This research aims to investigate the near-bed turbulent flow characteristics in a meandering channel with both mobile bed and immobile bed conditions. Experiments were performed in a prismatic rectangular meandering channel with a non-uniform sand bed of size d50 = 0.523mm. The three-dimensional instantaneous fluid velocity was collected using the Acoustic Doppler velocimeter which will provide important results related to the flow turbulence such as mean flow velocity, turbulence intensity, Reynolds shear stress, turbulent kinetic energy, skewness, kurtosis and turbulent anisotropy. The secondary current flow and the exchange of momentum in the form of turbulence kinetic energy, Reynolds shear stress and turbulent intensity at the inner layer of the flow are identified more in a mobile bed condition as compared to an immobile condition, which causes sediment transport. For the inner layer of the flow, turbulence intensity and turbulent kinetic energy are decreased in magnitude and gradually increase in the outer layer of flow for both the bed conditions. Higher turbulence anisotropy is noticed in the mobile bed condition than in the immobile bed condition, which shows more nonuniformities near the bed level for the mobile bed condition. This study may help in understanding the effect of sediment transport due to a turbulent flow structure in a sinuous alluvial channel.

  • Comparison of turbulence between mobile and immobile bed conditions.

  • The near-bed longitudinal velocity profile increases with an increase in distance from the bed surface.

  • Negative values of Reynolds shear stress due to a narrow channel.

  • At the bend portion, the mobile bed has higher TKE than the immobile bed and vice versa at the cross-over section.

  • Turbulent anisotropy shows more nonuniformities of flow in the case of mobile beds.

The interaction of flow in a river with the sediment can generate bed aggradation and degradation processes, which are relevant in river management engineering. The movement of sediment at the bed level through the flow of water in the channel or river is one of the most essential properties of a fluvial bed. Most natural channels have a sinuous shape in their alluvial plane where erosion from the outer apex and deposition occurs at the inner curve (Esfahani & Keshavarzi 2011). The dynamic nature of the sinuous channels, which consist of a sequence of loops, turns or bends in their course has fascinated investigators. The flow features in a sinuous bend, including velocity distribution, Reynolds shear stress (RSS), Reynolds normal intensity and turbulent kinetic energy (TKE) are seen to be distinct from straight alluvial channels in both mobile bed and immobile bed conditions (Anwar 1986). The flow characteristics throughout the sinuous bend give a complete knowledge of the hydraulic processes related to erosion and depositional features.

According to Schumm (1963), meandering channels indicate a less aspect ratio. For the last 3–4 decades, numerous researchers have done multiple studies in the laboratory and the field to analyse the behaviours of meandering rivers thoroughly. According to their studies on a sinuous river, secondary flow is crucial to describing flow patterns (Rozovskiĭ 1961; Anwar 1986; Abad & Garcia 2009; Blanckaert 2009; Termini 2009). The nature and turbulent flow behaviour in a sinuous river differ from straight channels. Generally, the velocity profile is not exactly logarithmic in straight channels (Anwar 1986; Graf & Blanckaert 2002; Booij 2003; Sukhodolov & Kaschtschejewa 2010). De Vriend & Geldof (1983) investigated the flow velocity in a sharply curved small bend. They discovered that the maximum velocity tends to move towards the inner bend when the flow stage increases. In extremely narrow open channel bends, which had an aspect ratio of 3.6, Blanckaert & Graf (2001) found two secondary currents cells (one in the centre and the other on the outer bank). They stated that the centrifugal force was the primary source of helical motion in the central portion, which occupied the entire water depth, whereas circulations on the outer side bank were important in bank erosion processes. Rameshwaran & Naden (2004) determined the free-surface turbulent flow in a two-stage meandering channel by using three-dimensional modelling. Keshavarzi & Gheisi (2006) developed a new bursting approach that accounted for all fluctuating velocities in three directions. They investigated the bursting behaviour in a vortex chamber and discovered that sweep events cause sediment transport. Several laboratory tests in meandering channels have observed bed growth at multiple angles of deflection (θ). The eroding and sedimentation features are evident at the cross-overs for small, whereas these are focused around the bend apexes for large, as per da Silva et al. (2006). Over 11 years, Engel & Rhoads (2012) investigated the bed geometry and channel plan-form and flow dynamics in a compound meandering loop. They concluded that the near-bank velocity and turbulence are the major drivers of bank erosion and channel movement.

Many researchers (Blanckaert 2002; Blanckaert & De Vriend 2005) concluded that a meandering channel has a different RSS and turbulence intensity than a straight channel. An experiment carried out at a 200° deflection angle of a compound bend channel by Abad & Garcia (2009) concluded that TKE depends on normal shear stress. Another experiment having a large amplitude of in a laboratory flume was tested by Termini (2009). It was discovered that the aspect ratio (b/d) is an important aspect to show the presence of cross-circulation motion. According to Esfahani & Keshavarzi (2011) the chance of bursting events reduces as the channel's curvature length increases. They also found with less aspect ratio (width/depth = 2.8) in a sinuous channel, the transverse motion of sediment particles occurs at the apex portion. The circular motion of sediment particles occurs due to more stress at the convex portion and fewer stresses at the concave portion. The erosion is most prevalent in the outer bend due to the high stress at the bank that causes high-momentum flux of the channel. But according to Engel & Rhoads (2017), the outer bank circulation cell was not observed in a real-field scenario. Keshavarzi et al. (2016) discovered scouring at the meandering river's innermost bank and found maximum longitudinal velocity at the inner bank. The stresses at the channel's bank present the high-momentum flux near the bank regions where erosion and deposition activities dominate. Taye et al. (2021) examined the turbulent flow characteristics and bursting events at the centre of the bend in a meandering channel with a uniform sand bed and contribute that the sweep events are maximum nearer to the channel bed. Graf & Blanckaert (2002) studied experiments in a 120° sharp bend and discovered a large and a small secondary rotation cell at the centre and outer region of the apex, respectively.

Several authors claim that the velocity is maximum in the inner flow region (Dietrich et al. 1979; De Vriend & Geldof 1983). Various studies in sinusoidal channels with fixed beds and floodplain flows have also been conducted, e.g., Ervine et al. (1993), Willetts & Rameshwaran (1996), Shiono & Muto (1998), Shiono et al. (2008), Rao et al. (2022) and Spooner & Shiono (2003) . They analysed different flow characteristics such as secondary flow, turbulence, as well as the expansion and contraction of the flow in a main channel. A rectangular meandering channel with an aspect ratio (b/h) of 2.83 was estimated for the detailed measurement of secondary turbulence flow by Shiono & Muto (1998). The most significant reason for the difference between the straight compound channel and the meandering channel is the generating mechanism of secondary flow and turbulence mixing.

Lyness et al. (1998) demonstrated that the roughness coefficient of the effective main channel increases significantly under relatively shallow overbank flow. However, they are similar in an overbank flow which is relatively deep. This implies that variation occurs in the bedform and flow structure of a meandering channel during a flood. Various studies in a meandering channel with a mobile bed condition have been identified, e.g., Lyness et al. (1998), Ishigaki & Muto (2001), and Wormleaton et al. (2004). It is observed that bedform alters with overbank flow depths for mobile bed conditions. Wormleaton et al. (2004) observed velocity distribution having a movable bed in a sinusoidal channel with an emergent element that resembled bushes on the floodplain. This research indicates that the movement of sediments and secondary flows is dominated rather than by direct floodplain flow by centrifugal force. In a three-dimensional simulation of turbulent flow in sinusoidal channels and rivers, Nguyen et al. (2007) found that for a single bend, the maximum velocity moved closer to the convex bank as it entered the curve and gradually crossed the concave bank. In order to explore the turbulent flow in a meandering compound open channel with a trapezoidal cross-section, Jing et al. (2011) performed numerical calculations in three dimensions. They found that there was a strong correlation between the simulations and the experimental data, showing that the Reynolds stress model can correctly determine the complex flow phenomenon. In order to test the turbulent flow structure inside the meandering channel, Esfahani & Keshavarzi (2013) studied three physical models of river meanders representing strongly curved bends, mild bends, and elongated symmetrical meander loops. They discovered that the presence of 3D fluctuating velocities at various locations inside the river meanders, in addition to the influence of average flow velocity and turbulent flow characteristics are the reasons for sediment transport. In the case of the turbulent structure and bursting process in multi-bend meander channels, Liu & Bai (2014) observed that the contribution chances of the classes of the rightward ejection, rightward sweep, leftward ejection, and leftward sweep are higher compared to other classes. According to an analysis by Taye et al. (2020), the variation in average velocities over time does not approach the logarithmic law; instead, the eddy length decreases near the bed due to the scale of turbulence and bursting event in the case of a well-defined meandering channel bend. The previous literature works (Ab. Ghani & Azamathulla 2011; Azamathulla et al. 2012) used a numerical approach to predict the sediment transport in open channels.

According to the above literature study, it is understood that researchers have thoroughly studied the influence of bend, and loop, on turbulence flow characteristics of a meandering channel in the laboratory and at on-site locations. However, a lot of studies have been carried out to figure out the mean flow velocity in a mobile bed with uniform sand bed, gravel bed and heterogeneous bed in a meandering channel and also various papers have shown the effect of water flow in floodplain areas and the presence of vegetation. In contrast, the comparison of turbulence behaviour between the mobile bed and immobile bed (clear water condition) conditions with non-uniform bed materials is yet to be explored. The majority of the experimental studies are performed to analyse the turbulent flow characteristics and bed morphology on the plane and fixed beds. The cross-sectional channel shape of an alluvial river is governed by its hydraulic geometry, referring to the interrelationship among water discharge, channel width, flow depth, velocity, and so forth. Since most natural channels have a sinuous shape (Esfahani & Keshavarzi 2011), therefore, the objective of this research is to observe turbulent flow characteristics, which include mean flow velocity, RSS, Reynolds normal stress (RNS), TKE, skewness, kurtosis and turbulent anisotropy in the mobile bed condition and clear water condition in a meandering channel and to compare the results between them. The present study examines the role of turbulent flow in the development of sediment transport by applying a discharge to maintain mobile bed conditions with non-uniform sand bed material. The interaction of flow in a river with the sediment can generate bed aggradation and degradation processes, which are relevant in river management engineering.

The experiments were carried out at the Hydraulics Laboratory of the National Institute of Technology Rourkela, India. The plan and side view of the experimental setup is shown in Figure 1. The layout of the meandering channel has a size of 10 m in length, a width of 1.7 m, and a height 0.9 m with a fixed incline plane bed of slope 0.001. The cross-section of the meandering compound channel (main channel) is rectangular-shaped with 0.28 m of width and 0.12 m of depth. Table 1 contains the channel's detailed specifications. The test sections were chosen at the middle portion of the meandering compound channel. The effect of upstream and downstream are less and have sinuosity of 1.06° and 30° of deflection angle constructed by a Perspex sheet with a channel roughness of n = 0.01 and a thickness of 7–10 mm. A Reinforced Cement Concrete overhead tank was placed upstream of the flume to supply water in the experimental channel bed, and it helps maintain the steady flow condition in the channel. The steady flow was maintained in the channel by keeping a constant depth of water in the overhead tank and continuous flow was carried out without switching off the pump. Water that has overflowed is sent back to the sump tank. All flowing water through the channel is collected in the volumetric tank and allowed into the sump tank and a considerable circulation process was going on. Three 10-HP limit of diffusive siphons with suction and conveyance pipes are installed for the water supply distribution network to the channel. To maintain subcritical flow and to reduce the turbulence in the flow, an arrangement of baffles in a stilling chamber is installed near the channel's entrance. On the downstream side of the channel, an adjustable tailgate setup plan is installed to achieve a consistent level in the channel. By adjusting the tailgate downstream of the channel, the quasi-uniform flow was established. After flowing water for 3–4 h in the channel, the instantaneous velocity readings were recorded at each test section. The 2.25-m long test section was chosen at a distance measuring 3.8 m (distance measured from the intake part in flow direction), where the flow was completely formed and devoid of backwater effects. The main channel bed is covered with sand having a size of 0.523 mm. The experimental setup was placed over a moving bridge, which was installed over the width of the channel.
Table 1

Specifications of channel parameters

Sl no.Channel descriptionSymbolValue
Channel type – Meandering channel 
Length of flume 10 m 
Width of the flume 1.7 m 
Slope of the channel  0.001 
Sinuosity of the channel Sr 1.06 
Meandering belt width Bm 0.61 m 
Wavelength of the channel  2.23 m 
Depth of the main channel 0.12 m 
Width of the main channel 0.28 m 
10 Main channel arc angle  30 
11 Aspect ratio  2.33 
Sl no.Channel descriptionSymbolValue
Channel type – Meandering channel 
Length of flume 10 m 
Width of the flume 1.7 m 
Slope of the channel  0.001 
Sinuosity of the channel Sr 1.06 
Meandering belt width Bm 0.61 m 
Wavelength of the channel  2.23 m 
Depth of the main channel 0.12 m 
Width of the main channel 0.28 m 
10 Main channel arc angle  30 
11 Aspect ratio  2.33 
Figure 1

(a) Plan view and (b) lateral view of the experimental setup.

Figure 1

(a) Plan view and (b) lateral view of the experimental setup.

Close modal

The readings of three-dimensional instantaneous velocity were recorded using the advanced instrument known as Son Tek 16 MHz Micro-Acoustic Doppler Velocimetry (ADV). It is a four-beam down-looking probe with a very small sample volume situated 0.05 m underneath the central transmitter. Hence, the ADV could not capture data from the water surface to a depth of 0.05 m. The instantaneous velocities U, V and W represent the streamwise (X-direction), transverse (Y-direction) and vertical(Z-direction) directions, respectively. The data were recorded at the centre line of the apex portion where the curvature impact is high and cross-over portions, over the testing section. At each location, 6,000 samples were taken at a sampling rate of 50 Hz for a duration of 120 s near the channel bed (4 mm from bed level). After the fully developed flow is observed in the channel, measurements of velocity at each location were recorded. Around 15–20 velocity points were collected at the centre of each section in a vertical direction. The sample has to be post-processed at each measurement point to eliminate the spikes in the data caused by the transmission and receiving of the signals. During data filtration, the signal-to-noise ratio (>15) and correlation (>70%) were maintained. The spikes were removed using WINADV software.

In this experiment, the meandering channel was composed of a non-uniform sand bed of particle size = 0.523 mm, = 0.9025 mm and = 0.3705, which was found from the particle size distribution curve by performing the sieve analysis according to the Indian Standard Code IS: 2386 (Part I). The Geometric standard deviation was calculated by using the formula and the gradation coefficient G was calculated from the formula. Here, the geometric standard deviation is calculated as 1.725, greater than the value 1.4 and the gradation coefficient defines that the sediment mixture is non-uniform. The shear velocity () was obtained by using the TKE approach (Stapleton & Huntley 1995) given as follows:
(1)
where TKE (turbulent kinetic energy) is a measure of turbulence intensity which is denoted as:
(2)
where , , are root mean square (provides some knowledge about the magnitude of the fluctuations hence also known as turbulence intensity) in the streamwise direction, transverse direction and vertical direction, respectively. Here, , and are corresponding velocity fluctuations in streamwise, widthwise and vertical direction, respectively. In Equation (1), is bed shear stress. For various flows, is set as 0.19 (Stapleton & Huntley 1995), is the water density and the proportionally constant identified for a wide range of flow (Soulsby 1983).

The experiments were carried out by considering two different discharges taking two different conditions: mobile bed condition and immobile bed condition. For both the bed conditions, 2 cm of sand bed was arranged at the test section. In the mobile bed case, the discharge was maintained such that a small amount of sediment gets eroded, but in the immobile bed case, the discharge was managed so that no sand particles should move in the channel. In this study, the Reynolds numbers are 61,315 and 49,441 in the case of both mobile bed and immobile bed conditions, respectively, which shows the turbulent flow and Froude numbers are less than 1, which shows subcritical condition. All detailed values are given in Table 2.

Table 2

Flow parameters in the experiments

Rectangular sinuous channelDischarge (Q) Flow depth (h) mMean flow velocity Froude number Reynolds number Manning's roughness (n)Geometric standard deviation Shear velocity mm/s
Mobile bed 0.007128 9.34 0.27256 0.183 61,315 0.017 1.725 4.8694 
Immobile bed 0.006493 10 0.2319 0.160 49,441 0.02 1.725 4.6578 
Rectangular sinuous channelDischarge (Q) Flow depth (h) mMean flow velocity Froude number Reynolds number Manning's roughness (n)Geometric standard deviation Shear velocity mm/s
Mobile bed 0.007128 9.34 0.27256 0.183 61,315 0.017 1.725 4.8694 
Immobile bed 0.006493 10 0.2319 0.160 49,441 0.02 1.725 4.6578 

Manning's roughness coefficient n was derived to determine the effect of roughness on the flow in a sand bed channel. To find Manning's n, the general equation was used, which is given as follows:
(3)
where n, u, and S represent the Manning coefficient, velocity of flow, hydraulic radius, and energy slope, respectively.

Mean flow velocity

The instantaneous velocity components in the longitudinal (U), transverse (V) and vertical directions were calculated as:
(4)
(5)
(6)
where , are the time-averaged velocity components where n is the number of samples and , and are corresponding velocity fluctuations in streamwise, width wise and vertical direction, respectively.
Figures 2 and 3 show the mean velocity profile of each section (S1, S2, S3, S4 and S5), which explores the flow behaviour of the immobile and mobile bed cases by utilising the three-dimensional measured velocity data. The longitudinal, vertical and transverse time-averaged velocity components at each section were normalised by dividing the corresponding shear velocity () (i.e., , and and the profiles are plotted against the normalised flow depth (z/h), where z is the depth from bed level and h is the flow depth. The velocity generally increases in a zig-zag manner from the near-bed (z = 4 mm) level in both cases. It is noticed that in mobile bed (Figure 2), the depth of water changes after the transportation of bed particles with the flow. Sections S-1, S-2, S-3 and S-5 show deposition of bed material, whereas section 4 shows erosion of bed material causes morphological changes in the middle of the main channel. The near-bed longitudinal velocity profile in the mobile bed case shows the velocity increases with an increase in distance from the bed surface and observes the scattered values of velocity within the near-bed region. The velocity in the lateral direction indicates that the velocities are more scattered up to 0.2 h from the bed surface; thereafter, the velocity increases smoothly and gives a positive value. Quite similar longitudinal and lateral velocity profiles were found at the apex of the sinuous channel (Taye et al. 2021). The velocity in the vertical direction gives both negative and positive values and shows more randomness due to the tiny reverse flow occurring at the bend portion.
Figure 2

Vertical profiles of time-averaged velocity in (a) longitudinal, (b) transverse and (c) vertical directions for mobile bed conditions.

Figure 2

Vertical profiles of time-averaged velocity in (a) longitudinal, (b) transverse and (c) vertical directions for mobile bed conditions.

Close modal
Figure 3

Vertical profiles of time-averaged velocity in (a) longitudinal, (b) transverse and (c) vertical directions for immobile bed conditions.

Figure 3

Vertical profiles of time-averaged velocity in (a) longitudinal, (b) transverse and (c) vertical directions for immobile bed conditions.

Close modal

In the immobile bed (Figure 3), the depth of water was not changed because no sedimentation occurred at the channel bed. The longitudinal velocities at each section increase with depth, but the velocities are more at the bend portion than in the cross-over section. The velocities at the lateral direction seem more random due to higher flow resistance. In the vertical direction, velocity has a more significant number of negative values with a small magnitude due to the fixed channel. The result concludes that the magnitude of velocities in mobile bed conditions is higher than in clear water conditions, whereas more fluctuations are found at the downstream section in both cases. The observed velocity patterns in both conditions are quite symmetrical in the longitudinal direction and random values of velocities are found in the lateral direction.

Reynolds stresses

The development of time-mean velocity components () in turbulent flow is influenced by velocity fluctuations , which increase the resistance to deformation. This ultimately leads to apparent stresses known as Reynolds stresses. These Reynolds stresses give crucial information about the flow behaviour. The Reynolds equations or more explicitly Reynolds-averaged Navier–Stokes (RANS) equations are used to find out Reynolds stresses:
(7)
(8)
(9)
where gx, gy and gz are the gravity components in longitudinal, lateral and vertical directions of flow and is the time-average pressure intensity. These last terms offer additional stresses which are generated from the cross products of velocity fluctuation components. Thus, they are also known as turbulent stresses or Reynolds stresses. The RANS equations are multiplied throughout by the fluid mass density in order to turn the acceleration dimension into stress, as dimension of acceleration is present on both sides:
(10)

There are two components of Reynolds stresses: RSS and RNS, which are symmetric second order tensor components. The components of stresses, i.e., the diagonal component (RNS) and the off-diagonal component (RSS) were defined by Pope & Pope (2000).

Reynolds shear stresses

Because of flow turbulence, the RSS is a component of the shear stress occurring on the X–Y plane parallel to the flow direction. The streamwise RSS on the channel bed on the X–Y plane is important because turbulent shear acts on the bed particles. Physically, it shows the transport of instantaneous streamwise momentum normal to the X–Y plane. RSS can be calculated by the Equation (7). The study of RSS gives details on the momentum flux at the central location of the bend (S-1, S-3 and S-5) and cross-over (S-2, S-4) for both mobile bed and immobile bed conditions. In contrast to straight flow, Blanckaert (2002) reported both positive and negative values in the RSS distribution of a meander bend. And the discontinuous distribution of RSS was observed, which attributes to the presence of helical flow in the apex portion of the meandering channel. The sediment in the outer bend indicated high stresses and deposition in the inner bend showed fewer stresses:
(11)
(12)
The RSS is presented in Figure 4. The horizontal axis represents the non-dimensional RSS and the vertical axis shows the dimensionless water depth. For mobile bed flow condition, it is clearly observed that the RSS distribution at the central part of each section follows a zig-zag profile at sections S-1, S-2 and S-4 and further, the magnitude of RSS decreases by increasing the distance from bed level, which shows more disturbances of particles. However, it is observed that in sections S-3 and S-5, a smooth increase of the RSS magnitude with the increase in water depth from bed level where the sediment bed level increases at the centre line due to erosion and deposition process and eventually provides higher flow resistance. The additional turbulent forces induced due to the bend with the sand bed involve higher sediment transport. Since the longitudinal flow velocity is lower in the vicinity of the bed surface and the secondary currents transfer the sediment from upstream to downstream, as a result, the sediment concentration at the surface near to bed level is higher. In the case of an immobile bed, each section shows a similar profile up to z = 0.25 h, whereas, above that depth, it shows a scattered profile. This was occurring due to the less flow resistance and reduction in flow velocity as compared to the mobile bed channel. RSS in the mobile bed flow at each section is higher than that of clear water flows due to sediment transport. The outer layer of each section in case of clear water flow is observed negative values, whereas in the case of mobile bed conditions, negative values are observed at sections S-1, S-2 and S-4 above the height of 0.25 h. Taye et al. (2021) confirmed that a negative value of RSS can be observed in a meandering channel. The negative values of RSS come because of the narrow meandering channel.
Figure 4

Vertical profiles of RSS for (a) mobile bed and (b) immobile bed conditions.

Figure 4

Vertical profiles of RSS for (a) mobile bed and (b) immobile bed conditions.

Close modal

Reynolds normal stresses/turbulence intensity

Reynolds normal stresses arise due to turbulent fluctuation and are represented by time-average values of quadratic terms of the velocity fluctuation. As the root mean square provides some knowledge about the magnitude of the fluctuations, it is called turbulence intensity. The turbulent intensity is normalised by dividing it by shear velocity . Hence the normalised turbulence intensities can be denoted as (in streamwise direction), (in transverse direction) and (in vertical direction). Figures 5 and 6 shows the normalised turbulence intensity against the normalised depth at the centre line of each test section (three bend section and two cross-over section). In mobile bed, the turbulence intensities at the apex point are reduced up to z=0.17 h height from bed level, whereas at sections S-1, S-2 and S-4, a sharp increase in turbulence intensity occur from z = 0.25 h. Hence the increase in turbulence intensity in the mobile bed may increase sediment transport, leading to modifications in the alluvial channel bed. While the contribution of fluctuations causes circular flow at the bend centre. In an immobile bed, the turbulent intensity across the depth is more uniform for each section and increases up to z = 0.3 h from the bed surface; thereafter it tends to decrease.
Figure 5

Vertical profiles of turbulence intensity in (a) longitudinal, (b) transverse and (c) vertical directions for mobile bed conditions.

Figure 5

Vertical profiles of turbulence intensity in (a) longitudinal, (b) transverse and (c) vertical directions for mobile bed conditions.

Close modal
Figure 6

Vertical profiles of turbulence intensity in (a) longitudinal, (b) transverse and (c) vertical directions for immobile bed conditions.

Figure 6

Vertical profiles of turbulence intensity in (a) longitudinal, (b) transverse and (c) vertical directions for immobile bed conditions.

Close modal

Turbulent kinetic energy

TKE is a measure of turbulence intensity. TKE can be calculated by the Equation (2). The dimensionless TKE (DTKE) can be expressed as:
(13)
where is the mean flow velocity. TKE distribution is shown in Figure 7 for both the mobile bed and immobile bed conditions. In the mobile bed case, it is noticed that profiles of DTKE for each section have a distinct regularity change along with the flow depth and also it is seen that DTKE at cross-over sections (S-2, S-4) are higher than the apex bend (S-1, S-3 and S-5). Less TKE indicates the zone of sedimentation and less velocity fluctuation due to the energy and momentum exchange. Whereas in immobile bed conditions, the profiles of DTKE for each section have quite similar, which shows the absence of a zone of sedimentation indicating sediment particles are not transferred in the longitudinal direction, but slight vibration of sand particles might be there. By comparing both mobile bed and immobile bed conditions, TKE at the bend portion is higher in the mobile bed than an immobile bed, while the result is quite opposite at cross-over section due to the coherent structure formation.
Figure 7

Vertical profiles of TKE in (a) mobile bed and (b) immobile bed conditions.

Figure 7

Vertical profiles of TKE in (a) mobile bed and (b) immobile bed conditions.

Close modal

Skewness

The skewness of velocity fluctuations can be shown by Figures 8 and 9 show the profile of third-order correlation skewness at each section for mobile bed and immobile bed conditions. Here a clear distinction between mobile bed and immobile bed was seen. However, the following discussion could be made. In both the case, S(u) (the longitudinal flux of the longitudinal RNS ) starts with small negative values near the bed surface and found less magnitude of skewness in mobile bed as compared to immobile bed conditions. Whereas, S(v) (the lateral flux of the lateral RNS ) and S(w) (the vertical flux of the vertical RNS ) start with small positive and negative values at the near-bed surface and change over to negative and positive values by forming zig-zag profile for both the flows. In the mobile bed, a higher negative value of S(u) in the vicinity of bed region is observed in section 3, signifying the increasing trends of the streamwise momentum of RNS and dominance of sweep events in this region, which increases the turbulence in the mobile bed case. However, in the immobile bed case at sections S-2, S-3 and S-5, a higher negative magnitude with distance from bed surface is observed in a streamwise direction. The result suggests that the bed mobility influences the skewness by changing the flow condition.
Figure 8

Vertical profiles of skewness in (a) longitudinal, (b) transverse and (c) vertical directions for mobile bed conditions.

Figure 8

Vertical profiles of skewness in (a) longitudinal, (b) transverse and (c) vertical directions for mobile bed conditions.

Close modal
Figure 9

Vertical profiles of skewness in (a) longitudinal, (b) transverse and (c) vertical directions for immobile bed conditions.

Figure 9

Vertical profiles of skewness in (a) longitudinal, (b) transverse and (c) vertical directions for immobile bed conditions.

Close modal

Kurtosis

The coefficient of Kurtosis is the fourth-order correlation, which shows the intermittency of turbulence. The variation of kurtosis was calculated by formula , where K(u), K(v) and K(w) indicate the kurtosis in the streamwise, lateral and vertical directions, respectively. Figures 10 and 11, respectively, show the profiles of kurtosis against the normalised flow depth z/h for both mobile bed and immobile bed conditions. It is observed that the magnitude of kurtosis in the mobile bed is less than 3 which indicates a flat characteristic (platykurtic distribution or too flat) for the flow interacting with the bed surface. In the case of immobile bed, some of the kurtosis data have a magnitude of more than 3 indicating a slight peaky signal pattern of intermittent turbulence. At the near-bed region, the average value of K(u), K(v) and K(w) were higher in the immobile bed than in the mobile bed condition which suggest that a higher level of turbulence intermittency with immobile bed.
Figure 10

Vertical profiles of kurtosis in (a) longitudinal, (b) transverse and (c) vertical directions for mobile bed conditions.

Figure 10

Vertical profiles of kurtosis in (a) longitudinal, (b) transverse and (c) vertical directions for mobile bed conditions.

Close modal
Figure 11

Vertical profiles of kurtosis in (a) longitudinal, (b) transverse and (c) vertical directions for immobile bed conditions.

Figure 11

Vertical profiles of kurtosis in (a) longitudinal, (b) transverse and (c) vertical directions for immobile bed conditions.

Close modal

Turbulence anisotropy

The degree of flow anisotropy is an empirical constant that can be expressed as . The vertical profiles of turbulence anisotropy are plotted against normalised flow depth. From Figure 12, it was found that the flow is highly anisotropic as , which shows the nonuniformities in the flow near the bed level for both mobile and immobile bed conditions. In the mobile bed condition, the ratio of varies from 0.178 to 0.281 at the inner layer of each section, whereas this range is from 0.168 to 0.334 in immobile bed conditions, which shows more generation of rotational acceleration of a fluid element in case of mobile bed conditions.
Figure 12

Vertical profiles for turbulent anisotropy at (a) mobile bed and (b) immobile bed conditions.

Figure 12

Vertical profiles for turbulent anisotropy at (a) mobile bed and (b) immobile bed conditions.

Close modal

An experimental study has been conducted to observe the turbulence flow characteristics in a meandering channel for both mobile bed and immobile bed conditions. By comparing the results at both conditions, the following conclusions are found.

  • 1.

    The normalised time-averaged flow velocity in mobile bed conditions is found less compared to immobile bed conditions. The time-averaged velocity profile in both cases presented an inflected shape because of turbulence created in the meandering channel.

  • 2.

    The reduction in RSS near the bed region in the existence of sediment transport provides momentum from the main channel flow to continue the sediment transport overcoming the bed resistance. The damping of RSS distribution in the flow inner layer for mobile bed resulting from a fall in velocity fluctuating components in the near-bed region. The sediment transport in mobile bed conditions increases the streamwise velocity, resulting in a reduction of bed resistance with the mobile bed. It shows the bed resistance in mobile bed is lower than in immobile bed conditions.

  • 3.

    TKE decreases with the distance from the bed surface that is up to z = 0.15 h, then increases with an increase in z/h for the mobile bed. In the immobile bed case, the TKE magnitude is reduced with the flow depth that is up to z = 0.35 h; thereafter increases with flow depth. Less magnitude of dimensionless TKE is found in mobile bed cases as compared to immobile beds, which associate with sediment transport.

  • 4.

    The third-order correlation or skewness shows both positive and negative values in mobile bed cases revealing dominance of sweep event. The higher value of kurtosis in longitudinal, transverse and vertical direction cases shows more degree of turbulence intermittency in the immobile bed cases. In both cases, turbulent anisotropy is less than 1 showing high nonuniformities of flow. It is found that the fluid elements generate more rotational acceleration in mobile bed conditions than in immobile bed conditions.

From the present study, River Engineers will get knowledge about events of turbulent flow linked with sediment transport in the meander mobile bed channel since turbulence governs the morph dynamical changes by entraining and depositing the sediments. The experimental data reported in the present study provide a benchmark to calibrate and validate the advanced turbulence models required for practical applications in the meander alluvial river. The flow characteristics throughout the sinuous bend give a complete knowledge of the hydraulic processes related to erosion and depositional features. The present study of turbulent flow is limited to the meandering channel over rough beds within the present experimental conditions. The present study can be extended for various grain sizes and for the various flow discharges to understand the flow behaviour and the bed morphology of the channel. Also, future researchers can do the numerical analysis of turbulence using different models such as ANSYS, CFD, and FLOW 3D and validate with the experimental results.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.

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