Effect of equilibrium and non-equilibrium sediment transport flows on the shear velocity in an open channel.

Equilibrium and non-equilibrium sediment transport flow in natural rivers and artificial channels can result in degradation or aggradation of the river bed, which will affect many hydraulic parameters, one of which is shear velocity. This study evaluates the influence of sediment transport on shear velocity in open channels. In this study, laboratory experiments were carried out using a sediment-recirculating flume, and measurements of the velocity and Reynolds shear stress distributions were measured using a Sontek-acoustic Doppler velocimeter (ADV). This experimental study measured 120 velocity distributions, and Reynolds stress profiles, consisting of 12 different sets of measurements involving flow with sediment transport and movable sand bed. The results showed an average shear velocity, u*, difference between sediment feeding and without sediment feeding by 9.41%. For the integration constant Br value, the average difference between sediment feeding and without sediment feeding was 5.58%.


Introduction
Sediment transport is a vital river process as it significantly influences channel morphology.Understanding the behaviour of sediment transport in open channels is vital for various hydraulic engineering applications.The natural phenomenon of flow in open channels can be equilibrium or nonequilibrium sediment transport flows.Equilibrium sediment transport is characterized by a situation where the rate of sediment transport is balanced with the available sediment supply, resulting in a relatively stable channel morphology over time.Meanwhile, non-equilibrium sediment transport has the characteristics of unbalanced sediment supply and transport, causing changes in channel geometry and sediment deposition or erosion.
Mechanic of sediment transport involves the movement of sediment particles suspended or bed-load, such as silt, sand, and gravel, along the channel bed due to the energy of flowing water.The processes associated with these events are best observed in natural streams, with feedback relationships between velocity, turbulent flow, sediment transport, bedforms, and shear velocity [1], [2].Numerous researchers have explored the relationship between flow velocity and shear velocity in open channels with various types of channel bed materials, such as sand and gravel, observed in various natural environments.These observations include smooth and gravel beds with and without bed load [3][4][5][6][7][8][9][10] and suspension flows 1311 (2024) 012013 IOP Publishing doi:10.1088/1755-1315/1311/1/012013 2 [11].Additionally, many studies on sediment transport have developed concepts and techniques for predicting velocity related to shear velocity to estimate sediment discharge in movable-bed river models, such as techniques developed by Alam and Kennedy [12], Einstein and Barbarossa [13], Engelund [14], and Garde and Ranga Raju [15].
The shear velocity, which represents the average velocity of water flow along the channel bed, is an important hydraulic parameter in estimating total sediment discharge and overall channel geomorphology.Under equilibrium and non-equilibrium sediment conditions, the sediment transport process has a direct impact on the shear velocity within the channel.This study evaluates the influence of sediment transport on shear velocity.In this study, laboratory experiments were carried out using a sediment circulation flume, and measurements of the velocity distribution and Reynolds shear stress distribution were measured using ADV.Therefore, this study is significant because it provides further insight into the flow characteristics of sediment transport compared to earlier studies.The study has contributed fundamental knowledge to calculating the shear velocity of transport flows.

Experimental Setup and Measuring Equipment
This research is a laboratory experiment using a sediment recirculation flume with specifications of 1000 cm in length, 60 cm in width, and 45 cm in height.This flume can flow a maximum discharge of 150 l/s and a maximum sediment feeding discharge of 500 gr/s with a maximum sediment particle diameter of 3 mm.This research simulates a movable bed with coarse sand material of uniform diameter, d50 = 0.92 mm (see Figure 3) to obtain equilibrium sediment transport conditions by controlling the sediment feeding discharge ranging from 6.6 gr/s to 110 kg/s and variation discharge 35 l/s to 50/s [16].
Measurements were carried out in 2 sections, namely section 1 with a distance of 560 cm and section 2 with a distance of 660 cm from the flume entrance (see Figure 2).Five vertical measurements were carried out on half of the flume cross-section with the position shown in Figure 1.The equipment used to measure the flow velocity distribution and Reynolds shear stress distribution used a SONTEK-ADV, the 16-MHz MicroADV Probe 3D down-looking type with an accuracy level of 99% [17].Due to the limitations of the down-looking type ADV tool, there is an area that cannot be measured, namely 5 cm from the surface of the flow and 5 cm from the wall flume (see Figure 1).while the three-dimensional flow velocity measurement point starts from 0.5 mm from the bed channel to 50 mm (5 cm) from the water surface.

Data Reduction Methods
Instantaneous velocity data processing methods from ADV measurements, such as processed 3dimensional velocity data, must threshold the criteria of SNR>15dB and correlation score>70% [6].Meanwhile, to determine the shear velocity, u*, in uniform flow [6] uses two methods, namely Clauser and Reynolds.The procedure for determining shear velocity using the Clauser method is analyzing velocity distribution measurement data in the inner region y/H≤0.2Hand using the log-law in Equation (1).Then, the second method uses Reynolds stress distribution measurement data and Equation (5).
Calculation of shear velocity using the Clauser method based on measurements from distribution profile data (y/H≤0.2H)and using Equation ( 1) from the concept of logarithmic velocity distribution (log-law), which is a universal law of walls as described by Kironoto and Graf [6], as: Where y is the depth of the measuring point from the channel bed, Br is the integration constant,  is the Karman constant, and   , is the value of the Nikuradse bed roughness.The fundamental roughness value of Nikuradse,   , can be calculated using Nikuradse and El-Samni for uniform sand materials.The necessary roughness takes   = ds, and for non-uniform sand materials,   = d50.While the depth of reference level  0 , according to Einstein and El-Samni [18], can be taken as  0 = 0.20   .
The instantaneous velocities,   ,   and   , can be seen in Equations ( 2) to (4) as: Where , , and  represent the mean-point velocities in the longitudinal, vertical, and transverse directions, while   ,   and   represent the velocity component fluctuations.
To calculate the shear velocity using the Reynolds method from data processing of the Reynolds shear stress distribution.To obtain the Reynolds stress value by averaging the instantaneous velocity value     with Equation (5) as follows: (5)

Description of Measurements
The running experimental will be given a name or code to simplify calculations and further discussion.
Numbering or coding is based on differences in measurements and variations in measurements of crosssectional positions and observation points relative.The naming code measurement uses three characters consisting of letters and numbers.The first character is NSFMB, indicating the research is without sediment feeding, while the flow with sediment feeding is coded as SFMB.The second characters, A to F, indicate variations in flow discharge and channel slope, and codes 1 and 2 are the cross-section positions.For example, a measurement with the code SFMBF1 means that the measurement is carried out in a flow with a sediment-feeding movable bed, with code F being a combination of a discharge variation of 35 l/s and a slope of 0.0030.Then, code 1 is a measurement carried out in cross-section 1.
The results of measurements and data collection in the laboratory and final analysis regarding slope, discharge, flow velocity, Clauser method shear velocity, and Reynolds shear stress method shear velocity, which are classified as main flow parameters, are presented in detail in Table 1.

Velocity Distribution
Typical measurement results of velocity distribution profiles for flows with and without sediment feeding can be seen in Figure 4.It can be seen in Figure 4(a) that the velocity distribution from the bed of the channel to the surface of the flow becomes greater.Then, Figures 4(b) and 4(c) show that the velocity contour decreases as it approaches the channel wall due to friction with the channel wall.Next, a more detailed discussion of Figure 4(a) shows a comparison between flows without sediment feeding flow (non-equilibrium) and with sediment feeding flow (equilibrium).This figure shows the difference in the u/U velocity distribution profile of a flow with sediment feeding; the velocity profile in the inner region (y/H < 0.2) tends to be "slender", and the velocity value tends to decrease compared to without sediment feeding flow.In contrast, the velocity distribution in the outer region (y/H > 0.2) increases, as shown by the arrow direction in Figure 4(a).

Shear Velocity and Integration Constant Based on The Clauser Method
Kironoto and Graf [6] demonstrated that shear velocity, u*, is determined based on the measured velocity profiles of the inner region (y/H < 0.2) by applying Clauser's Method.Velocity data obtained from the measurements were plotted with the value of ln(y/ks), then the value of the shear velocity (u*) and constant integration (Br) with a value of κ = 0.4 can be obtained, as shown in Figure 5(a).Based on the figure, it can be seen that the value of measurement points from data with sediment feeding flow are in a linear line, so it can be concluded that logarithmic Law (log-law) can be used for the data in the inner region (y/H < 0.2), but in the outer region value of measurement points show does not follow of the logarithmic line.Figure 5(b) shows that the shear velocity running without and with sediment feeding flow in the transverse direction of the channel tends to decrease towards the side walls of the channel.This difference is visible in the flow with sediment feeding.Br values also show a similar trend, as shown in Figure 6.In the present study, Br values also show a decrease approaching the channel edge in the transverse direction.In the centre part of the channel (z/B=0.5), the average Br value for flows without sediment feeding is 7.16 ± 0.85, and for flows with sediment feeding is 6.88 ± 0.99 [16].These values are smaller than those in the literature (see Kironoto and Graf [6]) on clear water flows without bed-load sediment transport in rough flow regimes (Br = 8.5 ± 15%; [19]).The decrease in Br values obtained in this study in the presence of bed-load may be influenced by bed-load sediment transport.According to Nikuradse [20], for rough flow regimes, the Br value should range from 8.6 to 8.75 for uniform flow and rough hydraulics.In general, the present data shows that sediment transport (bed load) can cause an increase in shear velocity.Conversely, the Br value shows that sediment transport (bed-load) causes a decrease in Br values, see Figure 11.The results showed an average shear velocity difference between sediment feeding (equilibrium) and without sediment feeding (non-equilibrium) by 9.41%.While for the integration constant Br value, the average difference between sediment feeding and without sediment feeding was 5.58%.

Determining Shear Velocity Based on The Reynolds Shear Stress Data
From instantaneous velocity measurement data in 3 dimensions with an ADV device, the Reynolds shear stress profile −    ̅̅̅̅̅̅, can be calculated as shown in Figure 7 and the Reynolds shear stress contour in Figure 8.In Figures 7(a) and 7(b), the Reynolds shear stress profile at each measurement from VA to VE is normalized by the shear velocity at the channel centre (VA) obtained from the Clauser method −    ̅̅̅̅̅̅/ * 2 .It can be seen that the value of the Reynolds shear stress from the bottom to the surface of the flow decreases.This result shows that the Reynolds shear stress still follows the linear distribution theory for both flows without and with sediment feeding.Seen from the transverse direction of the channel, the Reynolds shear stress values for flows without and with sediment feeding tend to decrease from the centre (1/2B) of the channel toward the side walls of the channel.Reynold's shear stress contour shown in Figure 8(a) for flows without sediment feeding (non-equilibrium) in the inner region tends to be greater than the flow with sediment feeding in Figure 8(b).flow with sediment feeding shows that the feeding sediment particles will suppress the Reynolds shear stress.This Reynolds stress suppression occurs more dominantly near the bed of the channel or inner region (y/H < 0.2).To determine the shear velocity directly from the Reynolds shear stress profile data, namely by using the least squares fitting method to the Reynolds stress profile variable at y = 0 and equating this value with  * 2 , then the shear velocity denoted by u*r can be derived.In Figure 9, the shear velocities obtained from the Reynolds shear stress profile data, u*r, are plotted and compared with the u*-values evaluated by Clauser's method.The comparison results shown in Figure 9 show that the u* and u*r values are very good, with a maximum deviation of less than 5%; the average difference is 1.96%.

Effect of Sediment Transport on Shear Velocity
Sediment transport, particularly bed-load transport, can significantly impact shear velocity.Maini et al. [16] described that hat sediment transport (bed load) in a channel can cause the flow to become more turbulent, which can increase the shear velocity, which in turn influences the flow resistance.The data presented in Figure 10 illustrates the relationship between two key parameters: U/u* and R/ks of flow resistance.The U/u* ratio value is a comparison between the average cross-sectional velocity (U) and the shear velocity (u*).In contrast, the R/ks ratio value shows the ratio between the hydraulic radius (R) and the roughness height of the bed material (ks).This ratio reflects the flow's relative size compared to the riverbed's roughness (relative submergence), which can be formulated as (see Kironoto and Graf [6]): For large relative submergence, R/ks > 20 There is extensive research literature on uniform flow in open channels with bed materials of gravel and rough plate (see Kironoto and Graf [6]) and movable gravel beds with bed load (see Song, Graf, shown in Figure 10.The data obtained in this study for coarse sand bed material fall into the "large submergence (small roughness)" range, indicating that the sediment particles were fully submerged under the flow.This condition is often observed in rivers located in fluvial areas.
In general, in U/u* vs. R/ks data, the non-equilibrium tends to be greater than the equilibrium, but the data spread between the two types of flow data cannot be completely distinguished.The results of this study indicate that non-equilibrium sediment transport flows will cause changes in the channel bed over time.In contrast, equilibrium sediment transport flows have the potential to produce a relatively stable bed.In summary, Figure 10 presents various studies' data on bed conditions and sediment transport regimes.It shows that the U/u* ratio varies depending on the submergence level (bed roughness) and whether the sediment transport is in equilibrium.Overall, Figure 10 and the accompanying data provide valuable insights into the complex interactions between flow velocity, bed roughness, and sediment transport flow (bed-load) conditions.The roughness of the bed channel created by the sediment (bedload) increases the resistance to water flow, which increases the energy required to maintain flow.

Figure 10. Friction factor versus relative submergence
However, the influence of sediment bed load on shear velocity is indirect, and it depends on some factors, including sediment particle size, velocity, and flow regime.In general, the effect of bed-load sediments on shear velocity in running movable beds with and without sediment feeding, the presence of bed-loaded sediments can cause an increase in shear velocity.In contrast, the effect of bed-load on the integration constant, Br, can cause a decrease in Br values (see Figure 11).
The results showed an average shear velocity difference between sediment feeding (equilibrium) and without sediment feeding (non-equilibrium) by 9.41%.While for the integration constant Br value, the average difference between sediment feeding and without sediment feeding was 5.58%.These findings highlight the complex interplay between sediment feeding, bed-load sediments, and flow dynamics.The

Conclusions
The results of this experimental study show that the shear velocity without (non-equilibrium) and with sediment feeding flow (equilibrium) in the transverse direction of the channel tends to decrease towards the side walls of the channel.In general, the effect of bed-load sediments on shear velocity in running movable beds with and without sediment feeding, the presence of bed-loaded sediments can cause an increase in shear velocity.In contrast, the effect of bed-load on the integration constant, Br, can cause a decrease in Br values.The results showed an average shear velocity difference between sediment feeding and without sediment feeding by 9.41%.For the integration constant Br value, the average difference between sediment feeding and without sediment feeding was 5.58%.

Figure 2 .Figure 3 .
Figure 2. Documentation of model: (a) overall view of the experimental installation; (b) ADV

Figure 4 .
Figure 4.The typical contour of velocity normalized with mean cross-section velocity,u/U: (a) comparison between NSF and SF at vertical A, (b) velocity contour of NSFMBA1, (c) velocity contour of SFMBA1.

7 Figure 5 .Figure 6 .
Figure 5. (a) Typical example of shear velocity, u*, calculated using Clauser's method; (b) the resulting average u* per vertical plotted with the distance measurement (z/B)

Figure 9 .
Figure 9.Comparison of shear velocity between the Clauser method (u*) and Reynolds shear stress (u*r) 5]).All of them are based on the Weisbach-Darcy flow resistance equation.Br is usually taken by 6.25 for large relative submergence, say R/ks >20, and Br = 3.25 for small relative submergence, say R/ks <4.A transition region in the 4 < R/ks <20 experiment data of Song, Graf, and Lemmin [5], as Present data of NSF (non-equilibrium) Present data of SF (equilibrium) Song, Graf and Lemmin [5transport flow (equilibrium and non-equilibrium) on shear velocity can be different for different flow conditions.It may also change over time as the bed adapts to sediment transport.

Figure 11 .
Figure 11.Effect of sediment transport flows (bed-load) on the integration constant, Br