirculation zone, the main flow reattaches to the bed, creating the

‘flow reattachment region’ (Figure 6). Inside this region, the flow is considerably turbulent and the

velocities are quite small. The observed maximum scour depth point (1.06 m away from the weir) is

located close to the end of this region. When the flow passes the maximum scour depth cross section,



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no obvious reverse velocities can be seen on the centreline longitudinal section, and a relatively

uniform flow is redeveloped downstream of the end of the scour hole.

Figure 7(a, b, c)

The time-averaged velocity vector distributions in 3 transverse cross sections (here taken as section U,

M and D respectively, see Figure 5), which are located at X=-0.50 m, 1.06 m, and 2.75 m respectively,

are presented in Figure 7. These vectors are determined from the mean velocities of the transverse and

vertical velocity components. As indicated in Figure 7, secondary flows develop at all three cross

sections. For the U and D cross sections (see Figures 7a, 7c), especially for the former one, the

magnitude of the velocity vectors is relatively small compared with those in the maximum depth cross

section M (Figure 7b). This is driven by cross-sectional anisotropic turbulence (Prandtl 1952), the

strong secondary flows observed in the maximum depth cross section M (Figure 7b), being

categorized as ‘Prandtl second kind’ (driven by turbulence). The secondary flows are characterized by

paired circular flow cells, which are quasi-symmetrically located at both sides of the centreline sand

ridge. A similar flow pattern can be seen in Figure 7c. Figure 7c also shows non-symmetry in flows,

this being related to the non-symmetrical bed surface. The pattern of cellular secondary flows and the

associated observed sand ridge in this research is consistent with the observations and theory of Nezu

et al. (1984; 1988). These secondary flows have a significant effect upon the development of the scour

hole and the final bed geometry. They also account for the formation of the centreline sand ridge and

help to explain the deepest point of scour hole being found close to the side wall, rather than on the

centreline of the flume. The ratio of the maximum scour depth on the centreline to the maximum

scour depth in the scour hole is 84% (127 mm / 151 mm), which implies that the effect of secondary

flows cannot be ignored when studying clear water scour at submerged weirs in a relatively deep flow.

It should be noted that the flow aspect ratio (flume width/flow depth) at section M is around 1.5,

which means side wall effects also contribute to the formation of secondary flows in the scour hole

and to the scour hole geometry. In a large river, the flow aspect ratio is larger, which might increase

the number of secondary flow cells and change the scour hole geometry.



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Bed shear stress

At the equilibrium stage of clear water scour, the stability of sediment particles in the scour hole is

based on the equilibrium conditions of the forces acting on them, which can be simplified as a balance

of flow drag force FD, lift force FL, and submerged weight of sediment particles FG. Accordingly, the

critical shear stress 'c of sediment particles resting on a bed, sloping in the stream-wise direction, can

be defined by the following equation:

tantan

1cos'

c

c

(1)

where 'c is critical shear stress on a sloping bed, c is critical shear stress on a horizontal bed

(calculated as 2*cu =0.45 Pa), θ is bed slope (measured from an horizontal datum), φ is submerged

angle of repose of sediment (taken as 36˚, as measured in this study). A complete analysis of incipient

sediment motion on non-horizontal slopes can be found in Chiew and Parker (1994). Inside the

equilibrium scour hole, reversed velocity vectors are observed on the upstream slope (see Figure 6).

According to past research (Kim et al. 2000; Biron et al. 2004; Pope et al. 2006), four common

methods can be used for the estimation of bed shear stress with experimental data: (a) reach average

method, (b) current velocity profiles (Law of the Wall, or Log Profile method), (c) Reynolds stress

measurement, and (d) TKE (Turbulence Kinetic Energy) method. The assumptions, suitability and

limitations of these four methods have been critically reviewed by Kim et al. (2000) and Biron et al.

(2004). Considering the applicability of these four methods, two of them are employed in this study,

namely Reynolds shear stress measurement and TKE method. The Reynolds shear stresses, zx , , are

defined as '' wu . The turbulent kinetic energy density, E, is calculated from:

222 '''21

wvuE (2)



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where 'u , 'v , 'w are fluctuation velocity components along the downstream, transverse and vertical

directions, respectively. A simple relationship between TKE and bed shear stress has been formulated

as CE0 (Soulsby 1981), where 0 is bed shear stress and C is an empirical coefficient. The

empirical factor C was found to be 0.20 (Soulsby 1981), while 0.19 has been adopted by others

(Stapleton and Huntley 1995; Thompson et al. 2003; Pope et al. 2006) and has been found to apply to

a complex flow fields (Biron et al. 2004). Therefore, C= 0.19 has been used in this study. The critical

question of obtaining bed shear stress estimates using single point measurements is how to determine

the appropriate measurement height above the bed. According to the recommendation of Biron et al.

(2004), the best option for using single point measurements to estimate bed shear stress is to position

the instrument at around 10% of the flow depth. Then, it is above the thickness of the roughness layer

and is less affected by unexpected increases in SNR or Doppler noise that may occur closer to the bed

(Finelli et al. 1999; Kim et al. 2000). The measured points for estimating bed shear stresses in this

study were all set at 10 mm above the bed. The measured and calculated values for these near bed

points were used for direct estimation of bed shear stress.

Figure 8

Threshold bed stresses, measured Reynolds shear stresses and calculated bed stresses were obtained

and a comparison of the experimental bed shear stresses and local threshold bed shear stresses

obtained from Equation (1) is presented in Figure 8. It should be noted that the values of critical bed

shear stresses on the upstream slope of the scour hole are negative, which corresponds to the direction

of the bottom reverse flow, while in Figure 8 only absolute values are used for comparison. It can be

seen that for the approach flow and near the end of the scour hole, bed stresses obtained from the

observed Reynolds shear stresses and from the TKE method do not exceed the threshold. This is

consistent with the experiment being conducted under conditions of no general sediment transport.

Although reverse flows are observed on the upstream slope of the scour hole, the values of measured

Reynolds shear stresses are still positive in this region, which is consistent with the velocity gradients

still being positive close to the bed (see Figures 6 and 8). For this case, estimation of bed shear stress

from near bed Reynolds shear stress measurements may be unreliable, because the measurement



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equipment is incapable of acquiring data in the negative velocity gradient layer, which is very thin

(less than 10 mm) and just above the bed. At the upstream end of the recirculation zone, the

experimental bed stresses considerably exceed the absolute threshold values, which is in agreement

with our experimental observations. In this area, frequent sediment recirculating movements were

observed during the experiment, including at equilibrium, but they did not result in deepening of the

scour hole. Elsewhere within the scour hole, measured Reynolds shear stresses are around or below

the threshold and calculated bed shear stresses are slightly greater than the threshold values.

Considering the form of equation (2), the TKE method takes into account the three dimensional

velocity fluctuations, thus it is less applicable when used for two-dimensional estimation, especially

when secondary flows exist. This may account for the over estimation in the scour hole. On the

downstream slope of the scour hole, near bed velocity accelerates as flow depth decreases, which

causes a reduction to the velocity gradient. As a result, the measured Reynolds shear stresses are very

close to zero and are below the threshold values.

Turbulence Characteristics

Turbulence intensities

Contours of the turbulence intensity distributions for the longitudinal direction and three transverse

cross sections (U, M and D) are presented in Figures 9 and 10, respectively. The contour values for

the downstream, transverse and vertical directions are calculated from:

0

2'

Uu

TIu , 0

2'

Uv

TIv , 0

2'

Uw

TIw

(3)

where U0 is the average approach flow velocity. For the centreline longitudinal section, the turbulence

intensities for all three directions show a very similar distribution (see Figures 9a, 9b, 9c). More

specifically, the values of TIu, TIv and TIw upstream of the weir are rather small compared with those

in the scour hole. The peak values are found immediately downstream of the weir and above the

original bed level. Downstream of the locations of the peak values, the turbulence intensities are



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damped, as the distance from the weir increases. It is important to note that the positions where the

peak values of turbulence intensities occur are found at the upstream end of the recirculation zone.

Furthermore, the measurements of the turbulence intensities in the centreline longitudinal section

show the turbulent flow to be anisotropic, with ''' 7.12.1 wvu .

Figure 9

Figure 10 shows turbulence intensity distributions in three transversal cross sections (U, M and D).

For section U (see Figures 10a, 10b and10c), although the turbulence intensities are very small

compared with those in the scour hole, a trend can be observed. The areas of very low turbulence

intensities correspond with areas of high stream-wise velocities. The same can be observed in straight

natural rivers. For section M (see Figures 10d, 10e and 10f), turbulence intensities are highest around

5 cm above the original bed level and reduce as the distance from the bed decreases. The decrease of

turbulence intensities closer to the bed, which is in line with the dissipating trend of upstream

turbulence intensities, is caused by the damping effect of bed boundaries. With respect to section D

(see Figures 10g, 10h and 10i), turbulence intensities in all directions are damped, resulting in

considerably smaller values, less than those in the scour hole, whilst still exceeding values observed in

the upstream cross section U. The distributions of TIu, TIv and TIw show a certain degree of

irregularity, compared to the distributions in the upstream cross section.

Figure 10

The distribution of normalized TKE, which is calculated from 20UE , in the centreline longitudinal

section, is shown in Figure 11, and highlights a similar pattern to that observed for turbulence

intensities. As previously reported (Bradshaw et al. 1967), TKE reflects the energy extracted from the

mean flow by the motion of the turbulent eddies. Thus it is possible to conclude that the strongest and

largest eddies are developed at the upstream end of the recirculation zone.

Figure 11

Reynolds shear stress



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Figures 12 and 13 present the distributions of normalized Reynolds shear stresses for the centreline

longitudinal section and three transverse cross sections (U, M and D). The Reynolds stresses values

here are calculated from:

2*

''

uwu

uw , 2*

''

uvu

uv , 2*

''

uwv

vw

(4)

where *u is the average approach flow shear velocity. It can be seen from Figure 12 that the largest

Reynolds shear stresses uw occur immediately downstream of the weir, with values dissipating in the

scour hole and further downstream. As supported by the distribution of TKE (see Figure 11) and the

distribution of uw (see Figure 12) in the centreline longitudinal section, it is possible to infer that the

large magnitude of turbulence structure on the upstream slope of the scour hole governs the scour hole

size (maximum scour depth and length). This is in agreement with work undertaken by Ben Meftah

and Mossa (2006).

Figure 12

As seen in Figures 13a, 13d and 13g, Reynolds shear stresses uw and uv are dominant, while vw

values are relatively small in all three cross sections. It also can be seen that the highest Reynolds

shear stress values are found near the bottom of the sections, for both U and D, whilst for section M

they are observed around the original bed level. Thus bottom friction at sections U and D was the

dominant factor to account for shear stress distributions, but for section M the distributions of

Reynolds shear stresses are strongly dependent on upstream dissipating shear stresses.

As discussed above, secondary flows are observed at all three sections (U, M, and D, see Figure 7).

The values of uv in Figures 13b, 13e, and 13h also reveal secondary flows. Negative uv values are

found on the left side of the flume centreline, while positive values are observed on the right side, as

seen in Figure 13e, showing a certain degree of symmetry. Similar patterns can be seen in Figures 13b

and 13h. Since the values of uv and vw should be zero when no secondary flows exist, the Reynolds



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shear stress values not only reveal the concentration of turbulence, but also indicate the intensities of

secondary flows.

Figure 13

Conclusions

The results of an experimental study of flow patterns, bed shear stresses and turbulence structures in

the approach flow towards a submerged weir, and the resulting scour hole are presented. The

experiments were undertaken in clear water scour conditions in a laboratory flume. The equilibrium

scour hole condition was obtained. The three-dimensional flow field data was obtained by a Nortek

Vectrino+ acoustic velocimeter.

The results show that the presence of a submerged weir considerably changed the flow structure.

Along the flume centreline longitudinal direction, a recirculation zone and a flow reattachment region

are developed. The turbulence structures at the upstream end of the recirculation zone govern the

dimensions of the scour hole, as indicated by the observed maximum turbulence intensities, TKE and

Reynolds shear stresses on the upstream slope of the scour hole. The location of maximum scour

depth is found at the rear of the flow reattachment region and close to the left flume glass wall. The

observed Reynolds shear stress near the bed and the calculated bed shear stresses from TKE method

are larger than absolute values of critical bed shear stresses immediately downstream of the weir, and

smaller than critical bed shear stresses elsewhere in the scour hole and further downstream.

For the transverse direction, strongly paired cellular secondary flows are observed in the scour hole. A

certain degree of symmetry of Reynolds shear stress uv distributions at cross sections are observed,

which directly account for the formation of secondary flows. These secondary flows have a significant

effect upon the development of the scour hole and the final bed geometry. Their effect should be

considered in the study of scour at low head structures in a relatively deep flow.

Acknowledgements



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The authors would like to thank China Scholarship Council (CSC) for the financial support of this

research.



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15

Notations

C empirical factor used in TKE method for calculating bed shear stress

d50 median diameter

ds maximum scour depth

dse maximum scour depth at the equilibrium phase

E turbulence kinetic energy density

FD flow drag force exert on a sediment particle

FG submerged weight of a sediment particle

FL lift force on a sediment particle

g gravity

TIu, TIv, TIw turbulence intensities along the downstream, transverse and vertical directions

respectively

ls maximum scour length

t scour time

u, v, w mean velocity components along the downstream, transverse and vertical directions

respectively

'u , 'v , 'w fluctuation velocity components along the downstream, transverse and vertical

directions respectively

cu* average approach flow critical shear velocity

*u average approach flow shear velocity

U0 average approach flow velocity

y approach flow depth

yt tail water depth

0 bed shear stress

c critical shear stress on a horizontal bed

'c critical shear stress on a sloping bed



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uw , uv , vw normalized Reynolds shear stresses

θ bed slope

φ submerged angle of repose of sediment

c critical Shields parameter

ρ water density

ρs sediment density

Δ relative submerged particle density

σg standard deviation

ν kinematic viscosity of fluid, considered as 1×106 m2/s



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17

References

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Figure Captions

Figure 1. Schematic display of the flume

Figure 2. Approach flow velocity profile (Semi-logarithmic coordinate system)

Figure 3. Sensor arrangement for measuring water surface and bed profiles

Figure 4. Temporal development of the maximum scour depth

Figure 5. Scour geometry at the equilibrium phase, contours in mm

Figure 6. Velocity vectors distribution in the centreline longitudinal section

Figure 7. Velocity vectors distribution in the U, M and D cross sections

Figure 8. A comparison of estimated shear stress and threshold shear stress along the centreline

upstream and downstream of the submerged weir

Figure 9. Turbulence intensity distributions in the centreline longitudinal section, downstream (a),

transverse (b), and vertical directions (c), respectively

Figure 10. Turbulence intensity distributions in the U, M and D cross sections

Figure 11. TKE distribution in the centreline longitudinal section

Figure 12. Normalized Reynolds shear stress distribution in the centreline longitudinal section

Figure 13. Normalized Reynolds shear stresses distributions in the U, M and D cross sections



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�

1

10

100

1000

0.22 0.24 0.26 0.28 0.3 0.32 0.34

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water surface level 150mm

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0

40

80

120

160

0 5 10 15 20 25

d s(m

m)

t (day)

dse

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Longitudinal Direction (m)

Tran

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(mm

)

0

00

0-2

0

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0-2

0

-40

-60 -8

0

-100

-120

-140

-140

-120

-100

-80

-60

-40

-20

0

20

-0.5 0 0.5 1 1.5 2 2.5 3-200

-100

0

100

200Section DSection MSection U




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Flow reattachment region




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150(b) Section M

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50

100

150(c) Section D


0

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100

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Ver

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0.02 m/s 0.02 m/s




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200


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1

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Flow

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Scour Hole




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0.090.1 0.10.11

TIv

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0.070.07

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0.08

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0.0380.035

0.04

0.04

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-100

-50

0

50

100

150

Ver

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dis

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m)

0.34

0.36

0.36

0.32

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0.28

0.26

0.28

0.26

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0.280.24

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0.220.2

0.2

0.18

0.16

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0.10.12

0.16 0.18

0.16

Section M

-150 -100 -50 0 50 100 1500

50

100

150


Ver

tical

dis

tanc

e (m

m)

0.15 0.120.1

0.12

0.10.085

0.10.15

0.1

0.10.085

-150 -100 -50 0 50 100 150Transversal distance (mm)

0.1 0.10.12 0.1 0.150.12

0.10.120.18 0.180.120.1 0.1

0.1


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0.040.05

0.05

0.050.04 0.040.035

Section D(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

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-0.5 0 0.5 1 1.5 2 2.5

-100

0

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200


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0.15

0.12 0.10.08

0.06 0.040.02

0.060.08

0.10.15

0.06




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0

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12

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66

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12 1 2 1

0

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0

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0

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-1 1

2

0

Section M

0

50

100

150V

ertic

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ista

nce

(mm

)�

uw

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0.70.50.5

0.30.2 0.3 0.2

0.080.08

0.7

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0.5

0.5

0.3

0.1

-0.1

-0.3 -0.1

0

0 0

-0.1

-0.3

0.30.1

�vw

-0.08-0.05 00

0.03

0.060.03 0 0

0 0.030.06 0

-0.05

0

0.03

Section U

-150 -100 -50 0 50 100 1500

50

100

150


Ver

tical

dis

tanc

e (m

m)

0.21 0.6

0.6 0.611.51

0.2

1

0


0.2

00.2

0

0.50.80.8

0.5

0.2 0

-0.5


0.15 0 0

0

0

-0.15-0.15-0.3

0

0.3

Section D(a) (b) (c)

(g) (h) (i)

(f)(e)(d)

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flow patterns and turbulence structures in a scour hole downstream of a submerged weir

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