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( a ) Isolines of normalized downstream velocity, v s / U . ( b ) Normalized depth-averaged downstream velocity, U s / U ; normalized unit discharge, ( U s Bh ) / Q . ( c ) Vertical profiles of
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Secondary currents are a characteristic feature of flow in open-channel bends. Besides the classical helical motion (centre-region cell), a weaker and smaller counter-rotating circulation cell (outer-bank cell) is often observed near the outer bank, which is believed to play an important role in bank erosion processes. The mechanisms underlying the...
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... outer-bank cell comes into existence when the v s -profiles are so strongly deformed that the driving term changes sign in the upper part of the water column (cf. figure 3c in § 6). For the axisymmetric curved flows investigated in these numerical models, the outer-bank cell was only slightly weaker than the centre-region cell. ...
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... vectorial representation of the measured cross-stream velocity field, (v n , v z ), normalized by the overall mean velocity U = Q/(BH ), is shown in figure 3(d). The centre-region cell reflects the 'classical' helical motion that is characteristic of flow in bends. ...
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... circulatory part of the cross-stream motion is reflected by the downstream vorticity, ω s , which is shown in figure 3(e). The centre-region cell and the outer-bank cell, separated by the (ω s = 0)-contour, are clearly visible in the vorticity field. ...
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... distribution of the normalized downstream velocity component, v s /U , is given in figure 3(a). Its depth-averaged value is nearly constant over most of the measuring area: U s /U ≈ 1.35 (figure 3b), which means that the depth-averaged velocity there is well above the overall mean velocity. ...
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... depth-averaged value is nearly constant over most of the measuring area: U s /U ≈ 1.35 (figure 3b), which means that the depth-averaged velocity there is well above the overall mean velocity. Figure 3(b) also shows that the distribution of the normalized unit discharge, U s Bh/Q, with h denoting the local water depth, is concentrated in the deep outer part of the cross-section. Integration of this profile shows that about 80% of the discharge passes through the investigated outer half of the cross-section. ...
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... of this profile shows that about 80% of the discharge passes through the investigated outer half of the cross-section. The core of maximum velocity, marked by in figure 3(a, b), is found near the transition between the two circulation cells. Figure 3(c) compares some measured v s / U s -profiles with a logarithmic profile for a friction factor C f = 0.008, which corresponds to the value in the experiment as estimated by Blanckaert & Graf (2001). ...
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... core of maximum velocity, marked by in figure 3(a, b), is found near the transition between the two circulation cells. Figure 3(c) compares some measured v s / U s -profiles with a logarithmic profile for a friction factor C f = 0.008, which corresponds to the value in the experiment as estimated by Blanckaert & Graf (2001). The profiles shown are averaged over the outer-bank region (n = −20 to −14 cm), the transition zone (n = −14 to −8 cm) and the centre region (n = −8 to 0 cm). ...
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... (figures 3e, 5 and 6) Integrated over the water depth, the centrifugal term in the vorticity equations (4)- (6) is always positive, which complies with the sense of rotation of the centre-region cell. Due to advective momentum transport by the centre-region cell, the velocity maximum in the present experiments is in the lower part of the water column ( figure 3c). As a consequence, the centrifugal term -(∂/∂z)(v 2 s /R) in the vorticity equation is negative in a significant part of the water column (figure 5a), thus opposing the observed sense of rotation of the centre-region cell. ...
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Secondary currents are a characteristic feature of flow in open-channel bends. Besides the classical helical motion (centre-region cell), a weaker and smaller counter-rotating circulation cell (outer-bank cell) is often observed near the outer bank, which is believed to play an important role in bank erosion processes. The mechanisms underlying the...
Citations
... The regression lines become nearly horizontal, indicating lack of correlation between migration rates and curvature, despite some regressions still being statistically significant (Fig. 4c). Whereas saturation of migration rates for C > 0.3 appears unrelated to vegetation and is likely better explained by the complex flow structures that arise in sharp bends 46,53,[65][66][67] , the observed differences in m for C ≤ 0.3 can be attributed to the lack (or sparsity) of riparian vegetation. In particular, the diminished proportionality between migration rate and curvature, coupled with the relatively higher migration rates observed in semi-vegetated and non-vegetated rivers (as curvature approaches zero) underscore the impact of lack of vegetation on bank stability and sediment transport processes. ...
Stabilization of riverbanks by vegetation has long been considered necessary to sustain single-thread meandering rivers. However, observation of active meandering in modern barren landscapes challenges this assumption. Here, we investigate a globally distributed set of modern meandering rivers with varying riparian vegetation densities, using satellite imagery and statistical analyses of meander-form descriptors and migration rates. We show that vegetation enhances the coefficient of proportionality between channel curvature and migration rates at low curvatures, and that this effect wanes in curvier channels irrespective of vegetation density. By stabilizing low-curvature reaches and allowing meanders to gain sinuosity as channels migrate laterally, vegetation quantifiably affects river morphodynamics. Any causality between denser vegetation and higher meander sinuosity, however, cannot be inferred owing to more frequent avulsions in modern non-vegetated environments. By illustrating how vegetation affects channel mobility and floodplain reworking, our findings have implications for assessing carbon stocks and fluxes in river floodplains.
... According to Chang (1984), even for small curves without flow separation, flow resistance or the energy cost caused by transverse flow can be extremely large. Many researchers have studied flow dynamics in a wide variety of channel bend configurations using various methods owing to the major significance of this content (Tominaga and Nagao, 2000;Blanckaert and Graf, 2001;Booij, 2003;Blanckaert and De Vriend, 2004;Lu et al., 2004;Bodnar and Prihoda, 2006;Roca et al., 2007;Blanckaert, 2009;Zhou et al. 2009). These studies aim to collect data on flow variables in channel bends and analysis of the results that have provided the knowledge base for understanding the bend flows. ...
In this study, the CCHE2D model is used to analyse the flow pattern in a meander reach of the Gomati River. The finite volume method is used by the numerical model to solve the depth-averaged two-dimensional equations with 𝑘−𝜀turbulence closure. The numerical findings were compared with field data for two different flow rates in order to calibrate the CCHE2D model using various Manning's roughness coefficients. The results show that for the minimum and maximum discharges, a smaller Manning's roughness factor (0.015≥𝑛≥0.025)is more favorableto a higher Manning's roughness factor(0.030≤𝑛≤0.040). The results of the numerical model demonstrated that fluctuations in hydraulic parameters including shear stress, velocity, flow depth, and Froude number in the river bend are greatly influenced by the existence of centrifugal force and helical cells. The linear relationship between velocity and shear stress is presented across the whole study reach, as indicated by the R-squareand linear correlation coefficient (r) components. The results of the model show that the flow field within the river bend can be accurately simulated by the computational model.
... The primary characteristic of flow in river bends is the creation of eddy flows from secondary and main flow interactions. Secondary flow occurs when the two pressure gradients and centrifuge forces interact [1], and are caused by turbulence anisotropy (Prandtl's secondary flows of the second kind) [2]. Secondary currents at the water's surface move low-momentum fluid from the side walls to the middle of the channel, while high-momentum fluid is inhibited below the free surface. ...
... The cross-vane, W−Weir, and J-hook vane are examples of structures that can be used to maintain or improve river stability and functionality, as well as to accomplish various other objectives. These structures have been effectively used in natural channel design for recreational boating, irrigation diversions, fish habitat improvement, bank stabilization, grade control, and river restoration [1,[10][11][12][13]. ...
Different flow-altering methods, such as W−Weirs, have been developed to reduce erosion. For this study, we performed two experiments: (1) installing a W−Weir in various positions to determine the best angle for placement, and (2) investigating the variation of flow patterns and bed shear stress distribution in a 90-degree sharp bend by measuring the 3D components of flow velocities, with and without W−Weirs, where the greatest scour depth occurs. The results from the three installation angles indicate that less scour depth and volume of sediment removal occur when the weir is located close to the end of a bend. In addition, the value of the secondary circular power without a weir was higher than the position with a weir; however, this value significantly increased at 70 degrees due to turbulence flow near the W−Weir. This secondary flow power reduction at 45 degrees with a W−Weir increased by 65.8 percent for a Froude number value of 0.17, and by 29.8 percent for a Froude number value of 0.28, compared to values without the W−Weir, respectively.
... Many experimental and numerical studies reported that outer bank cell suddenly comes into existence with increasing curvature but center region cell exists even in the weak curvature bends [18,23,33,57]. Actually, the occurring of an outer bank cell, which has a counter-rotating direction, becomes a common characteristic in the most sharply curved bend flows [4,7,9]. Through numerical simulating for outer bank cells in an axisymmetric flow, Christensen et al. [19] concluded that outer bank cell strengthens with the increasing ratio of flow depth to bend radius (H/R), varies oppositely to the center region cell and even occurs in wide channels with a weak curvature. ...
... Instead, the numerical simulation could present all the interesting information of bend flow in the whole bend. So, next, we will firstly review some specific flow characteristics in the simulated case, which also occurs in other studies on the sharply curved bends [9,42]. And then, we will focus on the evolution process of the outer bank cells ...
... In Blanckaert's bend experiments, the core of maximum velocity was observed in the lower part of the water depth but close to the outer bank in the downstream part. However, their experiment has a varying bottom in the cross section, which means that the bed topography maybe steer the streamwise velocity [9]. In Kashyap's experiment and numerical simulations conducted in a rectangle flume bend, for the cross sections of 105 • and 135 • , it can be observed that the maximum streamwise velocity is always in the lower part of the water depth. ...
Understanding the developing mechanism of an outer bank cell is benefit for making full use of its important function to protect the concave bank from erosion in alluvial river bends. This study employs a bend flume experiment and a 3D renormalized group with κ-ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa -\epsilon$$\end{document} closure numerical model to investigate outer bank cells. Results obtained from the physical experiment and numerical simulations elucidate that (1) outer bank cell does not develop at the same time as the occurrence of center region cells, but it often yields later; (2) in sharply curved bends, outer bank cells are originated from the mutual effect of the centrifugal force created by channel bends and the pressure differences due to transverse water surface slopes; (3) a parameter β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document} was derived and also testified effectively for quantitatively evaluating the occurrence of an outer bank cell and influence of flow parameters on the development of outer bank cells in sharply curved open channel bends.
... Nevertheless, Reynolds-averaged Navier-Stokes models usually overpredict the bed shear stresses near the inner bank of the bend apex (on average by about 20%) and the middle of the channel, and are also unable to capture the persistence of outer-bank secondary cells (precisely, the residual of the main secondary cell of the previous bend) until the exit of the bend (Blackaert & de Vriend, 2004;Ottevanger et al., 2011;Stoesser et al., 2010). Therefore, the real channel migrations will be weaker than the effective simulations presented in this study, and river management on the basis of our results will be conservative enough. ...
The initial space settings of suitable environments for plants strongly affect the mutual feedback evolution of the river landscape and terrestrial plants. Thus, based on the morphological characteristics of newly-defined systematic out-branching channels in nature, this study performs an effective simulation of the flow of a designed moderately curved bend with a single short branch. The practice-based channel curvatures and branch on–off conditions are controlled in ANSYS FLUENT. The results show that: (1) the core zone of the depth-averaged primary velocity excess is approximately inversely equivalent to the channel migration potential; (2) the existence of the branch can strongly promote the formation of a new core vorticity zone and the conflicting development of the inner-negative and outer-positive vorticity zone after the bifurcation site at the cross-sections; (3) the free-flowing branch can greatly diminish the downstream helical flow strength; overall, the variation tendency of the ratio of helical flow strength to discharge squared is immune to the small range of change in stable inflow; and (4) the downstream channel is a strongly erosive region with the branch outlet closed, judging by the shear stress distribution; otherwise, it is a deposition region. The findings lay the groundwork for harmonious optimization of branch and plant configurations in river-bend systems.
... The existence of secondary currents in curved channels has been reported in previous studies (Bathurst et al., 1979;Blanckaert and de Vriend, 2004). Different opinions have been developed regarding the function of the outer-bank cell. ...
River restoration aims to apply environmentally-friendly structures for bank protection in meandering rivers to restore their natural habitat. Enhanced Permeable Groin (EPG) is a novel river restoration technique that can improve the fish habitat environment in a river system by creating a series of eco-friendly scour pools. This study reports the results of two groups of 3D velocity measurements in a 180-degree channel bend in cases with and without an EPG for clear water conditions to characterize the mechanisms leading to the primary stages of the scouring phenomenon. The analysis revealed that the presence of an EPG amplified the velocity magnitude in the regions near the tip of the vane and increased its value in the middle of the channel 1.13 times the bend without the structure. In addition, the comparison showed that the EPG reduced the velocity magnitude in the recirculation zone by an average of 38%. Secondary currents including main and outer bank cells were observed in the case without the structure. The presence of the EPG in the flow field effectively increased the outer-bank cell strength by 11 times compared to that without the structure. The low-value contours of the bed shear stresses were observed in the zone downstream of the structure for a distance of 6 times the effective length of the structure. Based on the results of this study, the generation of a recirculation zone with low-velocity and shear stress values can provide suitable conditions for aquatic habitats, deep-bodied fish assemblages, aquatic vegetation, shrub roots, and tree roots along the outer bank.
... To evaluate the effect of secondary current on pollutant transport, the vectors of secondary flow and contours of vorticities in typical cross-sections are presented in Figure 9. The vectors are non-dimensional with bulk velocity Uav, and the vorticities Ωθ are normalized through bulk velocity Uav and hydraulic radius R. As can be observed, there exists more than one large flow circulation in each section which are often called center-region cells [29]. Moreover, a flat circulation cell near the bottom that spans more than half of the section can be noticed, with an opposite rotational direction to that of cells located in the middle and upper part of the section. ...
The process of pollutant mixing is significantly influenced by secondary flow and turbulence in meandering rivers. To investigate the influence of different point source release positions on the pollutant mixing process in sinuous open channel flows, a 3D large-eddy simulation (LES) model based on OpenFOAM was established to simulate the process of passive scalar transport in a sinuous channel with a rectangular cross-section. After verification by a flume experiment, two sets of cases in which the point sources were arranged at identical intervals in spanwise and streamwise directions were configured to evaluate the mixing efficiency. The effect of flow structure, secondary motion, and the turbulent viscosity on the scalar transport and mixing was discussed. The distribution of scalar as well as the scalar flux was analyzed in detail, and the fluctuation characteristics were also described. The results demonstrate that due to the existence of secondary flow in the sinuous channel, different transverse and streamwise release positions of the point source have significant influence on mixing efficiency and spatial distribution of the pollutant. The point source placed near the center of the cross-section in transverse or near the apex of the bend in streamwise result in higher mixing efficiency. Mixing efficiency calculated by different indices can be different, which requires comprehensive assessment.
... This can generate significant lateral circulation in the plane perpendicular to the depth-averaged along-channel flow (Rozovskiĭ, 1957), consisting of cross-channel flow (lateral flow) and vertical flow. Lateral circulation can play a major role in lateral transport of sediments and estuarine exchange flows Yang et al., 2014;Lerczak and Geyer, 2004;Blanckaert and De Vriend, 2004;Geyer and MacCready, 2014;Zhou et al., 2021), because lateral advection could be significantly related to these dynamic processes. Lateral circulation in tidally dominant estuaries is driven by various mechanisms, including centrifugal force created by channel curvature (Kalkwijk and Booij, 1986;Geyer, 1993), Coriolis acceleration caused by the Earth's rotation (Ott et al., 2002), the lateral baroclinic pressure gradient (Valle-Levinson et al., 2000;Lacy and Monismith, 2001), lateral bathymetric variability (Valle-Levinson et al., 2000), boundary mixing on a sloping bottom , and differential advection of longitudinal density gradients (Lerczak and Geyer, 2004). ...
Field observations were conducted at an inflection point of two bends of the Oujiang River Estuary, China, to investigate lateral circulation and its driving mechanisms, and the effect of stratification in a macrotidal estuary. Repeated cross-channel transect measurements of velocities were obtained by vessel-mounted acoustic Doppler current profiler at the inflection point during neap and spring tides. Conductivity, temperature, and depth were collected at both ends of the transects to estimate the lateral moment budget. We observed asymmetry of lateral circulation in intra-tidal and inter-tidal regions, with strong single-cell lateral circulation during the neap ebb tide. In contrast, during the flood, lateral circulation was weak but structurally complex. During the spring tide, lateral circulation only appeared at peak ebb and peak flood. This asymmetric variation in lateral circulation is induced by an asymmetric driving mechanism, investigated thoroughly and connected to water stratification. The significant effect of nonlinear advective acceleration in both highly stratified water and well-mixed water indicates the important influence of an inflection point of two bends on lateral circulation. Besides, the strong stratification plays a role to suppress the lateral circulation due to the tilted pycnocline spin opposite to lateral circulation. The Oujiang River Estuary is an important shipping area, and the results have practical significance for the development and utilisation of port and channel resources.
... The controversy surrounding secondary motions persists even outside the field of confluences, such as in the field of curved open-channels (e.g., Blanckaert and de Vriend, 2004) and in the field of open-channel flow over roughness patches (e.g., Talebpour and Liu, 2019). The study of secondary cells is important, as these motions play a crucial role in mixing and sediment transport phenomena (e.g., Ashmore, 1982;Penna et al., 2018;Birjukova Canelas et al., 2020). ...
Confluences of open-channel flows commonly occur in natural and artificial water networks and in hydraulic structures. The flow in these junctions is complex, three-dimensional and is steered by the shape of the bed.
This research focuses on schematized confluences with a T-shaped planform in which the bed level of the tributary channel is higher than the one in the main channel. This phenomenon is ubiquitous in natural river confluences, but also frequently occurs in human-made configurations.
The effect on the flow of such a difference in bed elevations between the two channels is investigated by means of numerical simulations and laboratory experiments. Also, the effect on the mixing of suspended or dissolved substances in merging water streams is explored. The applied Large Eddy Simulations allow not only the study of the time-averaged flow features but also their time-dependent behaviour.
Besides providing fundamental knowledge, this work also contributes to the optimization of artificial confluences.
... flux of energy from smaller scales to larger scales to the mean flow) in particular regions of the flow. This conjecture is supported by Blanckaert & De Vriend (2004) experiments. ...
Large-eddy simulations of turbulent flow in partially filled pipes are conducted to investigate the effect of secondary currents on the friction factor, first- and second-order statistics and large-scale turbulent motion. The method is validated first and simulated profiles of the mean streamwise velocity, normal stresses and turbulent kinetic energy (TKE) are shown to be in good agreement with experimental data. The secondary flow is stronger in half- and three-quarters full pipes compared with quarter full or fully filled pipe flows, respectively. The origin of the secondary flow is examined by both the TKE budget and the steamwise vorticity equation, providing evidence that secondary currents originate from the corner between the free surface and the pipe walls, which is where turbulence production is larger than the sum of the remaining terms of the TKE budget. An extra source of streamwise vorticity production is found at the free surface near the centreline bisector, due to the two-component asymmetric turbulence there. The occurrence of dispersive stresses (due to secondary currents) reduces the contribution of the turbulent shear stress to the friction factor, which results in a reduction of the total friction factor of flows in half and three-quarters full pipes in comparison to a fully filled pipe flow. Furthermore, the presence of significant secondary currents inhibits very-large-scale motion (VLSM), which in turn reduces the strength and scales of near-wall streaks. Subsequently, near-wall coherent structures generated by streak instability and transient growth are significantly suppressed. The absence of VLSM and less coherent near-wall turbulence structures is supposedly responsible for the drag reduction in partially filled pipe flows relative to a fully filled pipe flow at an equivalent Reynolds number.
