The numerical investigation of turbulence and scour interaction around the permeable groynes at the channel bend

Turbulence, particularly Reynolds Stress, plays a significant role in the flow field surrounding groynes, causing local scour. A limited number of studies have comprehensively analyzed the flow and turbulence structures encompassing a series of groynes in channel bends. This study numerically investigated the interplay between turbulence, sediment deposition, and scouring in a sharp channel bend with permeable groynes. The results show that the inner bank maintained high velocity, while permeable groynes decreased longitudinal velocity near the outer bank. Implementing permeable groynes structures reduced bottom velocity and increased flow separation. Turbulent kinetic energy distribution across the bend, particularly streamwise, influenced scour development more than vertical motion.


Introduction
Secondary flow and turbulence are key features of channel bend flow structures, affecting streamwise velocity distribution in transverse and vertical dimensions [1], [2], [3].Surface water flows outward, while near riverbed water flows inward, causing erosion and deposition.Turbulence, particularly Reynolds Stress, plays a significant role in the flow field surrounding groynes, causing local scour [4], [5], [6].As shown in Figure 1, structures like groynes in the direction of flow can bring about significant modifications in the flow pattern.These structures commence at the riverbank with a root and culminate at the regulation line, facilitating flood control, navigation enhancement, and erosion prevention.
Moreover, they serve as an effective measure to promote diverse channel morphologies and riverine ecosystems.Groyne, obliquely angled structures constructed to redirect water flow from critical zones, typically comprise stone, gravel, rock, earth, or piles.Permeable groynes using concrete or wooden piles allow water to pass through at a decreased flow velocity.This type of groynes proves advantageous in a river with a particular amount of suspended sediment.When constructed against the flow, these structures, built in groups that extend from the riverbank into the stream flow, cause significant changes to the flow patterns within the channel [7], [8].Despite the advantageous effects of groynes, they give rise to an intricate flow structure encompassing flow separation from fixed points and reattachment of the shear layer.The narrowing of a groyne increases the average flow velocity and flow rate per unit width.This augmentation in the average velocity causes heightened gradient and turbulence.As a result, the bed experiences an average velocity increase and a large vortex on the bed material.At the same time, the turbulence causes the bed particles to rise and become transported by the flow.Additionally, the spacing and type of groynes within a series yield varying recirculating flow patterns [10], [11].
A recent study has shown that the dimensions and patterns of coherent structures and scour and the degree of turbulence within flows that occur in open channels are directly correlated [12], [13], [14].A comprehensive analysis of the mean flow and turbulence structures surrounding a series of groyne in straight channels has been conducted.In contrast, the existing literature presents only a limited number of investigations on the flow phenomena surrounding permeable groynes in sharp channel bends or meanders.
The study explores the intricate interplay of various elements in a 3D turbulent flow field, resulting in sediment deposition and scour patterns.The study comprehensively analyzes the three-dimensional flow field near the permeable groynes in a sharp channel bend.The findings significantly improve our comprehension and prediction of the local scour linked to the permeable groynes in natural fluvial channels.

Materials and Methods
In this study, using NaysCUBE on the river analysis platform, iRIC.The model was designed to solve the Reynolds-averaged Navier-Stokes equations and the continuity equation, utilizing a sophisticated adaptive mesh system incorporating moving boundaries.The non-linear k-epsilon model developed by Kimura et al. was employed to achieve turbulence closure.The model was effectively utilized to simulate the secondary current of the first and second kinds and displayed excellent reproducibility in each case.Those interested in further details on the fundamental equations, discretization methods, boundary conditions, and other pertinent information may find them on the iRIC website [15], [16].
Simulations were conducted for clear water scour.The approach segment reached the particle motion threshold with no sand grain movement.Meandering channel scouring and deposition are due to channel bend and groynes structure interaction.The simulation employed a 150-meter river reach with a slope of 0.0025.The river reach was located at a sharp curve with a radius of 75 meters, a bottom width of 12 meters, and a top width of 35 meters.The upstream supply consisted of a flood discharge of 53.67 m 3 /s, an average velocity of 1.4 m/s, and a Froude number of approximately 0.4.A Manning roughness coefficient of 0.025 was chosen for the uniform bed material with a D50 of 0.15 mm.The formulas of Meyer Peter Muller and non-linear kappa-epsilon were selected to model sediment transport and turbulence, respectively [17].A series of 8-m length permeable groynes with about 3 m in the interval were installed along the outer curvature bank.A 1 x 0.7 m rectangular grid cell size was utilized to construct the computational mesh.Regarding the curvature before, at the midpoint of, and after 1311 (2024) 012007 IOP Publishing doi:10.1088/1755-1315/1311/1/0120073 bending, three lateral segments have been designated for subsequent examination, as shown in Figure 2.

Figure 2.
The computational mesh utilized for the channel bend incorporates a series of permeable groynes with specific lateral sections selected for further analysis.

Result and Discussion
The present study employed a numerical model to comprehensively analyze the three-dimensional velocity, turbulence, and bed scouring patterns in a sharp channel bend with permeable groynes.The simulation duration based on hydrological data was 3.5 hours (12,600 seconds).The resulting bathymetry displays typical channel bend morphology with erosion and deposition on opposite sides of the bend.The deposition extends beyond the bend's exit.The findings are concisely summarized below.

Velocity, Bed Shear Stress, and Bed Changes
Figure 3 displays the variation in magnitude of the flow velocity component in the bottom and surface along section 1, section 2, and section 3, respectively.Notably, the inner bank of each section bend maintained a high velocity, which can be regarded as a characteristic feature of a sharp degree of undulation, marked by the significant curve.The placement of the permeable groynes caused a substantial decrease in longitudinal velocity near the outer bank, and the flow velocity increased, causing it to move toward the centre of the channel.The development of horizontal vortex in the outer bank was recognized before permeable groyne structures.
Figure 4 also illustrates the effect of deflecting permeable groynes on the velocity component parallel to the bend's direction.Implementing a sequence of permeable groyne structures constructed on the right bank resulted in a significant reduction in the bottom velocity of the outer bank.Moreover, due to the alteration in the direction of channel curvature in section 1, the flow separation of the inner bank gradually increased and remained consistently higher beyond section 3.

Secondary Velocity
Characterizing flow patterns in a curved bend can be effectively accomplished by examining the secondary motion perpendicular to the primary flow due to centrifugal forces arising from the bend geometry and water surface superelevation.The secondary flow in a bend results in a mean velocity field that alters the distribution of the maximum value of the primary velocity.A secondary flow induces transverse shear, which modifies the bed shear stress and the near-bed turbulent stresses.In the context of flow in a sharp bend, the main pattern is the appearance of secondary flow.It is due to the combination of velocity in the lateral and vertical components.The cross-stream velocity can most effectively demonstrate the secondary flow (̅ ) and vertical ( ̅) velocity.The representation of cross-stream and vertical velocity is accomplished by utilizing mean velocity, which has a magnitude of √̅ 2 +  ̅ 2 ).
Figure 5 displays the velocity projection in the cross-sections and cross-stream motions in three cross-sections, with color maps representing positive vorticity in anticlockwise and negative in clockwise rotation senses.Due to a strong flow separation and vortex system, positive and negative  The distribution of vertical velocity adjacent to groyne fields can be observed in Figure 6.A robust horseshoe vortex system in Section 2 significantly impacts the region near the permeable groyne, generating a substantial negative vertical velocity advected downstream (Section 3).To predict the erosion of a mobile bed, the parameter for bed shear stress is an essential factor.Despite not being perfectly aligned with the location of maximum erosion, it indicates a general pattern of erosion deposition (Figure 7).Near the head of the permeable groynes show lower bed shear stress values in the beginning curvature but increase toward the bend.These regions can efficiently reduce the inner bank deposition in a sharp meander.

Reynolds Shear Stress and Turbulent Kinetic Energy
Figure 8 shows that Reynolds Stresses (RS) and Turbulent Kinetic Energy (TKE) were widely employed to quantify turbulence magnitude.Nevertheless, it is essential to acknowledge that these measures do not offer details on the importance or extent of flow fluctuations or vortices.This information is critical to quantifying mixing lengths of sediment transport.According to Figure 8, the maximum primary Reynolds Stress location was close to the bend entrance and followed the path of the inner curve, which was in line with the initiation of the thalweg.The primary Reynolds Stress decreased during the bend traversal, while the other Reynolds Stresses experienced an increase and achieved dominance.Bend geometry's effect on turbulent stresses becomes apparent through RS and turbulent kinetic energy changes at different cross sections.On the other hand, the determination of Reynolds Shear Stress provides significant insights into the pressure exerted on the fluid due to turbulent fluctuations generating shear.When dealing with linear flow in an open channel setting, the primary RS (streamwise-vertical) is typically the most significant due to its greater magnitude.In straight channels, the primary RS (uw) takes precedence and is crucial for sediment transportation.In the case of bends with helical flow, the rise in secondary velocities leads to the significance of the other two components of RS terms, which may surpass the critical shear stress of Figure 9 shows the distribution of TKE in the nearby bed region and surface.The concentration of high TKE values was observed in the of the permeable groyne fields, and the area exhibiting high Turbulent Kinetic Energy expanded towards the central part of the channel.In section 3, a decline in TKE values on both banks was observed, which suggested a reduction in permeable groynes' impact on TKE downstream.The TKE distribution across the bend has been presented in figure 10.As was anticipated, the flow near the head of permeable groynes' proximity exhibited the most significant TKE values.However, TKE decreased with increasing water depths near the permeable groynes.Notably, the permeable groynes redirect strong streamwise flow away from the outer bank.Meanwhile, permeable groyne presence lead to sudden bed elevation alteration and more diverse bathymetry linked with scour holes.The incident brought about an upsurge in TKE, which could generate higher v' and w' values.

Vorticity
The presentation of the magnitude x,y, and z-vorticity within the flow field is illustrated in Figure 11.It was observed that the magnitude of stream vorticity across all sections was greater in proximity to the bed.Furthermore, as one approaches the water surface, the magnitude declines significantly, approaching zero throughout the bend, barring a small area near the inner bank where maximum vorticity was also detected.The occurrence happened when there was a significant elevation change and was located on the inner bank, probably due to the presence of shorter permeable groynes.The shorter permeable groynes cannot deflect high vorticity and secondary currents from the outer bank to the inner bank.
The inner bank exhibited the extreme x, y, and z-vorticity values.The findings are consistent with the flow separation observed in the inner bend and the presence of the secondary flow.Observations revealed the existence of negative z-vorticity on the outer bank, which was limited to the area near the head of the permeable groynes, while the positive value was in the inner bend.The research's key assumption affirms that streamwise vorticity and vertical motion are the primary drivers of local scour development in the outer bank i.e., in the vicinity of the groynes head.

Conclusions
The study analyzed a channel bend with permeable groynes, revealing erosion and deposition on opposite sides.The inner bank maintained high velocity, while permeable groynes decreased longitudinal velocity near the outer bank.Implementing permeable groyne structures reduced bottom velocity and increased flow separation.Turbulent kinetic energy distribution across the bend, particularly streamwise, influenced scour development more than vertical motion.

Figure 3 .
Figure 3. Contours of velocity and velocity vector near bottom (i) and surface (ii).

Figure 4 .
Figure 4.The vertical distribution of flow velocity at selected lateral sections.
recognized near the outer bank section 2. Following section 3, both the magnitude of positive and negative transverse velocity and spatial extent increased.

Figure 5 .
Figure 5.The contours of the velocity and velocity vector delineated at selected lateral sections.

Figure 6 .
Figure 6.The vertical distribution of z-velocity at selected lateral sections.

Figure 7 .
Figure 7. Contours of bed shear stress (i) and bed elevation changes (ii)

Figure 8 .
Figure 8.The contours of the Reynold Stress near the bottom and surface.The flow direction was from the bottom towards the upward direction.
The Reynolds Stress components relating to turbulent velocity fluctuations and momentum flux are expected to be the most significant in the bend.

Figure 9 .
Figure 9.The contours of Turbulent Kinetic Energy in proximity to the bed (i) and surface (ii).

Figure 10 .
Figure 10.The vertical distribution of TKE.

Figure 11 .
Figure 11.The contours depict the magnitude of x-vorticity, y-vorticity, and z-vorticity, respectively.The direction of the flow is from bottom to top.