Turbulent flow mechanisms in meandering channels with sediment transport

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 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.

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 channel .	Discharge (Q) .	Flow depth (h) m .	Mean 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 channel .	Discharge (Q) .	Flow depth (h) m .	Mean 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

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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.

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).

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.