Flow Patterns and Turbulence Structures in a ScourHole Downstream of a Submerged WeirDawei 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 turbulentflow field around the structures and the mobile channel bed. This paper presents the distributions of flow patterns, bed shear stresses, andturbulence structures in the approach flow and the scour hole downstream of a submerged weir. The experiments were conducted under theclear-water scour condition for an equilibrium scour hole. The experimental results show that the flow structures are considerably changed bythe 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 governthe dimensions of the scour hole. DOI: 10.1061/(ASCE)HY.1943-7900.0000803. © 2014 American Society of Civil Engineers.

Author keywords: Submerged weir; Scour; Flow pattern; Bed shear stress; Turbulence; Secondary flows.

Introduction

Submerged weirs (or dams) are low-head hydraulic structures con-structed in the channel of a waterway for the purpose of limitingexcessive channel-bed degradation, raising the upstream waterlevel, and reducing the flow velocity. The flow depth on the weircrest is deep enough for barges to get through, even during dryseasons. Thus, once built, such weirs will improve river navigationconditions. In sloping, straight channels, several consecutivesubmerged weirs can be constructed, if necessary. The effect ofa submerged weir is to suddenly change the channel-bed elevation.This sudden change of bed elevation at a submerged weir notonly influences the flow pattern, but also results in local scourdownstream of the structures.

For practical purposes, the most important scour parametersare the scour-hole dimensions (i.e., maximum scour depth ds andlength ls) at the equilibrium phase. Therefore, maximum scourdepth and length have been widely studied, providing a selectionof empirical equations (Bormann and Julien 1991; D’Agostino andFerro 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 holedownstream of submerged weirs. Ben Meftah and Mossa (2006)studied flow turbulence in an equilibrium scour hole downstreamof one weir in a sequence of weirs. Bhuiyan et al. (2007) were

the first investigators to detect the three-dimensional turbulencestructure downstream of a W-weir in a meandering channel.

In order to precisely predict the scouring downstream of sub-merged weirs, it is important to develop a good understandingof 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 shearstresses in the scour zone. The experiments were confined to theclear-water scour condition and the scour hole downstream of onesingle submerged weir at the equilibrium phase.

Experiments

Experimental Set-up

The experimental work was conducted in a 12-m-long, 0.38-m-deep, and 0.44-m-wide glass-sided, tilting flume (Fig. 1) in theHydraulic Laboratory of the University of Auckland. At the up-stream end of the flume, the water is fed into a mixing chamberand enters the flume through a honeycomb flow straightener, whicheffectively eliminates any rotational flow component induced in thereturn pipelines, so that uniform flow is obtained. At the down-stream end, sediment from the scour hole is trapped in a separatedhopper-like sump, from where pumps return the flow to the inletend of the flume.

The sediment used in the experiments was coarse sand, withmedian diameter d50 ¼ 0.85 mm and relative submerged particledensityΔ ¼ 1.65. The sediment size distribution was near uniform,with a standard deviation σg ¼ 1.3. The weir used in the experi-ments was a 10-mm-thick rectangular plastic plate, with the samewidth as the flume. In the experiments, the weir was inserted intothe bed with a 40-mm protrusion from the initial flat bed, and waslocated 4.5 m from the outlet of the flume. During the test, theapproach flow depth y and tail water depth yt were maintainedat 150 mm.

The upstream flow was fully developed in the experiment. Theaverage approach flow velocity U0 for this experiment was esti-mated from the vertical distribution of approach flow velocitieson the centerline of the flume in front of the weir, when the uniformflow was achieved as shown in Fig. 2. The approach average flow

1Ph.D. Student, Dept. of Civil and Environmental Engineering, Univ. ofAuckland, Private Bag 92019, Auckland 1142, New Zealand (correspond-ing author). E-mail: dgua324@aucklanduni.ac.nz

2Professor, Dept. of Civil and Environmental Engineering, Univ. ofAuckland, Private Bag 92019, Auckland 1142, New Zealand. E-mail:b.melville@auckland.ac.nz

3Lecturer, Dept. of Civil and Environmental Engineering, Univ. ofAuckland, Private Bag 92019, Auckland 1142, New Zealand. E-mail:h.friedrich@auckland.ac.nz

Note. This manuscript was submitted on August 9, 2012; approved onJuly 16, 2013; published online on December 16, 2013. Discussion periodopen until June 1, 2014; separate discussions must be submitted for indi-vidual papers. This paper is part of the Journal of Hydraulic Engineering,Vol. 140, No. 1, January 1, 2014. © ASCE, ISSN 0733-9429/2014/1-68-76/$25.00.

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velocity U0 ¼ 0.296 m=s was determined as the velocity at 0.368y(Yalin 1992). The average approach flow shear velocity, u� ≈0.014 m=s, was estimated from the logarithmic form of the velocityprofile (Fig. 2); the average approach flow critical shear velocityu�c ¼ 0.021 m=s was determined using the Shields diagram forthe respective particle size (Melville 1997). Thus, the ratio ofbed shear to critical shear velocity for the approach flow (u�=u�c ≈0.67) was calculated. The corresponding Reynolds number (R ¼Uy=ν) and Froude number (F ¼ U=

ffiffiffiffiffigy

p) were 44,400 and 0.24,

respectively.

Bed Profile and Velocity Measurement

Theoretically, for clear-water scour, the equilibrium of the scourprocess should be defined as the condition when the dimensionsof the scour hole do not grow with time. However, even in small-scale laboratory experiments, it may take several days or weeksto attain equilibrium conditions (Melville and Chiew 1999). Thusit is important to conduct continuing bed-profile measurements tounderstand the scour process and ensure the scour equilibriumphase is obtained. The three-dimensional scour geometry down-stream of the weir was measured throughout the experiment usingSeatek’s multiple transducer arrays (MTAs) (SeaTek Instrumenta-tion, Florida) as a function of time. This instrument is an ultrasonicranging system, comprising 32 transducers, which can detect thedistance from the sensors to reflective objects. The measuring ac-curacy of the system is approximately �1 mm. A detailed descrip-tion of this device can be found in Friedrich et al. (2005). Duringthe test, only 27 transducers were employed, among which twotransducers were used for water surface measurements, with a125-mm interval. The transducers were mounted in a rectangular

grid (see Fig. 3) on a carriage that can be moved along the top railof the flume. The system was operated at 5 Hz and allowed meas-urement of the whole scour region in about 1 min. Taking into ac-count the detection of suspended sediment particles, the outliers ofthe raw bed profile data were filtered in the data postprocessing.The procedure of the program was to use 3σ as the thresholdfor the outlier detection (well known as the 3-σ rule), where σis the standard deviation derived from the original data set. Thefiltered data were then analyzed by spline interpolation procedures.The final resolution of each processed bed profile is 10 × 10 mm.

At the start of the experiment, the sediment bed was levelledwith a scraper after setting the weir. The flume was then filledto the desired water depth. The filling process took place slowlyto avoid disturbance around the weir before the actual experiment.Water temperature was measured in order to set the initial exper-imental parameters for the MTAs. After starting both pumps withthe required settings, the water depth and the slope of the flumewere adjusted to get uniform flow for the approach flow upstreamof the weir, while the flow depth downstream of the weir was con-trolled by adjusting the location of an overflow pipe in the sump.When uniform flow was obtained, bed profiles and water surfacewere measured with 27 MTAs sensors as a function of time. Thescour process lasted around 23 days until the scour hole reachedequilibrium. The time evolution of maximum scour depth and finalscour geometry are shown in Figs. 4 and 5. As shown in Fig. 4, thetemporal development of the scour hole experiences three stages.The maximum scour depth ds develops very quickly during the firstday, then progresses at a decreasing rate over the following 19 days,as it approaches the equilibrium stage. During the final stage, thevalues of ds fluctuated around an average value of 151 mm, which

Fig. 1. Schematic display of the flume

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Flo

w D

epth

(m

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Time-averaged velocity (m/s)

water surface level 150mm

Fig. 2. Approach flow velocity profile (semilogarithmic coordinatesystem) Fig. 3. Sensor arrangement for measuring water surface and bed

profiles

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is taken as the maximum scour depth at the equilibrium phase (dse)in this study.

After the scour hole reached equilibrium, the flow fieldwas measured using a three-component, downward-facing NortekVectrino+ acoustic velocimeter (Nortek AS, Rud, Norway). Theprobe measures the velocities 50 mm beneath the acoustic transmit-ter, which must be submerged, and consequently velocities withinthe first 55-mm depth beneath the water surface were not measured.Measurements were taken along the centerline longitudinal sectionand on three other transverse cross sections. The velocimeter wasused with a sampling rate of 200 Hz. The sampling volume wascylindrical, having a 6-mm diameter and an adjustable height vary-ing from 1 to 7 mm. As suggested by Dey et al. (2011), the sam-pling height was set as 1–2.5 mm in the near-bed zone to avoidinterfering with sediment particles; a 4-mm sampling height wasused in the upper flow zone of the centerline longitudinal section,and a 7-mm height for the three other transverse cross sections.

The closest measuring location to the bed was always 5 mm fromthe bed surface. At each measurement point, 2-min samples werecollected. Throughout the experiments, the signal-to-noise (SNR)ratio for each beam was maintained above 15. After the experi-ments were completed, the output data from the velocimeter werefiltered using WinADV software (Wahl 2000). The filter was set toremove spikes [using the phase-space threshold method of Goringand Nikora (2002)] and data with low correlation (MinimumCOR < 70). Although the best configurations for the velocimeterwere carefully chosen during the experiments, the results for somelocations at 8.5 to 10 cm above the bed in the centerline longitu-dinal section still had relatively high noise and low correlations.These locations are called velocimeter weak spots or velocity holes,and are mainly caused by the return signal interference from theboundary (Martin et al. 2002). After filtering, around 55% of datafor these weak spots were of good quality and therefore retained.For all other measurement points, more than 80% of the data wereretained after filtering. The velocity power spectrum for the filtereddata points was examined with Kolmogorov’s −5=3 law, conform-ing that the data presented in this paper are of high quality.

Results and Discussion

Two-Dimensional Velocity Distribution

Fig. 6 shows the distribution of time-averaged velocity vectorson the centerline longitudinal section. The velocity vectors aredetermined from the average values of the streamwise and verticalvelocity components. It can be seen that the upstream flow is quiteuniform, even at the equilibrium stage. When this uniform flowapproaches the submerged weir, the flow pattern is altered by thesudden change of bed elevation. The approach flow is acceleratedat the crest of the weir, and a weak back flow is created immediately

0

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Fig. 4. Temporal development of the maximum scour depth

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Fig. 5. Scour geometry at the equilibrium phase, contours in millimeters

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Recirculation zone

Flow reattachment region

Fig. 6. Velocity vectors distribution in the centerline longitudinal section

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upstream of the weir. At the upstream base of the weir, a small scourhole (around 20-mm depth) was observed, which was produced byweak vortices, generated by the interaction of the approach flowand the associated back flow. Downstream of the weir, a largerecirculation zone developed (Fig. 6). Immediately downstream ofthe weir, vortices can be clearly observed, indicated by a recirculat-ing movement of sediment close to the weir. For other parts of thiszone, the occasionally random movement of sediment particles isseen at the equilibrium phase of scouring. At the rear of the recir-culation zone, the main flow reattaches to the bed, creating theflow reattachment region (Fig. 6). Inside this region, the flow isconsiderably turbulent, and the velocities are quite small. Theobserved maximum scour-depth point (1.06 m away from the weir)is located close to the end of this region. When the flow passes themaximum scour-depth cross section, no obvious reverse velocitiescan be seen on the centerline longitudinal section, and a relativelyuniform flow is redeveloped downstream of the end of thescour hole.

The time-averaged velocity vector distributions in three trans-verse cross sections (here taken as sections U, M, and D, respec-tively; see Fig. 5), which are located at x ¼ −0.50 m, 1.06 m, and2.75 m, respectively, are presented in Fig. 7. These vectors aredetermined from the mean velocities of the transverse and verticalvelocity components. As indicated in Fig. 7, secondary flows de-velop at all three cross sections. For the U and D cross sections [seeFigs. 7(a and c)], especially for the former one, the magnitude ofthe velocity vectors is relatively small compared with those in themaximum depth cross section M [Fig. 7(b)]. This is driven bycross-sectional anisotropic turbulence (Prandtl 1952); the strongsecondary flows observed in the maximum depth cross section M[Fig. 7(b)], being categorized as Prandtl second kind (driven byturbulence). The secondary flows are characterized by paired cir-cular flow cells, which are quasi-symmetrically located at bothsides of the centerline sand ridge. A similar flow pattern can beseen in Fig. 7(c); this figure also shows nonsymmetry in flows, thisbeing related to the nonsymmetrical bed surface. The pattern ofcellular secondary flows and the associated observed sand ridgein this research is consistent with the observations and theory ofNezu and Nakagawa (1984) and Nezu et al. (1988). These secon-dary flows have a significant effect upon the development ofthe scour hole and the final bed geometry. They also account forthe formation of the centerline sand ridge and help to explain thedeepest point of scour hole being found close to the side wall, ratherthan on the centerline of the flume. The ratio of the maximum scourdepth on the centerline to the maximum scour depth in the scour

hole is 84% (127 mm=151 mm), which implies that the effect ofsecondary flows cannot be ignored when studying clear water scourat submerged weirs in a relatively deep flow. It should be noted thatthe flow aspect ratio (flume width/flow depth) at section M isaround 1.5, which means side wall effects also contribute to theformation of secondary flows in the scour hole and to the scour-hole geometry. In a large river, the flow aspect ratio is larger, whichmight increase the number of secondary flow cells and change thescour-hole geometry.

Bed Shear Stress

At the equilibrium stage of clear-water scour, the stability of sedi-ment particles in the scour hole is based on the equilibrium con-ditions of the forces acting on them, which can be simplified as abalance of flow drag force FD, lift force FL, and submerged weightof sediment particles FG. Accordingly, the critical shear stress τ 0

c ofsediment particles resting on a bed, sloping in the streamwisedirection, can be defined by the following equation:

τ 0c

τ c¼ cos θ

�1þ tan θ

tanϕ

�ð1Þ

where τ 0c = critical shear stress on a sloping bed; τ c = critical shear

stress on a horizontal bed (calculated as ρu2�c ¼ 0.45 Pa); θ = bedslope (measured from an horizontal datum); and ϕ = submergedangle of repose of sediment (taken as 36°, as measured in thisstudy). A complete analysis of incipient sediment motion on non-horizontal slopes can be found in Chiew and Parker (1994). Insidethe equilibrium scour hole, reversed velocity vectors are observedon the upstream slope (Fig. 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 es-timation of bed shear stress with experimental data: (1) reach aver-age method, (2) current velocity profiles (law of the wall, or logprofile method), (3) Reynolds stress measurement, and (4) TKE(turbulence kinetic energy) method. The assumptions, suitability,and limitations of these four methods have been critically reviewedby Kim et al. (2000) and Biron et al. (2004). Considering the appli-cability of these four methods, two of them are employed in thisstudy, namely, the Reynolds shear stress measurement and the TKEmethod. The Reynolds shear stresses, τ̄ x;z, are defined as −ρu 0w 0.The turbulent kinetic energy density, E, is calculated from

E ¼ 1

2ρð ¯u 02 þ ¯v 02 þ w̄ 02Þ ð2Þ

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0.02 m/s

0.02 m/s 0.02 m/s

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

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where u 0, v 0, w 0 are fluctuation velocity components alongthe downstream, transverse and vertical directions, respectively.A simple relationship between TKE and bed shear stress has beenformulated as τ̄ 0 ¼ CE (Soulsby 1981), where τ̄0 is bed shearstress and C is an empirical coefficient. The empirical factor Cwas found to be 0.20 (Soulsby 1981), while 0.19 has been adoptedby others (Stapleton and Huntley 1995; Thompson et al. 2003;Pope et al. 2006) and has been found to apply to a complex flowfields (Biron et al. 2004). Therefore, C ¼ 0.19 has been used inthis study. The critical question of obtaining bed shear stress esti-mates using single point measurements is how to determine theappropriate measurement height above the bed. According to therecommendation of Biron et al. (2004), the best option for usingsingle-point measurements to estimate bed shear stress is to posi-tion the instrument at around 10% of the flow depth. Then, it isabove the thickness of the roughness layer and is less affectedby unexpected increases in SNR or Doppler noise that may occurcloser to the bed (Finelli et al. 1999; Kim et al. 2000). The mea-sured points for estimating bed shear stresses in this study wereall set at 10 mm above the bed. The measured and calculated valuesfor these near-bed points were used for direct estimation of bedshear stress.

Threshold bed stresses, measured Reynolds shear stresses, andcalculated bed stresses were obtained, and a comparison of the ex-perimental bed shear stresses and local threshold bed shear stressesobtained from Eq. (1) is presented in Fig. 8. It should be noted thatthe values of critical bed shear stresses on the upstream slope of thescour hole are negative, which corresponds to the direction of thebottom reverse flow, while in Fig. 8 only absolute values are usedfor comparison. It can be seen that for the approach flow and nearthe end of the scour hole, bed stresses obtained from the observedReynolds shear stresses and from the TKE method do not exceedthe threshold. This is consistent with the experiment being con-ducted under conditions of no general sediment transport. Althoughreverse flows are observed on the upstream slope of the scour hole,the values of measured Reynolds shear stresses are still positive inthis region, which is consistent with the velocity gradients stillbeing positive close to the bed (Figs. 6 and 8). For this case,estimation of bed shear stress from near bed Reynolds shear stressmeasurements may be unreliable, because the measurement equip-ment is incapable of acquiring data in the negative velocity gradientlayer, which is very thin (less than 10 mm) and just above the bed.At the upstream end of the recirculation zone, the experimental bedstresses considerably exceed the absolute threshold values, whichis in agreement with our experimental observations. In this area,

frequent sediment recirculating movements were observed duringthe experiment, including at equilibrium, but they did not resultin deepening of the scour hole. Elsewhere within the scour hole,measured Reynolds shear stresses are around or below the thresh-old and calculated bed shear stresses are slightly greater than thethreshold values. Considering the form of Eq. (2), the TKE methodtakes into account the three-dimensional velocity fluctuations, thusit is less applicable when used for two-dimensional estimation,especially when secondary flows exist. This may account for theoverestimation in the scour hole. On the downstream slope of thescour hole, near-bed velocity accelerates as flow depth decreases,which causes a reduction to the velocity gradient. As a result, themeasured Reynolds shear stresses are very close to zero and arebelow the threshold values.

Turbulence Characteristics

Turbulence IntensitiesContours of the turbulence intensity distributions for the longitu-dinal direction and three transverse cross sections (U, M, and D)are presented in Figs. 9 and 10, respectively. The contour valuesfor the downstream, transverse and vertical directions are calcu-lated from

TIu ¼ffiffiffiffiffiffiffiffiffiffiðu 0Þ2

qU0

; TIv ¼ffiffiffiffiffiffiffiffiffiffiðv 0Þ2

qU0

; TIw ¼ffiffiffiffiffiffiffiffiffiffiffiðw 0Þ2

qU0

ð3Þ

where U0 is the average approach flow velocity. For the centerlinelongitudinal section, the turbulence intensities for all three direc-tions show a very similar distribution [Figs. 9(a–c)]. More specifi-cally, the values of TIu, TIv, and TIw upstream of the weir arerather small compared with those in the scour hole. The peak valuesare found immediately downstream of the weir and above the origi-nal bed level. Downstream of the locations of the peak values, theturbulence intensities are damped, as the distance from the weirincreases. It is important to note that the positions where the peakvalues of turbulence intensities occur are found at the upstream endof the recirculation zone. Furthermore, the measurements of theturbulence intensities in the centerline longitudinal section showthe turbulent flow to be anisotropic, with u 0 ≅ 1.2v 0 ≅ 1.7w 0.

Fig. 10 shows turbulence intensity distributions in three trans-versal cross sections (U, M, and D). For section U [Figs. 10(a–c)],although the turbulence intensities are very small compared withthose in the scour hole, a trend can be observed. The areas of very

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Calculated Bed Shear Stress (TKE)

Threshold Bed Shear Stress

Flow

Original Bed Line

Scour Hole

Fig. 8. A comparison of estimated shear stress and threshold shear stress along the centerline upstream and downstream of the submerged weir

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low turbulence intensities correspond with areas of high streamwisevelocities. The same can be observed in straight natural rivers. Forsection M [Figs. 10(d–f)], turbulence intensities are highest around5 cm above the original bed level and reduce as the distance from

the bed decreases. The decrease of turbulence intensities closer tothe bed, which is in line with the dissipating trend of upstream tur-bulence intensities, is caused by the damping effect of bed boun-daries. With respect to section D [see Figs. 10(g–i)], turbulence

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Fig. 9. Turbulence intensity distributions in the centreline longitudinal section: (a) downstream; (b) transverse; (c) vertical directions, respectively

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

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-0.5 0 0.5 1 1.5 2 2.5

-100

0

100

200

Longitudinal distance (m)

Ver

tical

dis

tanc

e (m

m)

0.006

0.010.22 0.2

0.15

0.12 0.10.08

0.06 0.040.02

0.060.08

0.10.15

0.06

Fig. 11. TKE distribution in the centerline longitudinal section

-0.5 0 0.5 1 1.5 2 2.5

-100

0

100

200

Longitudinal distance (m)

Ver

tical

dis

tanc

e (m

m)

0.3

0.5 24 2010

105

3 5

3

15

0.3 10

10

3

5

3

3

0.3

1.5

1.5 0.5 0.3

0.5

Fig. 12. Normalized Reynolds shear stress distribution in the centerline longitudinal section

-2

02

0

-6 -4-2

-2

0

2

24 6

8

10

10

44

4

6 2

-2

0

2

-150

-100

-50

0

50

100

150

Ver

tical

dis

tanc

e (m

m)

6 10

12

10

86

1214

10 8

1010

12

8

6

6

8

42

4

12 12

1

0

20

-2

0

0

-1

32

12

0

1 1

0 01

0

-10

-1 1

2

0

Section M

0

50

100

150

Ver

tical

dis

tanc

e (m

m) uw

0.80.7

0.70.50.5

0.30.2

0.3 0.20.080.08

0.7

uv

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

Transversal distance (mm)

Ver

tical

dis

tanc

e (m

m)

0.21 0.6

0.6 0.611.5

10.2

1

0

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

0.2

00.2

0

0.50.80.8

0.5

0.2

0

-0.5

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

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)

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

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intensities in all directions are damped, resulting in considerablysmaller values, less than those in the scour hole, while still exceed-ing values observed in the upstream cross section U. The distribu-tions of TIu, TIv, and TIw show a certain degree of irregularity,compared to the distributions in the upstream cross section.

The distribution of normalized TKE, which is calculated fromE=U2

0, in the centerline longitudinal section, is shown in Fig. 11,and highlights a similar pattern to that observed for turbulenceintensities. As previously reported (Bradshaw et al. 1967), TKEreflects the energy extracted from the mean flow by the motion ofthe turbulent eddies. Thus it is possible to conclude that the strong-est and largest eddies are developed at the upstream end of therecirculation zone.

Reynolds Shear StressFigs. 12 and 13 present the distributions of normalized Reynoldsshear stresses for the centerline longitudinal section and three trans-verse cross sections (U, M, and D). The Reynolds stresses valueshere are calculated from

τuw ¼ −u 0w 0

u2�; τuv ¼

−u 0v 0

u2�; τvw ¼ −v 0w 0

u2�ð4Þ

where u� = average approach flow shear velocity. Fig. 12 showsthat the largest Reynolds shear stresses τuw occur immediatelydownstream of the weir, with values dissipating in the scourhole and further downstream. As supported by the distribution ofTKE (Fig. 11) and the distribution of τuw (Fig. 12) in the centerlinelongitudinal section, it is possible to infer that the large magnitudeof turbulence structure on the upstream slope of the scour holegoverns the scour hole size (maximum scour depth and length).This is in agreement with work undertaken by Ben Meftah andMossa (2006).

As seen in Figs. 13(a, d, and g), Reynolds shear stresses τuwand τuv are dominant, while τvw values are relatively small inall three cross sections. It also can be seen that the highest Reynoldsshear stress values are found near the bottom of the sections, forboth U and D, while for section M they are observed around theoriginal bed level. Thus bottom friction at sections U and D was thedominant factor to account for shear stress distributions, but forsection M the distributions of Reynolds shear stresses are stronglydependent on upstream dissipating shear stresses.

As discussed above, secondary flows are observed at allthree sections (U, M, and D; see Fig. 7). The values of τuv inFigs. 13(b, e, and h) also reveal secondary flows. Negative τuvvalues are found on the left side of the flume centerline, while pos-itive values are observed on the right side, as seen in Fig. 13(e),showing a certain degree of symmetry. Similar patterns can be seenin Figs 13(b and h). Since the values of τuv and τvw should be zerowhen no secondary flows exist, the Reynolds shear stress values notonly reveal the concentration of turbulence, but also indicate theintensities of secondary flows.

Conclusions

The results of an experimental study of flow patterns, bed shearstresses, and turbulence structures in the approach flow towardsa submerged weir, and the resulting scour hole are presented.The experiments were undertaken in clear-water scour conditionsin a laboratory flume. The equilibrium scour-hole condition wasobtained. The three-dimensional flow-field data was obtained bya Nortek Vectrino+ acoustic velocimeter.

The results show that the presence of a submerged weir con-siderably changed the flow structure. Along the flume centerline

longitudinal direction, a recirculation zone and a flow reattachmentregion are developed. The turbulence structures at the upstream endof 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 scourhole. The location of maximum scour depth is found at the rear ofthe flow reattachment region and close to the left flume glass wall.The observed Reynolds shear stress near the bed and the calculatedbed shear stresses from TKE method are larger than absolute valuesof critical bed shear stresses immediately downstream of the weir,and smaller than critical bed shear stresses elsewhere in the scourhole and further downstream.

For the transverse direction, strongly paired cellular secondaryflows are observed in the scour hole. A certain degree of symmetryof Reynolds shear stress τuv distributions at cross sections areobserved, which directly account for the formation of secondaryflows. These secondary flows have a significant effect upon thedevelopment of the scour hole and the final bed geometry. Theireffect should be considered in the study of scour at low-headstructures in a relatively deep flow.

Acknowledgments

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

Notation

The following symbols are used in this paper:C = empirical factor used in TKE method for calculating bed

shear stress;ds = maximum scour depth;dse = maximum scour depth at the equilibrium phased50 = median diameter;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;ls = maximum scour length;

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

t = scour time;U0 = average approach flow velocity;

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

u 0, v 0, w 0 = fluctuation velocity components along the downstream,transverse, and vertical directions, respectively;

u� = average approach flow shear velocity;u�c = average approach flow critical shear velocity;y = approach flow depth;yt = tail water depth;τ c = critical shear stress on a horizontal bed;τ 0c = critical shear stress on a sloping bed;

τuw, τuv, τvw = normalized Reynolds shear stresses;τ̄ 0 = bed shear stress;Δ = relative submerged particle density;θ = bed slope;ϕ = submerged angle of repose of sediment;ρ = water density;ρs = sediment density;σg = standard deviation; andν = kinematic viscosity of fluid, considered as 1 × 10−6 m2=s.

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ReferencesBen Meftah, M., and Mossa, M. (2006). “Scour holes downstream of bed

sills in low-gradient channels.” J. Hydraul. Res., 44(4), 497–509.Bhuiyan, F., et al. (2007). “Hydraulic Evaluation of W-Weir for River

Restoration.” J. Hydraul. Eng., 10.1061/(ASCE)0733-9429(2007)133:6(596), 596–609.

Biron, P. M., et al. (2004). “Comparing different methods of bed shearstress estimates in simple and complex flow fields.” Earth Surf. Proc-esses Landforms, 29(11), 1403–1415.

Bormann, N. E., and Julien, P. Y. (1991). “Scour downstream of grade-control structures.” J. Hydraul. Eng., 10.1061/(ASCE)0733-9429(1991)117:5(579), 579–594.

Bradshaw, P., et al. (1967). “Calculation of boundary-layer developmentusing the turbulent energy equation.” J. Fluid Mech., 28(03), 593–616.

Chen, Z., et al. (2005). “Experimental study on the upstream water levelrise and downstream scour length of a submerged dam.” J. Hydraul.Res., 43(6), 703–709.

Chiew, Y.-M., and Parker, G. (1994). “Incipient sediment motion on non-horizontal slopes.” J. Hydraul. Res., 32(5), 649–660.

D’Agostino, V., and Ferro, V. (2004). “Scour on alluvial bed downstream ofgrade-control structures.” J. Hydraul. Eng., 10.1061/(ASCE)0733-9429(2004)130:1(24), 24–37.

Dey, S., et al. (2011). “Near-bed turbulence characteristics at the entrain-ment threshold of sediment beds.” J. Hydraul. Eng., 10.1061/(ASCE)HY.1943-7900.0000396, 945–958.

Finelli, C. M., et al. (1999). “Evaluating the spatial resolution of an acousticdoppler velocimeter and the consequences for measuring near-bedflows.” Limnol. Oceanogr., 44(7), 1793–1801.

Friedrich, H., et al. (2005). “Three-dimensional measurement of laboratorysubmerged bed forms using moving probes.” Proc., XXXI IAHRCongress, Korea Water Resources Association, Seoul, 396–404.

Goring, D. G., and Nikora, V. I. (2002). “Despiking acoustic dopplervelocimeter data.” J. Hydraul. Eng., 10.1061/(ASCE)0733-9429(2002)128:1(117), 117–126.

Kim, S. C., et al. (2000). “Estimating bottom stress in tidal boundary layerfrom acoustic doppler velocimeter data.” J. Hydraul Eng., 126(6),399–406.

Marion, A., et al. (2004). “Effect of sill spacing and sediment size gradingon scouring at grade-control structures.” Earth Surf. ProcessesLandforms, 29(8), 983–993.

Marion, A., et al. (2006). “Sediment supply and local scouring at bed sills inhigh-gradient streams.” Water Resour. Res., 42(6), W06416.

Martin, V., et al. (2002). “ADV data analysis for turbulent flows: Lowcorrelation problem.” Proc., Hydraulic Measurements and Experimen-tal Methods 2002, ASCE, CO, 1–10.

Melville, B. W. (1997). “Pier and abutment scour: Integrated approach.”J. Hydraul. Eng., 10.1061/(ASCE)0733-9429(1997)123:2(125),125–136.

Melville, B., and Chiew, Y. (1999). “Time scale for local scour at bridgepiers.” J. Hydraul. Eng., 125(1), 59–65.

Nezu, I., and Nakagawa, H. (1984). “Cellular secondary currents in straightconduit.” J. Hydraul. Eng., 10.1061/(ASCE)0733-9429(1984)110:2(173), 173–193.

Nezu, I., Nakagawa, H., and Kawashima, N. (1988). “Cellular secondarycurrents and sand ribbons in fluvial channel flows.” Proc., 6th APD-IAHR Congress, APD-IAHR, Kyoto, Japan, 2(1), 51–58.

Pope, N. D., et al. (2006). “Estimation of bed shear stress using the turbu-lent kinetic energy approach—A comparison of annular flume and fielddata.” Cont. Shelf Res., 26(8), 959–970.

Prandtl, L. (1952). Essentials of fluid dynamics, Blackie and Son,London.

Soulsby, R. L. (1981). “Measurements of the Reynolds stress componentsclose to a marine sand bank.” Marine Geol., 42(1–4), 35–47.

Stapleton, K. R., and Huntley, D. A. (1995). “Seabed stress determinationsusing the inertial dissipation method and the turbulent kinetic energymethod.” Earth Surf. Processes Landforms, 20(9), 807–815.

Thompson, C. E. L., et al. (2003). “The manifestation of fluid-transmittedbed shear stress in a smooth annular flume—A comparison of meth-ods.” J. Coastal Res., 19(4), 1094–1103.

Wahl, T. L. (2000). “Analyzing ADV data using WinADV.” Proc., 2000Joint Conf. on Water Resources Engineering and Water ResourcesPlanning and Management, ASCE, Reston, VA.

Yalin, M. S. (1992). River mechanics, Pergamon Press, Oxford, U.K.

76 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / JANUARY 2014

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righ

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