Prediction of Progressive Penetration of Scour Hole into the Tributary Channel in Laboratory Channel Confluences
Confluences are basic building blocks in river networks at all scales. When two rivers merge at a confluence, rapid changes in fluid velocity and turbulence intensity cause changes in the bed geometry. Usually, a deep scour hole and a depositional point bar are present at the confluence. One important phenomenon that has been overlooked in previous studies is the progressive penetration of the scour hole into the tributary channel. This progressive penetration may jeopardize the structural safety of the lateral channel in the proximity of the main channel. In this study, dimensional analysis techniques are used to develop a general equation for the prediction of maximum scour hole penetration (Psc) into the tributary. Eventhough, the penetration of the scour hole into the lateral channel is a time-dependent process, in developing the formula the maximum value after the equilibrium condition has been achieved is used. A series of 73 experimental tests with different confluence angle (θ), lateral to downstream channel discharge ratio (Qr), lateral to main channel width ratio (Br) and downstream densimetric Froude number (Fg) in an asymmetrical confluence has been conducted to test the proposed formulation. The results show that Psc increases with Qr, θ and Fg and decreases with Br. The degree of penetration defines two types of scour holes: In the first type the scour hole penetration only reaches the toe of the lateral channel wall closer to the downstream junction corner whereas in the second type the scour hole reaches both lateral channel walls. The second type is associated with higher values of Qr, θ and Fg and lower values of Br. Statistical analysis showed that the mean error of the developed formula is of the order of 24%.
November 03, 2011; Accepted: December 22, 2011;
Published: February 22, 2012
Confluences are basic building blocks in river networks at all scales. When, two rivers merge at a confluence, rapid changes in fluid velocity and turbulence intensity cause changes in the bed geometry. Usually, a deep scour hole and a depositional point bar are present at the confluence. One important phenomenon that has been overlooked in previous studies is the progressive penetration of the scour hole into the tributary channel. This progressive penetration may jeopardize the structural safety of the lateral channel in the proximity of the main channel. The flow pattern, scour and sedimentation in confluences is complex and has attracted the attention of many researchers.
Past work on river channel confluences can be classified into two main groups.
The first group consists on theoretical and experimental studies focusing on
flow characteristic without the inclusion of sediment transport, such as Webber
and Greated (1966), Lin and Soong (1979), Best
and Reid (1984), Ramamurthy et al. (1988),
Hager (1989), Gurram et al.
(1997), Hsu et al. (1998a, b),
Bradbrook et al. (1998), Lane
et al. (1999), Weerakoon et al. (1991),
Biron et al. (1996), Weber
et al. (2001) and Huang et al. (2002).
These studies have considered parameters such as depth ratio, separation zone
dimensions, hydraulic jump conditions or three-dimensional flow effects. The
second group includes the analysis of sediment transport (Mosley,
1976; Best, 1988; Roy et al.,
1988; Biron et al., 1993, 2002;
Rhoads and Kenworthy, 1995, 1998;
Rhoads and Sukhodolov, 2001; Bryan
and Kuhn, 2002; Boyer et al., 2006; Parsons
et al., 2007; Ghobadian and Shafai Bejestan,
2007; Ghobadian et al., 2007). Concentrating
on confluence scour, sediment transport and bed morphology, effects of bed discordance,
shear layer turbulence and mixing.
The effects of confluence angle and momentum and discharge ratios have been taken into account in several studies but the effects of tail water depth and bed grain size have received less attention. None of the previous studies has concentrated on progressive penetration of scour hole into the tributary channel and developed a relation for prediction of the maximum value of it, as proposed herein.
In river confluence, many variables can affect the scour hole and point bar dimensions and maximum penetration of scour hole into the tributary channel. To developed general relation for predicting maximum value of penetration of scour hole into the tributary channel, one may consider the following dependence:
Applying dimensional analysis theory, the following non-dimensional equations
can be developed (Ghobadian, 2007):
In these equations Q2 and Q3 are flow discharges in the
lateral channel and in the main channel downstream of the confluence, respectively,
B2 and B3 are the corresponding channel widths, θ
is the confluence angle, So is the bed slope, Fg is the
densimetric Froude number and Re is the Reynolds number downstream
of the river confluence. Fg is computed as V3/[g (Gs-1)
D50]0.5, with V3 being the flow velocity downstream
of the confluence, g the acceleration of gravity. Gs the specific
gravity of the sediment and D50 the median particle size, while Re
is equal to ρV3Y3/μ with ρ and μ representing
density and dynamic viscosity of water, respectively. Δz is the bed elevation
All experimental tests in this study have been carried out under subcritical
conditions and therefore the bed slope has no significant effects on the flow
patterns (Gurram et al., 1997). For high Reynolds
number and rough boundaries, the Reynolds number effect can also be disregarded.
In this study B2 and B3 were kept constant and Δz
was set equal to zero. Therefore, Eq. 2 is reduced to the
Equation 3 is the basis for the analysis of the experimental data.
EXPERIMENTAL SETUP AND METHODOLOGY
The experimental setup consists of a main flume 9 m long with 75 cm deep for
the first 2 m and 45 cm for remaining 7 m and 35 cm wide and a lateral flume
3 m long, 45 cm deep and either 15, 25 or 35 cm wide. Both flumes had a horizontal
slope. At the upstream end of each flume a stilling box was installed to reduce
the kinetic energy of the entrance flow.
|| Plan view of experimental set up
A head tank provides a constant discharge to both stilling boxes. Discharge
is measured by an electronic flow meter with an accuracy of 0.01 L sec-1.
At the end of the main flume, a sluice gate controls the downstream water depth.
The lateral flume was connected to the main flume at three different confluence
angles, i.e., 60°, 75° and 90°. This study was conducted in hydraulic
laboratory at Shahid Chamran University, Ahvaz, Iran during 2005-2007. Figure
1 shows a plan view of the experimental setup.
An 11 cm layer of uniform sediment was laid on both channel beds. There was no sediment feeding or recirculation in these experiments. In order to extended the densimetric Froude number range, three different sizes of sediment (D50 = 1.05, 1.95 and 3.41 mm) were used. At the start of each run the flumes were filled slowly, keeping the tailwater gate closed. When, the flow depth was high enough to avoid initial disturbances on the bed, the flow discharges were increased to the desired values and the tailwater gate was gradually opened until the desired flow depth was achieved. This situation was kept unchanged for 5 h or until the scour hole dimensions remained constant. At the end of the run the pump was shut down, the water was drained and the bed topography was measured using surveying equipment.
RESULTS AND DISCUSSION
Maximum penetrations of scour hole into the tributary channel from 73 experiments were gathered during this study. Penetration is defined as the distance from the main channel of the furthest point in the tributary where any appreciable scour can be observed. Table 1 shows the range of the relevant dimensionless variables covered by the experiments.
As has shown in Fig. 2, the degree of penetration defines two types of scour holes, in the first type the scour hole penetration only reaches the toe of the lateral channel wall closer to the downstream junction corner (Fig. 2a) whereas, in the second type the scour hole reaches both lateral channel walls (Fig. 2b). The second type is associated with higher values of Qr, θ and Fg and lower values of Br.
Figure 3 shows that the penetration of the scour hole into
the lateral channel is a time-dependent process, as the scour hole depth increase
with time during the experiment. Parallel lines in Fig. 3
show the slope of scour hole during the experiment is almost constant and it
is not time dependent.
|| Range of variables in this study
||Penetration of scour hole into tributary channel. (a): Scour
hole reaches the toe of the lateral channel wall closer to the downstream
junction corner and (b): Scour hole reaches both lateral channel walls
||Time-dependent penetration of scour hole into tributary channel
Maximum values of penetration where recorded after equilibrium of the scour
The results corresponding to one set of the experimental tests are presented
in Fig. 4-6. All other sets showed similar
trends. In this study five different discharge ratios Qr = Q2/Q3
were analyzed and it can be seen that the discharge ratio has a significant
effect on the scour hole penetration development. Figure 4a
shows the variation of relative penetration (Psc/B3) with
the discharge ratio Qr showing that as Qr increases, the
ratio of (Psc/B3) increases. This is because as the scour
hole becomes larger, the equilibrium condition of its slope results in more
penetration into the tributary.
||(a-b) Variation of relative penetration (Psc/B3)
with densimetric Froude number Fg; (a) with the discharge ratio
Qr and (b) with the discharge ration of Fg
The effect of the downstream densimetric Froude number on (Psc/B3) is shown in Fig. 4b, where it can be observed that the maximum penetration of scour hole into the tributary channel increases as Fg increases. This behavior is due to an increase on the flow transport capacity for smaller sediment sizes (which decreased in sized as Fg increased) and results in a larger (and deeper) scour hole.
The variation of the maximum penetration of scour hole into the tributary channel with confluence angle is presented in Fig. 5, showing an increase of Psc/B3 with θ. This can be explained by the size of the separation zone that forms downstream of the confluence, which is minimal for small confluence angles and increases as the tributary becomes more perpendicular to the main channel. For larger separation zones the effective wide of the postconfluence channel is reduced and increased flow velocity causes more scour.
Figure 6 shows the variation of (Psc/B3)
with the width ratio B2/B3, showing a reduction of bar
height with an increase in B2/B3.
||Variation of relative penetration (Psc/B3)
with confluence angle θ, (a): in different Qr and (b): in
||Variation of relative penetration (Psc/B3)
with ratio B2/B3; (a): In different Qr
and (b): In different Fg
This trend results from a decrease in the momentum of the lateral channel
when the width ratio increases (all other parameters being constant) and a consequent
reduction of scour hole depth and penetration.
SCOUR HOLE PENETRATION EQUATION
To develop a relation for the prediction of the maximum penetration of scour hole into the tributary channel at river confluences, the following equation was obtained by multiple regressions on the experimental data (r = 75.96%):
The range of applicability of Eq. 4 is given by the values of Table 1 and it must be noted that it is valid when there is no movement of bed material upstream of the channel confluence.
||Observed values of relative penetration of scour hole versus
predicted values by Eq. 4
To investigating the accuracy of Eq. 4, observed values of relative depositional bar height have been plotted against the predicted values and the results are presented in Fig. 7. As, it can be seen from this figure most of data are between the 95% confidence bands statistical analyses. The relative error of the equation is about 24%. This means that Eq. 4 can be applied for as a guide in the prediction of maximum penetration of scour hole into the tributary channel in river confluences. The form of Eq. 4 clearly shows that the width ratio has a negative effect while the other parameters have positive effect on the relative penetration of the scour hole.
In this study and for the first time, a general dimensionless equation for the prediction of maximum penetration of scour hole into the tributary channel at river confluence has been developed. A series of 73 experimental tests with different confluence angle (θ), discharge ratio (Qr), width ratio (Br) and downstream densimetric Froude number (Fg) in an asymmetrical confluence have been conducted to test the proposed formulation. The results showed that the maximum penetration of scour hole into the tributary channel increases with increasing ratio of lateral channel discharge to total discharge. confluence angle and downstream densimetric Froude number. while it decreases with increasing width ratio. A relationship has also been developed that has a 24% relative error for prediction of scour hole penetration in to the tributary channel.
This study is part of a research project which has been financially supported by the Office of Water Research of Khuzestan Water and Power Authority with Grant No. 84-01-04-010. Part of this work was carried out while the first author was a visiting scholar at the University of Newcastle.
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