An experimental study of sediment transport in channel confluences

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An experimental study of sediment transport in channel confluences Abolfazl Nazari-Giglou, Aidin Jabbari-Sahebari, Ahmad Shakibaeinia, Seyyed Mahmood Borghei

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Received date: 19 November 2013 Revised date: 19 August 2014 Accepted date: 29 August 2014 Cite this article as: Abolfazl Nazari-Giglou, Aidin Jabbari-Sahebari, Ahmad Shakibaeinia, Seyyed Mahmood Borghei, An experimental study of sediment transport in channel confluences, International Journal of Sediment Research, http: //dx.doi.org/10.1016/j.ijsrc.2014.08.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

An Experimental Study of Sediment Transport in Channel Confluences Abolfazl Nazari-Giglou1, Aidin Jabbari-Sahebari2, Ahmad Shakibaeinia3*, Seyyed Mahmood Borghei4 1

Department of Civil Engineering, Islamic Azad University, Iran. Department of Civil Engineering, Queens University, Kingston, Canada. 3 Water & Climate Research Centre, University of Victoria, Victoria, Canada. 4 Deceased, Formerly Professor of Civil Engineering, Sharif University of Technology, Iran. 2

*corresponding author: Email address: [email protected] Tel: 250-363-8963 Fax: 250-363-3586

Abstract

Confluences are common features of natural and man-made channel systems where convergence of joining flows creates a complex flow and sediment transport pattern producing strong flow circulations and rapid changing in bed morphology. By the means of laboratory experiments on several mobile-bed channel confluences, this study (1) investigates and formulates the (not well-understood) flow and geometrical conditions leading to the incipient motion of sediments in channel confluences, and (2) characterizes the effect of flow and geometrical conditions on the main morphological features (e.g. scouring and deposition areas) in confluences. Of prime importance factors that are considered in this study are the flow Froude number, angle of confluence, discharge and width ratios and the bed martial properties. This experimental study provides an insight for better understanding mechanisms involved in sediment transport and bed morphology in channel confluences and also quantifies the influence of various flow and geometrical factors on sediment transport, which are great importance in river engineering designs and fluvial studies. Keywords: Channel confluences; Sediment transport; Bed morphology; Incipient motion of sediment; Scouring and deposition.

1. Introduction Channel confluences, where two or more branches of a channel system join together, are the key morphological elements in most of river systems as well as man-made channels. Confluences are subject to the rapid changes of flow structure, sediment transport and morphodynamics. Better understanding of the complex flow structure and morphology of channel confluences has long been of great interest of fluvial scientist and hydraulic/river engineers; however, the flow complexities at this point has always been challenging, especially when the channels bed and banks are erodible. A number of experimental and numerical research works in past and recent years have focused on studying the flow structure (e.g., Taylor, 1944; Best, 1987; Ashmore et al., 1992; Huang et al., 2002; Shakibaeinia et al., 2010; Baranya et al., 2013) and sediment transport (e.g., Mosely, 1976; Ashmore and Parker, 1983; Best, 1988; and Shakibaeinia et al, 2007) in channel junctions. Best (1987) characterized the flow in channel confluences by different flow zones such as deflection, stagnation, separation and contractions zones (see Fig. 1). The locations and sizes of these zones were further studied by Mosely (1976), Ashmor and Parker (1983), Best (1987 and 1988) and Shakibaeinia et al. (2010). These studies determined the main controllers on flow structure in a confluence to be discharge ratio (or alternatively momentum-flux ratio), confluence angle and the flow Froude number. Weber et al. (2001), by measuring the velocity in various points in a 90o experimental channel confluence, illustrated that the longitudinal velocity contours near the bed are distinctly different from the near surface velocity patterns. Ashmor et al. (1992), Bradbrook et al. (1998, 2000), Shakibaeinia et al. (2007, 2010) addressed the existence of strong secondary (as well as primary) circulations downstream of the confluence point. Biron et al. (1996), Huang et al. (2002), Boyer et al. (2006), Constantinescu et al. (2011) characterized turbulence structure in asymmetrical river confluences addressed turbulence structure in confluences with various geometries. By mean of three-dimensional numerical modeling Baranya at al. (2013) studied the flow structure in confluence of two medium-sized natural rivers. Best (1988) characterized the sediment transport and morphology channel confluence by a scour hole in center of the confluence, avalanche face and various deposition areas. Fig. 2 shows the

typical morphology of confluence. This study and some other works (e.g. Mosely 1976; Ashmore and Parker, 1983; Biron et al., 1993; Shakibaeinia et al., 2007 and 2011; Rhoads et al., 2009; Riley and Rhoads 2012; Barayana et al, 2013; Riley at al. 2014 ) investigated the shape, size and location of scour hole in the natural, experimental and numerical channel confluences. Ginsberg and Perillo (1999) studied characteristics of the scour holes at the junction of tidal channels in the Bahia Blanca Estuary (Argentina), in order to find possible origin and evolution of scour holes. Paphitis (2000) studied sediment incipient movement, under unidirectional flow, using an empirical threshold curves. Nazari (2003) and Borghei and Nazari (2004) conducted some experimental studies on sediment erosion and deposition in channel junctions to characterized the location and size of the scour hole for different flow and geometrical conditions (e.g., width and discharge ratios and sediment size). Shakibaeinia et al. (2007 and 2011) used a 3-D numerical model to simulate the sediment transport bed changes in the laboratory-sized and natural channel confluences in a broad range of confluence angles, discharge ratios. They concluded that a decrease in confluence angle as well as increase in discharge ratio can reduce the size of scour hole and move its location to the further downstream in the main channel. Borghei and Sahebari (2010) studied the scour patterns at the junction of two loose bed channels under clear-water conditions. Their experiment results showed that the position of the maximum scour depth temporally moves to the outer wall and upstream to the main channel, as affected by the discharge ratios. Leite Ribeiro et al. (2010) experimentally investigated the effect of the tributary channel widering on morphology of a 90 degrees confluence. For the case of natural confluent meander bends, Riley and Rhoads (2012) and Riley et al. (2014) investigated flow structure and bed morphology and studied the effects of channel curvature and confluence angle on confluence morpho-dynamics. Zinger et al, (2011) studied sediment transport in confluence of the Wabash and Ohio rivers. Sirdari at al. (2013) applied a numerical model to study the bed morphology and bed load transport for a natural confluence. Despite a great deal of research (including those by the authors), the morphology and sediment transport in channel confluences is still an open problem with not a clear understanding. While attention has, in the past, focused on morphological features, the mechanism involved in the threshold movement (or incipient motion) of sediments and the condition that leads to the incipient motion of sediment particles in the confluences remain rather poorly understood. Determining sediment incipient motion (the critical condition at which transport begins) plays a

significant role in study and modeling of sediment transport in natural and man-made channels. The precise flow condition and time leading to initial movement occurs is a subjective determination; therefore must be studied separately for each river channel feature such as confluence. In addition to sediment incipient motion further research efforts are required to characterize the evolution of the morphological features and the influence of various geometrical and flow conditions on the transport of the sediments. This research work aims to provide a clear understanding of the morphological development in river channel confluences, where special attention is given to the conditions leading to incipient motion of sediments and evolution of bed morphology. Various experimental setups are used for the purpose of this study. First set of experiments are conducted to investigate and formulate the influence of discharge ratio, confluence angle and flow Froude number on the condition at which the bed materials initiate to move. Second set of experiments focuses of evolution of morphological features (e.g. scour hole and deposition areas) under various flow and geometrical conditions (i.e. different sediment sizes, discharge and width ratios and the junction shape). 2. Experimental Setup Laboratory experiments are performed in three different geometrical configurations. The first configuration has an adjustable confluence angle while the second and third configurations have adjustable channel width. Fig. 3a, b shows the configuration of the first and second experimental setups. Geometrical and flow conditions of different setup are summarized in Table 1. The flumes walls are made of Plexiglas. A 45o chamfer can be installed at the downstream of junction point for flumes of setups #1 and #2. The bed is covered with the erodible noncohesive materials (initially flat). To elimination the effect of materials non-uniformity, as suggested by Melville (1997), bed materials were selected in a way to keep the value of σg less than 1.5, where σg=(d84/d16)0.5. All the experiments were conducted with clear water condition, i.e. no suspended or bed sediments are fed to the upstream of the junction. The water was circulated from the downstream tank to the upstream tank by a pump. The loose bed (sediment bed) was extended 2.5 m upstream from the junction to the main and tributary channels and 2.5 m downstream from the junction to the main channel. Also, in order to get a

better developed flow condition, the first 0.5 meter of the movable bed in the two channels were covered by coarse sediments with a d50 size between 5 and 15 m. Tests are run until bed equilibrium. Bed topography and sediment balance are recorded during the experiments. A digital sounding wire capable of moving along and across the flume is installed to measure the bed elevation and erosion/deposition depth. A graded rod is also used for measurements. The water is circulated from the downstream tank to the upstream tank by a pump. Discharge for the tributary channel (Qt) is adjusted by an upstream gate in the main channel and the water depth was controlled by an adjustable tailgate at downstream of the main channel. Because of the high flow velocity at the beginning of the experiments, the un-wanted initial erosion may happen especially at the upstream of the confluence point. To prevent such erosion, at the start of each experiment, the tailgate at the downstream of the main channel (for adjusting depth and velocity) was closed, then, the channels are filled very slowly so that no movement of sediment occurs, and then the tailgate is opened gradually. Next, the discharge is adjusted to the desired discharge using the upstream control gate.

Table 1: Summary of the experimental setups.

Variable

Set-up no. 1

Set-up no. 2

Set-up no. 3

Main channel width, Wm (m)

0.40

0.20

0.40

Tributary channel width, Wt (m)

0.40

0.10, 0.15, 0.20

0.20, 0.30, 0.40

Width ratio, Wr =Wt /Wm

1.00

0.50, 0.75, 1.00

0.50, 075, 1.00

Confluence angle, θ (degrees)

50, 70, 90

90

90

Discharge ratio (Tributary discharge/ Total discharge), Qr

0.3, 0.4, 0.6, 0.8

0.25, 0.5, 0.75

0.25, 0.5, 0.75

Length of main channel Lm(m)

12.0

5.0

8.0

Length of branch channel Lt(m)

3

2.0

3.5

Total (downstream) discharge, Qd (l/s)

7.5 to 15.5

14.4

28.8

Sediment size d50 (mm)

0.97

0.25, 0.5, 1.0, 1.5, 2.5

0.25, 0.5, 1.0, 1.5, 2.5

Downstream Froude Number (Fd)

<1

<1

<1

3. Results and Discussion 3.1. Sediment incipient motion The first experimental setup is used to study the threshold movement of the sediments. The experiments are started with a high flow depth. To find the threshold movement of the sediments, the downstream depth is reduced gradually leading to a gradual increase in the mean flow velocity and bed shear stress in the main, tributary and post-confluence channels. Once the bed shear stress reaches the critical shear stress (velocity reaches the threshold velocity), the sediment particles start to move. At the beginning a few sediment particles start to move ~1- 2 cm upward and downward as approaching the threshold condition, but no visible scouring occurs. By lowering the tailgate slightly more, the sediments at the downstream corner of the junction start to move slightly downward along the main channel. An scour hole initiates at the first few minutes of each experiment, and as time goes on several more successive holes start to form (Fig. 4) which can be related to high streamwise velocity region as well as secondary flows near the separation zone boundary (Shakibaeinia et al., 2007, 2011). These scour hole later join each other and for a larger scour hole at the middle of channel confluence. The rate of the sediments movement decreases with time and no movement is observed after around 20 minutes while some of the tests were run for more than 24 hours. Therefore, this situation, with occurrence of maximum 3 mm holes in 20 minutes, is taken as the threshold condition for this study. Other interpretations of the threshold movement can also be introduced (Henderson 1966). Fig. 4 shows the initial erosion configuration for the test with Qd=7.5 l/s, Qr=0.4, and θ=90o (Qd and Qr being the downstream discharge and discharge ratio, respectively). Dimensions and boundary limit of separation zone is calculated using the

mathematical relations provided by Gurram et al. (1997). As this figure shows, initial sediment movements occur near the boundary of separation zone. Therefore, it seems that the incipient high velocity cores and helical cells which are responsible for bed erosion initially form in the vicinity of the separation zone. Two common relations for determining threshold mean flow velocity in open channels (Vc) are given by Melville and Sutherland (1988) and Neill (1973) (developed for bridge pier scouring) as:

æ Vc y ö = 5.75log ç 5.53 ÷ u*c d50 ø è Vc = 1.58[( SG - 1) gd50 ]0.5 (

(1) y 0.167 ) d50

(2)

respectively, where u*c is critical shear velocity, y is the flow depth and g is the gravitational acceleration. In this set of experiments d50 is constant and equal to 0.97 mm, thus, the value of u*c will remain constant. Table 2 shows the calculated values u*c using three different approaches (θcr is Shields parameter and τc is critical shear stress). The values using different approaches are very close for u*c and, thus, for this study it is taken as ~0.023 m/s. Various dimensionless parameters such as Frm (upstream Froude number in the main channel), Frd (downstream Froude number in the main channel), Frt (Froude number in the tributary channel), discharge ratio Qr and the threshold velocity ratio V/Vc (the ratio of mean threshold flow velocity in a channel with confluence, V, to the mean threshold flow velocity in a regular open channel without confluence, Vc) are studied in threshold condition. The critical shear stress and sediment transport in channel confluences is affected by the confluence complex flow structure (characterized by strong primary and secondary circulations) in addition to the mean flow velocity as in a regular open channel (Shakibaeinia et al, 2007); therefore, the value of V/Vc can be a good indicator for the threshold movement condition in confluences. Among other dimensionless parameters in model tests, the Weber and Reynolds numbers can be important. In order to minimize the effect of surface tension (characterized by Weber number), the depth of flow should be greater than 30 mm (Novak and Cabelka, 1981) that is satisfied as

the minimum depth of flow is 99 mm in the experiments. Also, if the Reynolds number is greater than a certain value (for open channel the start of turbulent flow is 1000), the influence of the viscosity would be minimal. The minimum Reynolds of the carried experiment is around 1900 (greater than the laminar flow range), therefore the viscosity effects will be negligible.

Table 2. Critical values using different approaches θcr

τc(N/m2)

u*c(m/s)

Melville (1997)

0.034

0.529

0.023

Van Rijn (1993)

0.034

0.54

0.023

Chien and Wan (1983)

0.032

0.502

0.022

Froude number and discharge ratio effect Fig. 5 shows the relation between the two values of Frt and Frm at the threshold condition.

As illustrated, by increasing the main channel’s Froude number (Frm), a smaller value of Frt is required for the initiation of sediment movement. Furthermore, a higher confluence angle results in a lower values for the Froude numbers required for initial movement. As expected, a higher values of total discharge decreases the Froude numbers of threshold movement. The effect of the discharge ratio (Qr) versus downstream Froude number (Frd) is shown in Fig. 6. By increasing the discharge ratio, the threshold movement of sediments starts in a smaller

Frd values. Similar effect of the total discharge and confluence angle (θ) is observed, i.e. for the higher confluence angles and discharge values, a lower Frd is needed for the initiation of sediment movement. Threshold velocity

Of interest of this study is to find the threshold velocity for channel for different geometrical and flow conditions. Here the threshold velocity has been normalized using the threshold velocity in a similar open channel but without confluence (Vc). Using equation (1) to

find Vc, and the downstream threshold velocity for present experiments as V=Qd/Bdyd, the dimensionless threshold velocity (V/Vc) can be calculated for different experimental conditions. As the values of V/Vc approaches unity the threshold condition is less affected by the tributary channel flow (more similar to a regular straight open channel). In order to validate equation (1) for the case of this study, threshold of movement without tributary channel was checked in the main channel. The results showed that sediments initiate to move to downstream in flow velocity above approximately 95 percent of Vc calculated by this equation (less than 5% error). Fig. 7 shows the value of V/Vc versus Qr for different values of θ and downstream

discharges. By increasing Qr, for the same total discharge, the value of V/Vc decreases and it reaches as low as ~0.25 (for Qr=0.8 when θ=90o and Q=0.0155 m3/s). By the means of regression analysis for the data achieved from 56 sets of experiments the following mathematical relations between V/Vc, Qr, Frd and θ can be extracted.

ì Frt 7.65 1 ï3.29( ) 6.8 Qr Frd sin 0.2 q ï Fr V ï 1 = í3.6( t )6.1 5.17 Vc ï Qr Frd sin 0.18 q ï Fr 5.52 1 ï3.47( t ) 4.59 Qr Frd sin 0.17 q î

for

B / yd £ 2

( R 2 = 0.98)

for

2 < B / yd < 3

( R 2 = 0.98)

for

B / yd ³ 3

( R 2 = 0.96)

(3)

The regression coefficients of close to 1 show the reliability of the relations. Fig. 8 shows that the measured versus calculated values of V/Vc for all of test results, well covers the present data points with a tolerance of 5%. Furthermore, Fig. 9 provides the detail of the measured versus calculated values of V/Vc for different discharge ratios Qr and confluence angles θ. 3.2. Erosion and deposition pattern In addition to incipient motion of sediment, the evolution of bed morphology and the erosion/deposition pattern in channel confluences in a broad range of condition is also aimed to be studies in this paper. As it was mentioned the bed morphology in channel confluences is mainly characterized by a scour hole (and associated avalanche faces) at the junction point, and

various deposition areas at the flow separation area and downstream of the junction point. The effect of confluence angle on the shape and size of scour hole were investigated in experimental works of Borghei and Nazari (2004) and Borghei and Jabbari (2010). Here in this study, experimental setups #2 and #3 are used to address the effect of bed material, discharge ratio, width ratio and junction chamfer on shape and size of the scour hole and deposition features. Equilibrium condition

The rate of bed changes are studied to determine when bed topography reaches a relative equilibrium condition. Fig. 10 shows an example of the evolution of bed topography in the main channel at the confluence point. A scour hole forms and grows rapidly at the beginning of the experiments. The growth rate decreases as the time goes on and eventually reaches an equilibrium condition. The measurement where continued for about 48 hrs. Here in this study, the time when the erosion depth reaches to more than 90% of its final depth of 48 hrs (as in Paphitis 2001, Kenworthy 1995, Nazari 2003) is considered as equilibrium condition. In most of the experiments, the equilibrium condition happened within first 3 hrs of the experiments. Erosion in channel confluences is related to the increase of bed shear stress due to two main reasons. (1) The flow of main and tributary channel are combined and contracted (forced by flow separation) at the junction point and lead to a rapid increase in mean longitudinal velocity and hence bed shear stress. This results in sediment motion toward downstream. (2) Strong secondary currents after the confluences point (as addressed in Shakibaeinia et al 2007, 2010) are also increase the bed shear stress causing the sediments at the beginning of the post confluence channel (and also outer wall) to be eroded and deposited at the separation zone and further downstream (as the result of the decrease in flow velocity). The erosion/deposition processes continued up to the time that the bed shear stress decreases and reaches to the critical stress leading to a relative equilibrium condition. Fig. 11 shows the 3-D representation of experimental bed topography for the width and discharge ratios of 0.5 and bed material with d50 of 2.5 mm. As the figure shows the bed topography in the experimental confluence is characterized by three distinct features including (1) a scour hole in the beginning of the post

confluence channel, (2) avalanche face, (the upstream boundary of the scour hole), and (3) deposition area in separation zone and further downstream in post-confluence channel. Fig. 11 (a and b) also shows the effect of experimental geometry on the developed morphology. The discharge, length and width of the first experimental setup are half of those of second setup. The results show that for the same bed material, confluence angle, and width and discharge ratios, the second setup (i.e. larger scale experiments) has a slightly deeper scour hole (~15% deeper) which can be due to lower velocity of the tributary channel. The Effect of chamfer

For different discharge ratios, bed material diameters and width ratios, experiments were conducted with and without a 45˚ chamfer installed at the downstream corner of the junction. As known chamfer will affect the flow separation area and therefore, expected to affect the sediment transport pattern at the channel confluences. Fig. 12 compares the experimental bed topography (with d50=0.5mm, Wr=0.75, and Qr=0.5) with and without applying a chamfer at the downstream corner. Observation shows that applying a chamfer decrease the depth of scour hole (~15%) and stretches the scour hole further downstream. That can be due to the fact that, a chamfer reduces the size of flow separation area. A smaller flow separation leads to the weaker secondary flows and flow contraction at the post confluence channel which can decrease the scouring depth. Such pattern is also observes in other width and discharge rations (i.e., Wr=0.5 and 1.0, and Qr=0.25 and 0.75). Effect of width ratio

With the same discharge value, a smaller width ratio (width of tributary channel to that of main channel) results in a higher velocity of tributary channel. Such velocity increase lead to larger separation area and higher velocity (thus higher bed shear stress) at the beginning of the post confluence channel. Therefore, it is expected to have a more erosion for smaller width ratios. Fig. 13 shows the effect of width ratio, Wr, on the dimensionless scour depth, hs* (for various bed material sizes. dimensionless scour depth, hs* is defined as the ratio of the water depth at maximum scour location, hs, and at the upstream channels, (ht+hm)/2). As the figure illustrates, the higher width ratio the shallower scour hole forms at the confluence point. Such effect is more

significant for the cases with coarser bed materials (as the coarser material have higher critical shear stress which is hardly exceeded for larger width ratios). Effect of bed material size

The bed material size has a reverse effect on the critical bed shear stress and consequently the erosion rate. As Fig. 14 shows for a certain discharge ratio (here Qr=0.75) by increasing the bed material size (here characterized by d50) the scour depth has a relatively linear decrease. Such trend was also observed for other discharge ratios. Discharge Ratio Effect Another factor that can affect erosion pattern in channel confluences is discharge ratio. Fig. 15 shows the effect of discharge ratio (ratio of tributary to downstream discharge) on the scour depth for the experiments with different values of d50. It also compares the present reasech measurement with Best (1988) laboratory measurement and Shakibaeinia et al (2007, 2011) three-diemnsional numerical modeling results for the 90-degrees equal-width channel confluences. Observations show that higher discharge ratios (closer to one similar to condition in the bend flow) leads to a deeper scour hole. That can be due to fact that in the discharge rations closer to one, a larger separation zone forms contracting the flow streamlines at the junction point leading to higher velocity and bed sear stress. Furthermore, higher discharge ration can lead to stronger secondary flows and hence larger bed shear stress. A similar trend is apparent in Best (1988) and Shakibaeinia et al (2007, 2011) works, although the magnitude are different. Note that the differences in dimensionless scour depth magnitudes is due to difference in the geometrical and hydraulic conditions (for example the Froude number in present study is lower than both Best, 1998 and Shakibainia et al. 2007 studies).

4. Conclusion The influence of the important dimensionless factors of discharge ratio, Froude number and confluence angle on threshold movement of sediment in a loose-bed confluence was investigated and formulated. Result showed that Froude number in tributary channel (Fr t), downstream Froude number (Frd), discharge ratio (Qr) and the confluence angle (θ) play important roles in threshold movement of sediments. The derived mathematical relations between the mean threshold velocity and these controllers showed a very good correlation with the experimental data achieved from 57 sets of experiments. Needless to say that these relations limited to the geometrical and flow conditions of these experiments and one should

be careful about using them in different conditions. Thus, while for the set-up in this study the results are conclusive, but the present study needs to be confirmed with other conditions before a comprehensive conclusion can be reached. In addition to the experiments on threshold movement of sediments, further experiments were conducted to characterize the effect of different dimensionless factors such as discharge and width ratios, bed material size on the evolution and development of different morphological features (e.g. local scouring and various deposition areas). The experiment proved the formation a scour hole downstream of junction point and deposition areas at the flow separation zone and further downstream. Results showed that the depth of scour hole increases reducing the width ratio, increasing the discharge ratio and using finer grain bed martial. Use of a chamfer at the downstream corner of the junction point results in a shallower scour hole that is stretched further downstream along the main channel. Acknowledgments Authors would like to acknowledge Dr. Mustafa Ergil (Depatment of Civil Engineering, Eastern Mediterranean University) for his comments and advices.

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List of figures: Fig. 1. Flow characteristics of channel confluences (base on Best, 1987) Fig. 2.Typical bed morphology a channel confluence (based on Shakibaeinia et al., 2007, 2011 and Best, 1986) Fig. 3. Experimental configuration (a) setup no.1, (b) setup no.2 Fig. 4. Sample of scour holes at threshold condition for Qd=7.5 l/s, Qr=0.4, θ=90o, (all dimensions are in mm) Fig. 5. Frt versus Frm at threshold condition (Q is in m3/s and θ is in degree) Fig. 6. Frd versus Qr at threshold condition (Q is in m3/s and θ is in degree) Fig. 7. V/Vc versus Qr at threshold condition (Q is in m3/s and θ is in degree) Fig. 8. Measured versus calculated V/Vc (Eqs. 3) Fig. 9. Measured versus calculated V/Vc (by mean of developed relations) for different confluence angles and discharge rations, (a) Qr=0.3, (b) Qr=0.4 (c) Qr=0.6, and (d) Qr=0.8 (θ is in degree) Fig. 10. Time history of bed topography (Set-up no.2, Qr=0.5, Wr=0.75, d50=1 mm) Fig. 11. Experimental bed topography for d50=2.5mm, and Qr=0.5. (a) Setup no. 2; (b) Setup no. 3. Fig. 12. Experimental bed topography (a) with (b) without chamfer (d50=0.5mm, Wr=0.75, and Qr=0.5 in set-up no.2) Fig. 13. The effect of width on the maximum scour depth (Qr=0.75) Fig. 14. Effect of bed material size on dimensionless scour depth (for Qr=0.75) Fig. 15. Effect discharge ratio on dimensionless scour depth

Fig.1

Fig.1. Flow characteristics of channel confluences (based on Best, 1987)

Fig. 2

Fig.2. Typical bed morphology a channel confluence (based on Shakibaeinia et al., 2007, 2011 and Best, 1986)

Fig. 3

(a)

(b)

Fig. 3. Experimental configuration (a) setup no.1, (b) setup no.2

Fig. 4

Fig 4. Sample of scour holes at threshold condition for Qd=7.5 l/s, Qr=0.4, θ=90o, (all dimensions are in mm)

Fig. 5

Fig. 5. Frt versus Frm at threshold condition (Q is in m3/s and θ is in degree)

Fig. 6

Fig. 6. Frd versus Qr at threshold condition (Q is in m3/s and θ is in degree )

Fig. 7

Fig. 7. V/Vc versus Qr at threshold condition (Q is in m3/s and θ is in degree)

Fig. 8

0.6 +5%

0.55

V/Vc(measured)

0.5 -5%

0.45 0.4 0.35 0.3 0.25 0.2 0.2

0.25

0.3

0.35

0.4

0.45

0.5

V/Vc(calculated)

Fig. 8. Measured versus calculated V/Vc (Eqs. 3)

0.55

0.6

Fig. 9

Fig. 9. Measured versus calculated V/Vc (by mean of developed relations) for different confluence angles and discharge rations, (a) Qr=0.3, (b) Qr=0.4 (c) Qr=0.6, and (d) Qr=0.8 (θ is in degree)

Fig. 10

T=10 min

T=20 min

T=40 min

T= 90 min

Fig. 10. Time history of bed topography (Set-up no.2, Qr=0.5, Wr=0.75, d50=1 mm)

Fig. 11

Scour hole

Sediment deposition

Avalanche face

(a)

(b)

Fig 11. Experimental bed topography for d50=2.5mm, and Qr=0.5. (a) Setup no. 2; (b) Setup no. 3.

Fig. 12

(a)

(b) Fig. 12. Experimental bed topography (a) with (b) without chamfer (d50=0.5mm, Wr=0.75, and Qr=0.5 in set-up no.2)

Fig. 13

Fig. 13. The effect of width on the maximum scour depth (Qr=0.75)

Fig. 14

Fig.14. Effect of bed material size on dimensionless scour depth (for Qr=0.75)

Fig. 15

Fig. 15. Effect discharge ratio on dimensionless scour depth