Flow Patterns and Turbulence Structures in a Scour Hole Downstream of a Submerged Weir
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Dawei Guan 1; Bruce W. Melville, M.ASCE 2; and Heide Friedrich 3 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. 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 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
1 Ph.D. Student, Dept. of Civil and Environmental Engineering, Univ. of Auckland, Private Bag 92019, Auckland 1142, New Zealand (corresponding author). E-mail:
[email protected] 2 Professor, Dept. of Civil and Environmental Engineering, Univ. of Auckland, Private Bag 92019, Auckland 1142, New Zealand. E-mail:
[email protected] 3 Lecturer, Dept. of Civil and Environmental Engineering, Univ. of Auckland, Private Bag 92019, Auckland 1142, New Zealand. E-mail:
[email protected] Note. This manuscript was submitted on August 9, 2012; approved on July 16, 2013; published online on December 16, 2013. Discussion period open until June 1, 2014; separate discussions must be submitted for individual papers. This paper is part of the Journal of Hydraulic Engineering, Vol. 140, No. 1, January 1, 2014. © ASCE, ISSN 0733-9429/2014/1-6876/$25.00.
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 The experimental work was conducted in a 12-m-long, 0.38-mdeep, and 0.44-m-wide glass-sided, tilting flume (Fig. 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. The sediment used in the experiments was coarse sand, with median diameter d50 ¼ 0.85 mm and relative submerged particle density Δ ¼ 1.65. The sediment size distribution was near uniform, with a standard deviation σg ¼ 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 40-mm protrusion from the initial flat bed, and was 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 U 0 for this experiment was estimated from the vertical distribution of approach flow velocities on the centerline of the flume in front of the weir, when the uniform flow was achieved as shown in Fig. 2. The approach average flow
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Fig. 1. Schematic display of the flume
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velocity U 0 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 velocity profile (Fig. 2); the average approach flow critical shear velocity uc ¼ 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 (u =uc ≈ 0.67) was calculated. The corresponding Reynolds number (R ¼ pffiffiffiffiffi Uy=ν) and Froude number (F ¼ U= gy) were 44,400 and 0.24, respectively. 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 smallscale 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) (SeaTek Instrumentation, Florida) as a function of time. This 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. A detailed description of this device can be found in Friedrich et al. (2005). During the test, only 27 transducers were employed, among which two transducers were used for water surface measurements, with a 125-mm interval. The transducers were mounted in a rectangular
Fig. 3. Sensor arrangement for measuring water surface and bed profiles
grid (see Fig. 3) on a carriage that can be moved along the top rail of the flume. The system was operated at 5 Hz and allowed measurement of the whole scour region in about 1 min. 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 program 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 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 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 approach flow upstream of the weir, while 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 Figs. 4 and 5. As shown in Fig. 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 JOURNAL OF HYDRAULIC ENGINEERING © ASCE / JANUARY 2014 / 69
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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 cm above the bed in the centerline longitudinal 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 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.
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Results and Discussion Two-Dimensional Velocity Distribution Fig. 6 shows the distribution of time-averaged velocity vectors on the centerline longitudinal section. The velocity vectors are determined from the average values of the streamwise 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
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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 field was measured using a three-component, downward-facing Nortek Vectrino+ acoustic velocimeter (Nortek AS, Rud, Norway). The probe measures the velocities 50 mm 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 centerline 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 a 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 1–2.5 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 centerline longitudinal section, and a 7-mm height for the three other transverse cross sections.
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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 τ c0 of sediment particles resting on a bed, sloping in the streamwise direction, can be defined by the following equation: τ c0 tan θ ¼ cos θ 1 þ ð1Þ tan ϕ τc where τ c0 = critical shear stress on a sloping bed; τ c = critical shear stress on a horizontal bed (calculated as ρu2c ¼ 0.45 Pa); θ = bed slope (measured from an horizontal datum); and ϕ = submerged angle of repose of sediment (taken as 36°, as measured in this study). A complete analysis of incipient sediment motion on nonhorizontal slopes can be found in Chiew and Parker (1994). Inside the equilibrium scour hole, reversed velocity vectors are observed on 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 estimation of bed shear stress with experimental data: (1) reach average method, (2) current velocity profiles (law of the wall, or log profile method), (3) Reynolds stress measurement, and (4) 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, the Reynolds shear stress measurement and the TKE method. The Reynolds shear stresses, τ¯ x;z , are defined as −ρu 0 w 0 . The turbulent kinetic energy density, E, is calculated from 1 E ¼ ρðu¯02 þ v¯02 þ w¯02 Þ 2
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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 scourhole 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.
Vertical distance (mm)
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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 (Fig. 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 (Fig. 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, no obvious reverse velocities can be seen on the centerline longitudinal section, and a relatively uniform flow is redeveloped downstream of the end of the scour hole. The time-averaged velocity vector distributions in three transverse cross sections (here taken as sections U, M, and D, respectively; see Fig. 5), which are located at x ¼ −0.50 m, 1.06 m, and 2.75 m, respectively, are presented in Fig. 7. These vectors are determined from the mean velocities of the transverse and vertical velocity components. As indicated in Fig. 7, secondary flows develop at all three cross sections. For the U and D cross sections [see Figs. 7(a and c)], especially for the former one, the magnitude of the velocity vectors is relatively small compared with those in the maximum depth cross section M [Fig. 7(b)]. This is driven by cross-sectional anisotropic turbulence (Prandtl 1952); the strong secondary flows observed in the maximum depth cross section M [Fig. 7(b)], 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 centerline sand ridge. A similar flow pattern can be seen in Fig. 7(c); this figure also shows nonsymmetry in flows, this being related to the nonsymmetrical 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 and Nakagawa (1984) and Nezu et al. (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 centerline sand ridge and help to explain the deepest point of scour hole being found close to the side wall, rather than on the centerline of the flume. The ratio of the maximum scour depth on the centerline to the maximum scour depth in the scour
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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 Eq. (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 overestimation 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 Figs. 9 and 10, respectively. The contour values for the downstream, transverse and vertical directions are calculated from qffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffi ðu 0 Þ2 ðv 0 Þ2 ðw 0 Þ2 TI u ¼ ; TI v ¼ ; TI w ¼ ð3Þ U0 U0 U0 where U 0 is the average approach flow velocity. For the centerline longitudinal section, the turbulence intensities for all three directions show a very similar distribution [Figs. 9(a–c)]. More specifically, the values of TI u , TI v , and TI w 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 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 centerline longitudinal section show the turbulent flow to be anisotropic, with u 0 ≅ 1.2v 0 ≅ 1.7w 0 . Fig. 10 shows turbulence intensity distributions in three transversal cross sections (U, M, and D). For section U [Figs. 10(a–c)], although the turbulence intensities are very small compared with those in the scour hole, a trend can be observed. The areas of very
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where u 0 , v 0 , w 0 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 τ¯ 0 ¼ CE (Soulsby 1981), where τ¯ 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 ¼ 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. 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 Eq. (1) is presented in Fig. 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 Fig. 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 (Figs. 6 and 8). For this case, estimation of bed shear stress from near bed Reynolds shear stress measurements may be unreliable, because the measurement 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,
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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
low turbulence intensities correspond with areas of high streamwise velocities. The same can be observed in straight natural rivers. For section M [Figs. 10(d–f)], 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 Figs. 10(g–i)], turbulence JOURNAL OF HYDRAULIC ENGINEERING © ASCE / JANUARY 2014 / 73
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-2 10
10
8
-50
2 0
14
12
0
0 0
12
8
0
Section M
Vertical distance (mm)
10
12
12
-100
Vertical distance (mm)
10
0
(f)
-2
50
6
0 0.03 6 0.0
0 0 -0.08 -0.05
(e)
(d) 100
0.0 0.03 3
0
0.1 0.3
0
-0.05
-0.3
0.7
0.8
0 150
0. 0.08 2
(c) 03 0. 0.06
0.5 0.7
0
0.2 0.3 0.5 0.7
0.3
50
-0.1 0 0.1
0.08
-0.3
(b)
(a)
Section U
100
vw
uv
150
0.5
Vertical distance (mm)
Fig. 12. Normalized Reynolds shear stress distribution in the centerline longitudinal section
0 .3
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Fig. 11. TKE distribution in the centerline longitudinal section
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intensities in all directions are damped, resulting in considerably smaller values, less than those in the scour hole, while still exceeding values observed in the upstream cross section U. The distributions of TI u , TI v , and TI w show a certain degree of irregularity, compared to the distributions in the upstream cross section. The distribution of normalized TKE, which is calculated from E=U 20 , in the centerline longitudinal section, is shown in Fig. 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. Reynolds Shear Stress Figs. 12 and 13 present the distributions of normalized Reynolds shear stresses for the centerline longitudinal section and three transverse cross sections (U, M, and D). The Reynolds stresses values here are calculated from τ uw ¼
−u 0 w 0 ; u2
τ uv ¼
−u 0 v 0 ; u2
τ vw ¼
−v 0 w 0 u2
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 τ 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.
ð4Þ
where u = average approach flow shear velocity. Fig. 12 shows that the largest Reynolds shear stresses τ uw occur immediately downstream of the weir, with values dissipating in the scour hole and further downstream. As supported by the distribution of TKE (Fig. 11) and the distribution of τ uw (Fig. 12) in the centerline 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). As seen in Figs. 13(a, d, and g), Reynolds shear stresses τ uw and τ uv are dominant, while τ 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, while 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 Fig. 7). The values of τ uv in Figs. 13(b, e, and h) also reveal secondary flows. Negative τ uv values are found on the left side of the flume centerline, while positive values are observed on the right side, as seen in Fig. 13(e), showing a certain degree of symmetry. Similar patterns can be seen in Figs 13(b and h). Since the values of τ uv and τ vw should be zero when no secondary flows exist, the Reynolds shear stress values not only reveal the concentration of turbulence, but also indicate the intensities of secondary flows.
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 centerline
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 phase d50 = 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; TI u , TI v , TI w = turbulence intensities along the downstream, transverse, and vertical directions, respectively; t = scour time; U 0 = 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; uc = average approach flow critical shear velocity; y = approach flow depth; yt = tail water depth; τ c = critical shear stress on a horizontal bed; τ c0 = critical shear stress on a sloping bed; τ uw , τ uv , τ vw = normalized Reynolds shear stresses; τ¯ 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; and ν = kinematic viscosity of fluid, considered as 1 × 10−6 m2 =s. JOURNAL OF HYDRAULIC ENGINEERING © ASCE / JANUARY 2014 / 75
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References Ben 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 shear stress estimates in simple and complex flow fields.” Earth Surf. Processes Landforms, 29(11), 1403–1415. Bormann, N. E., and Julien, P. Y. (1991). “Scour downstream of gradecontrol structures.” J. Hydraul. Eng., 10.1061/(ASCE)0733-9429 (1991)117:5(579), 579–594. Bradshaw, P., et al. (1967). “Calculation of boundary-layer development using the turbulent energy equation.” J. Fluid Mech., 28(03), 593–616. Chen, Z., et al. (2005). “Experimental study on the upstream water level rise 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 nonhorizontal slopes.” J. Hydraul. Res., 32(5), 649–660. D’Agostino, V., and Ferro, V. (2004). “Scour on alluvial bed downstream of grade-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 entrainment 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 acoustic doppler velocimeter and the consequences for measuring near-bed flows.” Limnol. Oceanogr., 44(7), 1793–1801. Friedrich, H., et al. (2005). “Three-dimensional measurement of laboratory submerged bed forms using moving probes.” Proc., XXXI IAHR Congress, Korea Water Resources Association, Seoul, 396–404. Goring, D. G., and Nikora, V. I. (2002). “Despiking acoustic doppler velocimeter 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 layer from acoustic doppler velocimeter data.” J. Hydraul Eng., 126(6), 399–406.
Marion, A., et al. (2004). “Effect of sill spacing and sediment size grading on scouring at grade-control structures.” Earth Surf. Processes Landforms, 29(8), 983–993. Marion, A., et al. (2006). “Sediment supply and local scouring at bed sills in high-gradient streams.” Water Resour. Res., 42(6), W06416. Martin, V., et al. (2002). “ADV data analysis for turbulent flows: Low correlation problem.” Proc., Hydraulic Measurements and Experimental 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 bridge piers.” J. Hydraul. Eng., 125(1), 59–65. Nezu, I., and Nakagawa, H. (1984). “Cellular secondary currents in straight conduit.” J. Hydraul. Eng., 10.1061/(ASCE)0733-9429(1984)110:2 (173), 173–193. Nezu, I., Nakagawa, H., and Kawashima, N. (1988). “Cellular secondary currents and sand ribbons in fluvial channel flows.” Proc., 6th APDIAHR Congress, APD-IAHR, Kyoto, Japan, 2(1), 51–58. Pope, N. D., et al. (2006). “Estimation of bed shear stress using the turbulent kinetic energy approach—A comparison of annular flume and field data.” 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 components close to a marine sand bank.” Marine Geol., 42(1–4), 35–47. Stapleton, K. R., and Huntley, D. A. (1995). “Seabed stress determinations using the inertial dissipation method and the turbulent kinetic energy method.” Earth Surf. Processes Landforms, 20(9), 807–815. Thompson, C. E. L., et al. (2003). “The manifestation of fluid-transmitted bed shear stress in a smooth annular flume—A comparison of methods.” J. Coastal Res., 19(4), 1094–1103. Wahl, T. L. (2000). “Analyzing ADV data using WinADV.” Proc., 2000 Joint Conf. on Water Resources Engineering and Water Resources Planning and Management, ASCE, Reston, VA. Yalin, M. S. (1992). River mechanics, Pergamon Press, Oxford, U.K.
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