# The Straightening of a River Meander Leads to Extensive Losses in Flow Complexity and Ecosystem Services

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## Abstract

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## 1. Introduction

## 2. Methods

^{®}) as a virtual river system that coupled the surface water flow and groundwater movement in one domain. We describe the range of the channel curvature with variable C, defined as the ratio of the channel width, B to the centerline radius of channel curvature, R. A straight channel has a C = 0, while a high sinuosity meander bend might have a C > 0.5. Nine experiments with gradually changed curvature from a tight bend to a straight channel were simulated by maintaining equivalent cross-section profiles. The output of these simulations were then used to investigate the hydraulic complexity response to the channel curvature changes. Note that the purpose of this study is to investigate the flow responses to meander curvature changes solely, not to bedform topography. There was no sediment transport and associated self-adjusted river bedform evolution included in the experiment setup.

#### CFD Model

_{F}is the fraction volume open to flow, ρ is the fluid density, c is a constant (approximately the sound speed), p is pressure, t is time, A

_{i}is the area fractions for flow in the i(x, y, z) direction, and u

_{i}(u, v, w) denote the velocities in i directions, f

_{i}is the viscous acceleration terms. R and ξ are transformation coefficients depend on the choice of the coordinate system is in use. When Cartesian coordinates (x, y, z) are used, ξ = 0 and R = 1. When cylindrical coordinates (r, θ, z) are used, y derivatives in the equation will be converted to azimuthal derivatives:

_{m}/r, y = r

_{m}θ, and r

_{m}is a fixed channel radius. In the meantime, ξ = 1. Readers are referred to the FLOW-3D users manual (https://www.flow3d.com) for more information.

_{e}= 68 × 10

^{3}, and Froude number Fr = 0.41. A flume substrate particle diameter of 1.6 mm to 2.2 mm (d

_{50}= 2 mm) was used to obtain an equilibrium bed, which was defined as with sediment inflow equaling outflow [24]. Bedform topography of the bend was mapped using acoustic limnimeter to a 450 × 50 grid and made digitally available to the authors. Identical flume geometry settings and boundary conditions were imported into the CFD model for river flow simulations. The computational domain was constructed based on a cylindrical coordination system with 130 grids along the radial or transverse axis n (x in Cartesian coordinate), from 0 m to 1.3 m, 300 grids along the azimuthal or streamwise axis s (y in Cartesian coordinate), from 0° to 193°, and 50 grids along the vertical axis z, from −0.3 m to 0.2 m. Bedform roughness was represented using a recommended roughness height of 0.037 m for this very experiment [25]. The goodness of fit (R

^{2}) between observed and simulated velocity profiles were greater than 0.75 at most cross-sections, indicating the CFD model captured the major flow dynamic patterns in both streamwise and transverse directions and was adequately simulated the meander bend 3D river flows. The readers are referred to Figure 2 in Zhou and Endreny [21] for detailed model verification processes.

^{®}S series recirculating flume filled with 0.3 m depth sediment. The sediment bed had an average depth of 30 cm featuring a pool-riffle sequence with a wavelength of 0.5 m. Dye was released at multiple points along the surface of the sediment bed and was tracked through the transparent wall of the flume. The hyporheic flow vectors simulated by the CFD model agreed well with observations. We also successfully modeled and verified the penetration front movements with the results observed in Elliott and Brooks [26] Run9 experiment. Both model verification campaigns suggest that the CFD model adequately captured the hyporheic flow directions and velocity, as well as the depth of the active hyporheic zone in the bedform. The readers are referred to Figures 2, 4 and 6 in Zhou and Endreny [27] for more details about the hyporheic process verifications. After being verified by the observations, the CFD models have the potential to explore the flow behavior under different boundary conditions [28].

## 3. Hydraulic Complexity Variables

_{s}, v

_{n}, and v

_{z}velocity vectors representing flow in the s (streamwise), n (transverse), and z (vertical) directions, respectively. The hydraulic complexity variables were normalized when possible, and included (1) normalized flow surface elevation (h/H), where h is the local flow surface elevation, H is the average flow surface elevation; (2) normalized depth averaged streamwise and transverse unit discharge (q

_{s}/UH and q

_{n}/UH)., where q

_{s}and q

_{n}are the unit discharges at s and n directions, equal to <v

_{s}> × h and <v

_{n}> × h; U is the bulk velocity; “< >” denotes depth averaging; (3) normalized depth averaged streamwise velocity at bankfull depth (<v

_{s}>/U); (4) bed shear stresses distrubution, represented by the bed friction coefficient, ${C}_{f}=\frac{{u}^{{*}^{2}}}{{U}^{2}}$, where u

^{*}is the shear velocity at the boundary, ${u}^{*}=\frac{{u}_{b}}{{u}^{+}}$, u

_{b}is velocity magnitude at the bottom grid, u

^{+}is dimensionless velocity for a hydraulically rough wall computed with the modified wall function [29], ${u}^{+}=2.5ln\frac{{z}_{b}}{{k}_{s}}+8.5$ where z

_{b}is the grid size and k

_{s}is the roughness height which was 6 mm; (5) vertical hyporheic flow, represented by the vertical flux 2 cm below the water-sediment interface (v

_{zbed}/U); (6) secondary circulation represented by depth averaged normalized vertical velocity (<v

_{x}>/U) for the size; and normalized transverse stream function, ψ/UBH for the direction and strength (positive values indicate clockwise circulation when facing upstream). The ψ/UBH was computed as

_{i}and z

_{i}represent the cross-sectional and vertical coordinates.

## 4. Results

#### 4.1. Flow Surface Elevation

#### 4.2. Streamwise and Transverse Unit Discharge

_{s}/UH) (Figure 4) direction had relatively stable spatial patterns of maximum and minimum values with changing curvature. This suggests their spatial patterns were regulated by bed topography and the larger conveyance regions opened by pools and smaller conveyance regions constrained by point bars. This topographic control was illustrated by comparing streamwise unit discharge for C = 0.77, 0.33, and 0 at the left bank pool and the right bank point bar conveying. Nearly 90% of the downstream mass was conveyed along the left half (i.e., the pool side) of the channel for all curvatures, while along the right bank at station 2 s/B there was upstream mass transport, indicating the existence of backwater eddy and flow separation for all curvatures. The maximum streamwise unit discharge occurred at about 1.5 s/B, right above the deepest part of the pool. Differences in streamwise unit discharge patterns between C = 0.77 and C = 0 emerged along the left bank stations 2.5 s/B to 3.5 s/B, where mass transport increased by 50% as curvature increased. In this post-apex section of the meander bend there was greater sensitivity of streamwise mass flux to curvature.

_{n}/UH, were also largely insensitive to curvature, where C = 0.77, 0.33, and 0 each experienced a pronounced transport to the outer bank (positive values) upstream of the apex and transport to the inner bank further downstream (Figure 5). The impact of bed topography was noted in the damped oscillation patterns of q

_{n}/UH with the maximum leftward mass transport at 1 s/B, just upstream of the point bar, and rightward transport at about 2.3 s/B, downstream of the pool. As curvature increased, the single ovate shaped hot-spot of outer-bank directed mass transport that extended beyond the apex for C = 0.77, became split at the tip for C = 0.33, and then reduced to a smaller region for C = 0 (Figure 5). A parallel set of changes occurred in inner-bank-ward mass transport, where the initiation of this inner bank transport region moved further downstream as curvature reduced from C = 0.77 to C = 0. The differences in mass transport between the C = 0.33 and C = 0 simulations were only about 5% based on transversely averaging (< q

_{n}/UH >) (Figure 6). The inset of Figure 6 shows the likelihood (here we use coefficient of determination, R

^{2}) of < q

_{n}/UH > between each curvature and the straight channel condition (C = 0, R

^{2}= 1). The lower the R

^{2}, the transverse unit discharge is more complex than in the straight channel.

_{n}/UH, were also largely insensitive to curvature, where C = 0.77, 0.33, and 0 each experienced a pronounced transport to the outer bank (positive values) upstream of the apex and transport to the inner bank further downstream (Figure 5). The impact of bed topography was noted in the damped oscillation patterns of q

_{n}/UH with the maximum leftward mass transport at 1 s/B, just upstream of the point bar, and rightward transport at about 2.3 s/B, downstream of the pool. As curvature increased the single ovate shaped hot-spot of outer-bank directed mass transport that extended beyond the apex for C = 0.77, became split at the tip for C = 0.33, and then reduced to a smaller region for C = 0 (Figure 5). A parallel set of changes occurred in inner-bank-ward mass transport, where the initiation of this inner bank transport region moved further downstream as curvature reduced from C = 0.77 to C = 0. The differences in mass transport between the C = 0.33 and C = 0 simulations were only about 5% based on transversely averaging (< q

_{n}/UH >) (Figure 6). The inset of Figure 6 shows the likelihood (here we use coefficient of determination, R

^{2}) of < q

_{n}/UH > between each curvature and the straight channel condition (C = 0, R

^{2}= 1). The lower the R

^{2}, the transverse unit discharge is more complex than in the straight channel.

^{2}was greater than 0.8 in all channels and greater than 0.98 in C < 0.33 channels. With increasing channel curvature, the R

^{2}remained constant until it started to drop rapidly from 0.95 at C = 0.33 to 0.8 at C = 0.77.This analysis suggested that the transverse unit discharge is generally insensitive to curvature, especially in moderately curved channels (C < 0.33).

#### 4.3. Streamwise Velocity Distribution

_{s}>/U, had spatially varying sensitivity to curvature, which was most pronounced at the channel inlet (Figure 7). In the inlet the maximum was along the right bank in C = 0.77 but was along the left bank in C = 0. These differences in streamwise velocity are explained by curvature and its role in transverse velocity gradients. In C = 0.77 the shorter streamwise distance along the inner bank caused an increase in <v

_{s}>/U from the inner bank to the outer bank [30]. Curvature also caused differences in magnitude of <v

_{s}>/U between the C = 0.77 and C = 0 channels from 2.5 s/B to 4 s/B, with the maximum <v

_{s}>/U increased and concentrated near the outer bank area.

_{s}>/U, which is the center of gravity of the streamwise flow distribution, has an exact transverse location denoted by n/B, where n = 0 at the channel center and n/B = 0.5 at the left bank (Figure 8). For all planform curvatures the first moment of <v

_{s}>/U oscillated, originating near n/B = 0 at the channel inlet, approaching the left bank distance n/B > 0.2 at s/B = 1.5, and then returning toward the channel center n/B = 0.1 at s/B = 2. This oscillation was explained by flow separation upstream of the point bar, the subsequent relocation of maximum streamwise velocities near the outer bank, and the return of those maximum velocities toward the channel center at the meander outlet. Sensitivity to curvature was observed from 2 s/B to 4 s/B, where the amplitude of oscillation in the first moment of <v

_{s}>/U diminished with decreasing curvature; oscillating by 0.35 n/B for C = 0.77 and oscillating by 0.15 n/B for C = 0. For high curvature channels (C > 0.33) with tight meanders, flow entered the meander bend along the right half of channel due to a curvature induced potential vortex, while in moderately curved C < 0.33 channels flow entered the meander along the left half of the channel due to a point bar backwater effect. At channel location 2 s/B the maximum leftward amplitude was n/B = 0.4 from the channel center for the C = 0.77 simulation and n/B = 0.25 from the center for the C < 0.33 simulations. The coefficient of determination for the first moment of <v

_{s}>/U between C = 0 and other simulations resulted in R

^{2}> 0.95 for C < 0.33 channels, but ranged from 0.6 to 0.88 for the C > 0.33 channels (the insert in Figure 8). As the meander bend tightened and C approached 1.3 the R

^{2}varied greatly with curvature, while in channels with C < 0.33 the R

^{2}was relatively insensitive to changes in curvature, suggesting bedform topography was a stronger influence than planform curvature on the streamwise velocity distribution.

#### 4.4. Bed Shear Distribution

#### 4.5. Vertical Hyporheic Exchange

#### 4.6. Secondary Circulation Patterns

## 5. Discussion and Conclusions

- The loss of large magnitude bed shear stresses in the pool at the meander apex and establishment of a larger zone of near-zero bed shear about the point bar (Figure 9), and the related loss of large swaths of upwelling flow of groundwater into the channel at the apex along the outer bank and downstream of the apex along the inner half of the channel (Figure 10).

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Geometries and bed topography settings of the nine computational fluid dynamics (CFD) simulations with channel curvature (C) changed from 0.77 to 0.

**Figure 2.**Flow surface elevation (h) normalized by H at C = 0.77, C = 0.33, and C = 0 conditions. n denotes the lateral coordination with n = 0 at channel center and B denotes the channel width.

**Figure 3.**Normalized flow surface profiles for the nine simulations at the point bar apex 1.5 s/B. The insert plot shows the second order derivative of normalized flow surface elevation in the transverse direction, Fh″(n/B), which gives the convexity or concavity of the surface profile curves.

**Figure 4.**Streamwise unit discharge q

_{s}/UH for channel curvature C = 0.77, 0.33, and 0 conditions.

**Figure 5.**Transverse unit discharge q

_{n}/UH for channel curvature C = 0.77, 0.33, and 0 conditions.

**Figure 6.**Transverse unit discharge averaged over the transverse direction. The inset shows the R

^{2}of transverse unit discharge < q

_{n}/UH > between each curvature, C, and the straight channel condition (C = 0, R

^{2}= 1); a lower R

^{2}suggests greater hydraulic complexity for transverse unit discharge.

**Figure 7.**Normalized depth averaged streamwise velocity <v

_{s}>/U for channel curvature C = 0.77, 0.33, and 0 conditions.

**Figure 8.**The first moment of normalized depth averaged streamwise velocity <v

_{s}>/U, which represents center of gravity of the streamwise flow distribution, along the channel. The inset shows the R

^{2}of the first moment of <v

_{s}>/U between each curvature and the straight channel condition (C = 0, R

^{2}= 1); a lower R

^{2}suggests greater hydraulic complexity for the first moment of depth averaged streamwise velocity.

**Figure 9.**Distribution of river channel bed shear Cf for channel curvature C = 0.77, 0.33, and 0 conditions.

**Figure 10.**Normalized vertical hyporheic flux v

_{zbed}/U at 2 mm below sediment surface for channel curvature C = 0.77, 0.33, and 0 conditions. Positive indicates upwelling of groundwater into the river channel.

**Figure 11.**Normalized vertical velocity <v

_{z}>/U for channel curvature C = 0.77, 0.33, and 0 conditions, with positive values upward flows, negative values downward flows.

**Figure 12.**Transverse stream function distribution ψ/UBH reveals the secondary circulation of transverse flow cells rotating at the meander apex 1.5 s/B for channel curvature C = 0.77 (

**A**), C = 0.33 (

**B**), and C = 0 (

**C**), with positive values representing clockwise rotation direction when facing upstream, and negative values representing counter-clockwise rotation when facing upstream.

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**MDPI and ACS Style**

Zhou, T.; Endreny, T.
The Straightening of a River Meander Leads to Extensive Losses in Flow Complexity and Ecosystem Services. *Water* **2020**, *12*, 1680.
https://doi.org/10.3390/w12061680

**AMA Style**

Zhou T, Endreny T.
The Straightening of a River Meander Leads to Extensive Losses in Flow Complexity and Ecosystem Services. *Water*. 2020; 12(6):1680.
https://doi.org/10.3390/w12061680

**Chicago/Turabian Style**

Zhou, Tian, and Theodore Endreny.
2020. "The Straightening of a River Meander Leads to Extensive Losses in Flow Complexity and Ecosystem Services" *Water* 12, no. 6: 1680.
https://doi.org/10.3390/w12061680