Bed morphodynamics at the intake of a side channel controlled by sill geometry

Bed morphodynamics at the intake of a side channel controlled by sill geometry

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Bed morphodynamics at the intake of a side channel controlled by sill geometry T.V. de Ruijsscher, A.J.F. Hoitink, S. Naqshband, A.J. Paarlberg PII: DOI: Reference:

S0309-1708(19)30145-9 https://doi.org/10.1016/j.advwatres.2019.103452 ADWR 103452

To appear in:

Advances in Water Resources

Received date: Revised date: Accepted date:

13 February 2019 22 October 2019 26 October 2019

Please cite this article as: T.V. de Ruijsscher, A.J.F. Hoitink, S. Naqshband, A.J. Paarlberg, Bed morphodynamics at the intake of a side channel controlled by sill geometry, Advances in Water Resources (2019), doi: https://doi.org/10.1016/j.advwatres.2019.103452

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Highlights • Two bar features characterise the side channel intake at a longitudinal training dam

• Water and sediment import can be steered by the upstream sill geometry • The flow cross-sectional area over the sill determines the discharge division • The degree of sedimentation and erosion largely depends on the sill geometry • Most dynamic bed in the side channel emerges for a downstream decreasing sill height

1

2

Bed morphodynamics at the intake of a side channel controlled by sill geometry T.V. de Ruijsschera,∗, A.J.F. Hoitinka , S. Naqshbanda , A.J. Paarlbergb a Hydrology

and Quantitative Water Management Group, Department of Environmental Sciences, Wageningen University, PO Box 47, 6700 AA, Wageningen, The Netherlands b HKV Consultants, PO Box 2120, 8203 AC, Lelystad, The Netherlands

Abstract As part of a general trend towards river management solutions that provide more room for the river, longitudinal training dams (LTDs) have recently been constructed in the inner bend of the Dutch Waal River, replacing groynes. LTDs split the river in a main channel and a bank-connected side channel with a sill at the entrance. In the present study, a physical scale model with mobile bed was used to study morphological patterns and discharge division in the entrance region of such a side channel. Alternative geometric designs of the sill are tested to investigate the controls on the diversion of water and sediment into the side channel. After reaching a morphodynamic equilibrium, two bar features were observed in the side channel under low flow conditions. An inner-bend depositional bar emerged against the LTD, resembling depositional bars observed in sharp river bends. A second bar occurred in the most upstream part of the side channel, next to the sill, induced by divergence of the flow by widening of the channel and an increasing flow depth after the sill, hence defined as a divergence bar. The morphologically most active system in the side channel emerges for the configuration in which the sill height decreases in downstream direction. For such a geometry, the sediment that settles during low flow is largely eroded during high flow, reducing maintenance needs. A qualitative comparison based on a lab experiment mimicking field conditions demonstrates the realism of the experiments. Keywords: longitudinal training dam, river morphology, side channel, bifurcation, physical scale model

∗ Corresponding

author Email addresses: [email protected] (T.V. de Ruijsscher), [email protected] (A.J.F. Hoitink)

Preprint submitted to Elsevier

October 28, 2019

1

1. Introduction

2

Traditionally, groynes have been widely used to fix the planform geometry of low-

3

land rivers, with the aim to keep the river navigable, and to prevent ice jams (Przed-

4

wojski, 1995; Verheij et al., 2004; Yossef and de Vriend, 2011). Groynes are known

5

to have various side effects however, among which erosion pits at groyne tips and a

6

reduced ecological value in the riparian zone due to shipping waves (ten Brinke et al.,

7

1999; Collas et al., 2018) are the most severe. To improve the ecosystem services of

8

the river system, rivers are allowed more space within restricted boundaries (e.g. Rijke

9

et al., 2012; van Vuren et al., 2015), which has a proven positive effect on ecology

10

(van den Brink et al., 1993; Palmer et al., 2005) and mitigates climate change effects

11

(Giosan et al., 2014; Constantinescu et al., 2015).

12

Longitudinal training dams (LTDs) have been designed as a compromise between

13

purely nature-based solutions that favour ecological quality, and hard engineering struc-

14

tures that ensure navigability. They serve as a flood protection measure, secure the fair-

15

way depth for shipping and leave enough room for ecological development (Havinga

16

et al., 2009). An LTD is a groyne-like structure parallel to the river axis that splits

17

the river in a main navigation channel and a bank-connected side channel with a sill

18

at the upstream side. Due to its orientation parallel to the river axis, the flow resis-

19

tance is limited. This causes a lowering of the water level during floods, which adds

20

to flood-safety of the hinterland. During low discharges, the flow is mainly restricted

21

to the main channel. This effectively reduces the width of the river, leading to larger

22

water depths in the main channel, which benefits shipping. Finally, LTDs are expected

23

to limit bed degradation and to provide favourable ecological conditions compared to

24

groyne fields (Eerden et al., 2011; Havinga, 2016).

25

Although they have been present for years already in France (the Loire River) and

26

Germany (the Main, Rhine and Elbe Rivers), detailed studies on the hydraulic and mor-

27

phological effects of LTDs are limited. Recently, Collas et al. (2018) showed that LTDs

28

stabilise the flow behind the dam and reduce the influence of ship waves, which creates

29

favourable ecological conditions. The ability of sediment particles to be transported

30

into the side channel likely depends on the sill side slope and the angle at which wa-

31

ter flows over the sill (Jammers, 2017). In the presence of alternate bars in the main

32

channel, the two-channel LTD system is in general morphologically unstable, although

33

a stable configuration might be reached when the upstream end of the LTD is located 2

34

close to the bar top (Le et al., 2018b). In the latter case, cyclic morphological behaviour

35

may emerge, even without external periodic forcing (Le et al., 2018a).

36

The present work builds on prior work of Vermeulen et al. (2014), who—to the

37

authors knowledge—were the first to experimentally study LTDs. They based their

38

physical scale model (scale 1:60) on a future projection of the Waal River in the

39

Netherlands with prototype discharges of 1250 m3 s−1 and 4600 m3 s−1 . The studied

40

river section was a sand-bedded lowland river with particle size distributions charac-

41

terized by D50 = 1.2 mm and D90 = 2.0 mm. In the physical scale model, polystyrene

42

particles were used as a surrogate sediment with D50 = 2.1 mm, D90 = 2.9 mm and

43

ρs = 1055 kg m−3 . Scaling was based on the Shields number, keeping the Froude num-

44

ber close to prototype values. Vermeulen et al. (2014) concluded that local morpholog-

45

ical changes near the intake of an LTD side channel are expected to be limited. They

46

also showed that the sediment mobility is slightly overestimated by using polystyrene,

47

but dune height agrees well with corresponding prototype values, and fairway deepen-

48

ing agrees well with the realised river narrowing by the LTD.

49

In the present study, the physical model of Vermeulen et al. (2014) has been modi-

50

fied to match the design that has been built in the Waal River, in a pilot downstream of

51

the city of Tiel. On this location, LTD side channels replace former groyne fields over

52

a 10 km stretch in the inner bends of the river, where a riprap bank is present instead of

53

upstream groynes. The intake section of the side channel is chosen such that it matches

54

the location where in former times a natural side channel cut into the floodplain (Fig. 1).

55

At about three quarters downstream from the upstream end, a secondary opening with

56

a sill is present in the LTD to enable exchange of water between the two channels, even

57

during low discharges. In contrast to Vermeulen et al. (2014), no upstream groynes

58

are constructed, and the entrance of the side channel is marked by a sill in line with

59

the LTD itself. The latter is also different from the studies by Le et al. (2018a,b), who

60

did not use any regulatory structure at the entrance of the side channel, and used a thin

61

plate to model the LTD.

62

Prior studies also assumed a free inflow side channel, adopting 1-D (Bolla Pittaluga

63

et al., 2003; Kleinhans et al., 2008; Bertoldi et al., 2009; van der Mark and Mosselman,

64

2013), 2-D (Le et al., 2018b) and quasi-3-D (Kleinhans et al., 2008) numerical models

65

to explore bifurcation stability. Those studies elaborated on simple hypothetical rela-

66

tionships for sediment division (Wang et al., 1995). The equilibrium discharge diver-

3

0

500

1000 1500 m

1815

2017

Figure 1: Prototype LTD in the Waal River, downstream of the city of Tiel. Left: situation in 1815, where a natural side channel can be seen, which used to connect to the river during floods where nowadays the entrance of the LTD side channel is located. The arrow denotes the flow direction. Right: present situation of the study area. Source of maps: Kadaster (2018).

67

sion to side channels has been studied as a function of various geometrical parameters

68

by van Denderen et al. (2018). Detailed flow patterns have been analysed as a function

69

of various hydraulic and geometric boundary conditions (Hardy et al., 2011).

70

In the present contribution, we add an upstream control mechanism to the side

71

channel system, in the form of a sill. We aim to unravel how the geometry of this

72

sill affects morphological changes and flow patterns around the side channel intake,

73

which is important for navigability, ecology and dredging efforts. We are in particular

74

interested in 1) the morphological effects of possible flow separation downstream of the

75

side channel intake, 2) the morphological effects of flow divergence at the side channel

76

entrance, and 3) the effect of the sill on the discharge division over the two channels.

77

The experimental set-up is described in section 2, consisting of the physical scale

78

model and the measurement equipment used. Section 3 introduces the applied analysis

79

methods. The results are shown in section 4, addressing morphological changes, flow

80

characteristics and the discharge division. Thereafter, a comparison between lab and

81

field results is provided in section 5, followed by a discussion of the experimental

82

findings in section 6. Finally, conclusions are formulated in section 7.

4

83

2. Experimental set-up

84

2.1. Prototype

85

The LTD pilot in the Dutch Waal River (Eerden et al., 2011; Huthoff et al., 2011)

86

serves as a prototype for this scale model study. The Waal is a sand-bedded, mildly

87

curved lowland river and the main branch of the Rhine River in the Netherlands. Bed

88

morphology is predominantly determined by sediment transported in bedload mode,

89

with typical particle sizes of D50 = 1.2 mm and D90 = 2.0 mm. Flow velocities in the

90

Waal are typically around U = 1 m s−1 . Two characteristic hydraulic conditions were

91

defined, consisting of a mean water depth of d = 4 m (low flow) with a corresponding

92

discharge of Q = 1250 m3 s−1 and a mean water depth of d = 8 m (high flow) with

93

a corresponding discharge of Q = 4600 m3 s−1 . The LTD at the location of interest

94

creates a side channel with a typical width of 90 m on a main channel bankfull width of

95

230 m. The cross-sectional profile of the prototype LTD is a trapezoid with side slopes

96

of 1:2.5, an upper base of 2 m width, and a typical height of 6.5 m.

97

2.2. Physical scale model

98

The study’s experiments took place in a straight horizontal flume with recircula-

99

tion facilities for both water and sediment at the Kraijenhoff van de Leur Laboratory

100

for Water and Sediment Dynamics (Wageningen University & Research, The Nether-

101

lands). The flume measured 0.7 m×2.6 m×12.8 m internally (height × width × length).

102

At the upstream end of the flume, a stacked pile of PVC tubes served as a flow straight-

103

ener to suppress large turbulence generated by the inlet geometry. Inside the flume, we

104

constructed a scale model of an LTD with an upstream riprap bank (Fig. 2), adjusting

105

the model of Vermeulen et al. (2014). A solid base was located between the LTD and

106

the riprap bank, where an adjustable gravel sill could be built upon. The model was

107

geometrically scaled from the prototype with a scaling factor of nL = 60 in all dimen-

108

sions. The model represented a width of 156 m and a length of 720 m in the prototype.

109

A sediment layer of 20 cm thick completely covered the solid base of the flume, only

110

leaving the LTD (9.2 cm in height), the riprap bank and the sill uncovered. By recircu-

111

lating the sediment in the flume, the total volume of sediment in the system remained

112

constant throughout the experiment.

113

Four alternative sill geometries at the LTD side channel intake were studied (Fig. 3):

114

A) a uniform, low sill height, B) a downstream increasing sill height, C) a downstream 5

Figure 2: Scale model of the entrance region of the prototype LTD, looking upstream. The main flow direction is indicated by the arrow. From top to bottom, a riprap bank, the sill at the side channel entrance, and the LTD are visible. The sill is bounded by x-coordinates S u and S d .

115

decreasing sill height, and D) a uniform, elevated sill height. We chose these geome-

116

tries to investigate the effect of differences in total cross-sectional flow areas, through

117

comparison of alternatives A and D, and lateral differences in cross-sectional flow area,

118

through comparison of alternatives B and C. The side slope of the sill was kept con-

119

stant at 1:2.5 as is the case in the prototype in the Waal River, although the side slope

120

plays a significant role in sediment transport over the sill (Jammers, 2017). Each of

121

these geometries was studied under two hydraulic conditions that were scaled from the

122

earlier-mentioned low flow and high flow prototype conditions. For each of the sill ge-

123

ometries, measurements were carried out after reaching a morphodynamic equilibrium,

124

defined here as a dynamic equilibrium in which dune length in the main channel con-

125

verged to a constant value of typically 70 cm. Each high flow experiment was carried

126

out directly after the corresponding low flow experiment, again allowing the system to

127

reach a morphodynamic equilibrium.

128

To achieve dynamic similarity of both hydraulic characteristics and sediment trans-

129

port in the physical scale model, we used lightweight surrogate sediment particles

130

(polystyrene) with a density of ρs = 1055 kg m−3 and typical sizes of D50 = 2.1 mm and

131

D90 = 2.9 mm. Table 1 lists typical values for the hydraulic conditions and sediment

132

characteristics. For details on the underlying scaling method, we refer to Vermeulen

6

A2/B2

height LTD crest

A1/B1

main flow direction

7.5 cm sill

2.5 cm

polystyrene A

2.5 cm

z B

x C2/D2 C1/D1

7.5 cm

7.5 cm 2.5 cm

C Sd

Su

D Sd

Su

Figure 3: Schematic side view representation of the sill geometries and water levels used during the subsequent experiments along line segment S u S d (Fig. 2). The sill is shown in grey, and the water column in blue (low/high water level). The LTD crest height is indicated by the dashed line as a reference.

133

et al. (2014), who extensively discussed the method and the different non-dimensional

134

numbers.

135

2.3. Measurement equipment

136

To measure flow velocities, we used a Vectrino Profiler, which is a profiling acous-

137

tic velocimeter (Nortek AS, 2013). This device captures both magnitude and direction

138

of the velocity in vertical bins of 1 mm over a vertical range of 3 cm and at a frequency

139

of 50 Hz. The lower end of the vertical range coincided with the initial bed level height

140

(z = 20 cm), except on top of the sill (z = 25 cm). Additionally, a point measurement

141

of the bed level directly underneath the instrument is retrieved. We chose the measure-

142

ment period such that approximately one dune had migrated to minimise the effect of

143

bed mobility on the results. The probe of the profiler did not disturb the bed signifi-

144

cantly, as the probe was located well above the bed. With the gathered velocity data,

145

we investigated flow patterns around the intake of the LTD side channel and estimated

146

the discharge division over the two channels. For the latter, the water level was also

147

continuously monitored at eight points along the side walls of the flume. For this pur-

148

pose, eight wall-bound tubes were coupled to stilling wells outside the flume, with each

7

Table 1: Typical hydraulic conditions for low and high flow experiments: discharge Q, water depth d, characteristic flow velocity U, Froude number Fr, Reynolds number Re and Shields number θ. All values are averaged over the interval x ∈ [2000; 4000] mm in experiments B1 and B2, but are representative for the upstream conditions in all experiments. The lower part of the table shows characteristics of the polystyrene granulate: median (D50 ) and 90th percentile (D90 ) particle size, and sediment density ρs .

Q (m3 s−1 ) d (m) U (m s−1 )

low flow

high flow

2.04 × 10−2

3.55 × 10−2

0.14

0.15

9.68 × 10−2

1.46 × 10−1

Fr (−)

0.15

0.12

Re (−)

1.3 × 104

2.0 × 104

θ (−) D50 (m) D90 (m) ρs (kg m−3 )

0.25

0.29

2.1 × 10−3 2.9 × 10−3

1.055 × 103

149

stilling well containing a magnetostrictive linear position sensor. The total discharge

150

was also continuously monitored using an electromagnetic flow meter. Fig. 4 gives an

151

overview of the locations of velocity and water level measurements.

152

In addition to flow velocities and discharge, we monitored bed topography during

153

subsequent phases of the experiment using a line laser scanner. The use of a line laser

154

scanner for bed level monitoring is a measurement method in which the bed elevation

155

is detected from the reflection of light projected on the bed making use of a line laser

156

and a 3-D camera, allowing the bed level to be measured without disturbing the flow

157

(de Ruijsscher et al., 2018). The bed was scanned with an along-flow resolution of

158

2 mm and an average cross-flow resolution of approximately 3 mm, in eight parallel

159

partly-overlapping swipes. In this way, the initial dry-bed topography was determined,

160

as well as the initial bed topography under still water and the final bed topography.

161

Because we are only interested in the final bed topography, the flow was stopped before

162

measuring. This has the benefit of reducing the measurement error due to perturbations

163

at the free surface.

8

Figure 4: Locations of water level and velocity measurements shown on a greyscale background of the initial bed topography in experiment A1. Water level measurement locations are indicated by black crosses. Velocity measurement locations are indicated by blue circles (low water experiments, A1–D1), red pluses (high water experiments, A2–D2) and a purple triangle (only C2 and D2). These velocity measurements took 40 minutes per location, and were only conducted after a morphodynamic equilibrium was reached. Velocity measurements used for discharge estimation are indicated by green dots. These velocity measurements took 3 minutes per location.

164

3. Analysis methods

165

3.1. Bed level change

166

To determine bed level changes from the measured bed level values, the bed level

167

was interpolated to a regular grid by means of a LOESS algorithm (Vermeulen, 2016;

168

de Ruijsscher et al., 2018). Now the bed level change ∆zb per horizontal cell was

169

obtained according to

170

∆zb (x, y) = zb,final (x, y) − zb,0 (x, y) ,

171

with zb,0 the initial bed level. From this, the cumulative sedimentation for the side

172

channel was calculated by summing over all bed level cells in the side channel. This

173

results in ∆Vside =

174

X

∆zb (x, y)∆x∆y ,

(1)

(2)

x≥4000 mm y≤950 mm 175

with ∆x and ∆y the horizontal grid cell dimensions.

176

3.2. Flow velocities

177

3.2.1. Depth-averaged velocities

178

To analyse the measured flow velocities from the profiling velocimeter, spikes were

179

detected and removed using a bivariate Kernel distribution. This method has been

180

extensively described by Islam and Zhu (2013), based on earlier work of Duong and

181

Hazelton (2003) and Botev et al. (2010). Moreover, only data points with a correlation 9

182

of more than 70% for all four transducers are maintained (Lane et al., 1998) and spatial

183

cells with more than 50% missing values are omitted in further analysis. The remaining

184

velocity data after applying the above steps was interpolated using a cubic Hermite

185

spline. For each velocity measurement point, the time series was averaged over the 40

186

minute bursts, to average out turbulent fluctuations following u=

187

188

189

190

T 1X u, T t=1

(3)

with u the velocity component along the x-axis. A depth-averaged velocity was obtained by integrating the previous result over a vertical range [z1 ; z2 ] according to Z z2 1 u dz . (4) hui = z2 − z1 z1

191

Similar equations hold for the v and w components along y- and z-axis, respectively.

192

3.2.2. Flow angle

193

194

The inflow of water into the side channel was studied in more detail using the angle of the flow with the x-axis, calculated as  v θ = arctan − . u

195

(5)

196

The minus sign was needed to let θ > 0 indicate flow into the side channel. For high

197

water level experiments A2–D2, θ was calculated on top of the sill (y = 888 mm). For

198

low water level experiments A1–D1, this was not possible, due to limited water depth,

199

and θ was measured in the main channel (y = 1488 mm).

200

Only velocity data points for which the normalised standard deviation of veloc-

201

ity component v did not exceed an empirically determined critical value of 0.7 were

202

taken into account, to avoid misinterpretation of θ-values due to negligible near-bed

203

velocities. This normalised standard deviation criterion was defined as σv < 0.7 . ~u

204

205

3.2.3. Discharge estimation

(6)

206

An estimation of the discharge in both main and side channel was obtained by

207

depth-integrating velocity component u measured over a spanwise line and multiplying

208

209

with the grid cell size ∆y as N "Z z2 X  # 1 1 ˆ ˆ Q= u dz + (z1 − z0 ) u(z1 ) + (zWL − z2 ) u (z2 ) + u (zWL ) ∆y , 2 2 {z } | {z }n n=1 |z1{z } | I

II

III

10

(7)

210

with n the total number of grid cells in the spanwise direction. Term I is the integration

211

of time-averaged velocity u over the measured vertical range [z1 ; z2 ], term II is the

212

integration of linearly interpolated velocities between the lowest measured value u(z1 )

213

and u(z0 ) = 0 at the bed, and term III is the integration of the linearly extrapolated

214

velocity profile towards the water surface zWL , using the upper seven vertical cells.

215

216

To relate the discharge division to the cross-sectional area over the sill, this crosssectional area was defined as A = A0 −

217

218

Z

x2

(zsill (x) − z0 ) dx ,

x1

(8)

with reference cross-section A0 defined as A0 = (zLTD − z0 ) (x2 − x1 ) ,

219

220

where [x1 ; x2 ] = [4000; 7950] mm, and zLTD is the height of the LTD crest.

221

3.3. Flow contraction

(9)

222

An often used method to define flow contraction is based on the quotient µ of the

223

flow cross-sectional areas at the location of maximum contraction and downstream of

224

the contraction (Idel’chik, 1966; Hamill, 2001). Because the water level was only mea-

225

sured at a limited number of points, this is not feasible in the present study. Therefore,

226

an estimator was defined that depends both on the angle of the flow in the side channel

227

just downstream of the LTD head and on the relative height of the bed level close to the

228

LTD in the side channel:

229




! z590 − z0 2α , × µˆ = max π h − z0

(10)

230

where α = arccos

231

tor and the x-axis, z590 is the mean bed level at y = 590 mm, and h is the mean water

232

level in the main channel. The maximum of α was taken over the measured flow ve-

233

locity measurement locations within x ∈ [7985; 8985] mm and α was chosen such that

hui/|h~ui|

denotes the angle between the depth averaged velocity vec-

234

α ∈ [−π; π].

235

4. Results

236

4.1. Morphological changes in the side channel

237

Sedimentation and erosion patterns in the side channel of the LTD configuration

238

showed large differences between the high water level regime and the low water level 11

239

regime (filled contours in Fig. 5). In addition, significant differences are observed

240

in patterns between alternative sill geometries. In the following, we focus consecu-

241

tively on persistent morphological features including a depositional bar that developed

242

downstream of the LTD head (‘inner-bend depositional bar’), on a depositional bar in

243

the most upstream part of the side channel (‘divergence bar’), and on the cumulative

244

sedimentation for the entire side channel. A schematic overview of these phenomena

245

is provided afterwards, in section 6 (Fig. 11).

246

4.1.1. Inner-bend depositional bar

247

In the low flow experiments (Fig. 5), a depositional bar developed against the slope

248

of the LTD. The location and intensity of this region of sedimentation depends on the

249

geometrical characteristics of the sill. In situations A1 (low uniform sill height) and

250

C1 (downstream decreasing sill height) the general form of the bar showed to be iden-

251

tical, although the sedimentation was more intense in case C1. For B1 (downstream

252

increasing sill height), the bar started approximately 1 m more upstream with the re-

253

gion of sedimentation extending over the width of the side channel. No sedimentation

254

occurred in case D1, because the height of the sill was only just below the water level.

255

For cases A1–C1, the water flowed obliquely into the side channel, creating a channel

256

that curved around the above-mentioned inner-bend depositional bar. Because of this,

257

a region of erosion was created against the flume wall. The longitudinal location of this

258

erosion depends on the angle of inflow, and therefore on the sill geometry.

259

During the high flow experiments, most of the deposited sediment was eroded

260

again, and the inner-bend depositional bar disappeared. Still, a small region of sed-

261

imentation occurred against the LTD slope, but the differences between experiments

262

with alternative sill geometries were less pronounced. Although the flow still curves

263

into the side channel, flow velocities close to the LTD in the side channel were now

264

non-negligible, and quasi-parallel to the LTD and the main channel flow (Fig. 5, A2–

265

D2).

266

4.1.2. Divergence bar

267

In the most upstream part of the side channel, next to the sill, a region of sedi-

268

mentation occurred driven by flow divergence. Hence we adopt the term divergence

269

bar for this morphological feature. In the evolution towards a dynamic equilibrium,

270

this bar tilted under an increasing angle with the sill, and shifted slightly upstream (not 12

Figure 5: Sedimentation (orange) and erosion (purple) patterns with respect to the initial flat bed, overlaid on the scale model elevation (gray). Red (blue) arrows indicate depth-averaged velocities over the top (bottom) 1.5 cm of the measured vertical range. Velocities above the sill (y = 888 mm) are measured higher in the water column. The bed level could not be measured in part of the main channel in experiment D2 due to equipment failure.

13

271

shown). During the low flow experimental conditions, there were remarkable differ-

272

ences between runs with alternative sill geometries. First of all, the location of the di-

273

vergence bar was shifted more downstream for C1 (downstream decreasing sill height)

274

compared to A1 and B1. In addition to that—and similar to what was observed for the

275

inner-bend depositional bar—the deposition was spread out over a larger area for B1

276

and was absent for D1 due to the limited discharge into the side channel.

277

During the high flow experiments, the divergence bar hardly changed for A2. For

278

B2 the bar was diminished to its most upstream part, whereas for C2 it completely

279

disappeared. In terms of flow patterns, these differences were reflected in an inflow

280

over the downstream half of the sill for A2, and over the upstream part of the sill for

281

D2, eroding a deep inflow channel in the latter case (Fig. 5, A2 and D2). Geometries

282

B and C can be seen as intermediate stages between these two extreme situations, with

283

geometry C creating the most dynamic system in terms of morphological changes. In

284

the latter experimental set-up, a large inner-bend depositional bar and a divergence bar

285

were observed at low flow, whereas these were both almost completely eroded during

286

high flow. Moreover, the main inflow channel was shifted from close to the LTD head

287

to a more sill-parallel inflow over the upstream part of the sill.

288

4.1.3. Cumulative sedimentation

289

To quantify the net sediment import between the starting situation with flat bed

290

and the situation in morphodynamic equilibrium, the cumulative sedimentation in the

291

side channel is visualized in Fig. 6. Hardly any difference was observed in cumulative

292

sedimentation between experiments B and C, with a large sedimentation volume in

293

the side channel during low flow, and a net erosive effect at the end of a high water

294

period. For A (low uniform sill height, i.e. large cross-sectional area over the sill) there

295

was always net sedimentation with respect to the initial flat bed. For D (high uniform

296

sill height, i.e. small cross-sectional area over the sill) net erosion occurred under all

297

circumstances, although at low enough water levels, the flow through the side channel

298

is weak, and erosion is negligible.

299

The most dynamic system in terms of sedimentation and erosion occurred for in-

300

termediate flow cross-sectional areas over the sill, i.e. sill geometries B and C. This is

301

likely due to the divergence bar being situated next to the downstream half of the sill

302

(Fig. 5), which renders the bar more prone to erosion during high flow.

14

0.15

0:171

0:143

0:050

0

0:088

"Vside (m3 )

0.1 0.05

-0.05 -0.1

D D1 2

C 1 C 2

B 1 B 2

A A1 2

-0.15

experiment Figure 6: Cumulative sedimentation in the side channel for each experiment, with respect to the initial flat bed. For each sill geometry, the difference in sedimentation between the high and low water situations is indicated.

303

4.2. Flow patterns

304

4.2.1. Flow contraction

305

Both an inner-bend depositional bar and a flow separation zone can give rise to flow

306

contraction at the entrance of the side channel just downstream of the LTD head. To

307

quantify this effect, Equation (10) was used to calculate a flow contraction metric µ, ˆ

308

which peaks in experiments A1 and C1 (Fig. 7). This implies that during low water

309

levels, the flow is contracted downstream of the sill with geometries A1 and C1. High

310

flow experiments A2–C2 did not convincingly show this phenomenon, although it is

311

hard to draw conclusions on flow separation when no measurements are available in-

312

side the separation zone. For experiments B1 and D1, no reliable value of µˆ could be

313

determined, due to weak flow. For a high enough sill with uniform height, like e.g. in

314

situation D2, the morphological patterns suggest flow contraction in the side channel

315

(lower graph Fig. 5). However, this could not be confirmed based on µ, ˆ because it hap-

316

pened more downstream, outside the region where flow velocity measurements were

317

taken.

318

4.2.2. Inflow angle

319

As observed in Fig. 5, the angle of the flow into the side channel varied, depending

320

on both sill geometry and water level. To take a more detailed look at this, the inflow

321

angle θ as defined in Equation (5) is shown in Fig. 8 in (x, z)-space. For the low flow

322

regime (A1–D1), the inflow angle varied with the x-coordinate. In experiments A1

323

and B1, representing a low uniform sill height and a downstream increasing sill height,

324

respectively, the inflow angle higher up in the water column was of equal magnitude 15

0.15

^ 7

0.1 0.05 0

1

2

1

2 D

D

C

2

C

2

1

B

B

A

A

1

-0.05

experiment Figure 7: Flow contraction metric µˆ showing that flow separation is apparent in the low flow experiments A1 and C1, both with a low sill height downstream. For the high flow experiments, no flow separation in the horizontal plane was observed.

325

over the entire length of the sill. In experiment C1, where the sill height decreases

326

downstream, the flow angle increased in the downstream direction. This indicates that

327

the flow primarily entered the side channel over the downstream half of the sill, which

328

is reflected by the sedimentation patterns in Fig. 5. The fourth plot, representing exper-

329

iment D1, shows flow angles close to zero, caused by the side channel entrance being

330

almost completely blocked by the sill.

331

For high flow conditions—when flow exchange occurs over the entire length of

332

the LTD—the inflow angle was of equal magnitude along the entire sill (bottom three

333

plots of Fig. 8: A2–C2). Moreover, there were hardly any differences between the

334

alternative sill geometries, except for the depth ranges. Although the inflow angle was

335

mostly constant over depth, it increased with depth at the most upstream part of the sill.

336

4.3. Discharge division

337

The cross-sectional area over the sill was not equal for the experiments, which

338

influenced the fraction of the total discharge flowing into the side channel (Fig. 9).

339

This is relevant, because the water discharge division over the two channels controls the

340

morphological evolution in both main and side channel. For the low flow experiments,

341

the fraction of the discharge into the side channel increased with the cross-sectional

342

area, as expected, with river narrowing for low water levels and river widening for high

343

water levels. The side channel discharge fraction agrees reasonably well with values

344

observed in the field (J. Sieben, pers. comm., 2018) and in a numerical study by Huthoff

345

et al. (2011), although a slight underestimation is observed. There was no significant

346

difference between cases B1 and C1, which suggests that apart from the cross-sectional 16

Figure 8: Flow angle θ with respect to the main flow direction in (x, z)-space, based on Equation (5), with the scale indicated by the horizontal bars with length 0.02π (A1–D1) and 0.06π (A2–C2). A positive (negative) value indicates flow towards (away from) the side channel. S u and S d mark the upstream and downstream boundaries of the sill, respectively (Fig. 2). During low flow, the streamwise location x of maximum specific discharge into the side channel is determined by the sill geometry. For a downstream decreasing sill height (C1), flow enters more downstream. During high flow, the angle was of equal magnitude along the entire sill and hardly varied with depth.

17

^ main ) ^ side + Q ^ side =(Q Q

0.4 0.3 D2

C2

B2

A2 A1

0.2 C1

0.1 0 0.3

B1

D1 0.4

0.5

0.6

0.7

A=A0 Figure 9: Discharge through the side channel increases with increasing cross-sectional area over the sill during the low flow phase. This proceeds from the discharge division Qˆ side /(Qˆ side + Qˆ main ) as a function of relative cross-sectional area over the sill A/A0 in experiments A1–D1. During the high flow phase (experiments A2–D2), no significant differences are observed, due to flow exchange over the LTD crest. Bars indicate the error based on the measured total discharge. The dashed line denotes the division between increased fairway depth (river narrowing) and increased discharge capacity (river widening) (following J. Sieben, pers. comm., 2018).

347

area, the geometry of the sill did not influence the discharge division. In the high flow

348

experiments, there was no significant difference between the discharge division over

349

the two channels, related to flow exchange over the LTD crest.

350

5. Comparison with field pilot

351

To establish the realism of the experiments, a qualitative comparison was performed

352

between the final bed level of experiment A1 and bed level data from multi-beam

353

echo-soundings (MBES) in the field pilot. The sill at the side channel intake has a

354

uniform low height in the field, similar to the situation in experiment A1. The MBES-

355

measurements were performed on 7 February 2017, which is more than 15 months after

356

completion of the LTD pilot configuration. The total river discharge at Tiel (5 km up-

357

stream) was Q = 1448 m3 s−1 , whereas minimum, mean and maximum discharge over

358

2017 were Qmin = 543 m3 s−1 , Q = 1379 m3 s−1 and Qmax = 5088 m3 s−1 , respectively.

359

The crest of the LTD was above the water surface during the field measurements. At

360

the side channel bank, however, remainders of old groynes are present, which is differ-

361

ent from the vertical flume wall in the scale model. The presence of groyne remainders

362

is reflected by the wavy pattern of the shoreline. The river is mildly curved at the LTD

363

section, with the inflection point near the entrance of the side channel under study.

364

The qualitative comparison between the field pilot and experiment A1 shows that 18

270 mm

120 mm

Figure 10: Qualitative comparison of bed levels from lab and field measurements: both show the inner-bend depositional bar and the divergence bar in the side channel, although location and intensity differ. Left: bed level from multi-beam echo-soundings in the Waal River field pilot on 7 February 2017, with respect to Amsterdam Ordnance Datum (NAP). Right: bed level at the end of experiment A1, with respect to the flume bottom. The main flow direction is indicated by the arrow. Source of background image: Google.

19

365

the main morphological features are well reproduced (Fig. 10), but differences exist.

366

The erosion pit at the side channel flume wall is not observed in the field pilot. This may

367

indicate that the erosion pit is merely a flume wall effect, which does not occur in the

368

field pilot due to the mild slope of the bank. A second explanation lies in the presence

369

of old groyne remainders, which stabilise the bank. Another discrepancy between lab

370

experiments and field pilot regards the divergence bar in the most upstream part of

371

the field pilot side channel, which is less pronounced and located more downstream

372

than observed in the scale model. In the field pilot, less sediment is deposited against

373

the side channel slope of the LTD. The more pronounced sedimentation and erosion

374

patterns in the scale model side channel may be explained by the slightly exaggerated

375

mobility of polystyrene particles in the scale model (Vermeulen et al., 2014).

376

6. Discussion

III II

I

sedimentation erosion sill flow direction

Figure 11: Schematic overview of the bed morphology at the bifurcation, highlighting (I) the inner-bend depositional bar caused by flow separation, (II) the divergence bar, induced by widening of the river at the side channel entrance and an increasing flow depth just behind the LTD sill, and (III) an erosion pit along the side channel bank, which might result from the solid flume wall.

377

6.1. Inner-bend depositional bar

378

Fig. 11 offers a schematic overview of the bed morphology in the inlet region.

379

For low discharges, flow contraction due to the inner bend depositional bar occurs

380

especially in cases with a low sill height near the LTD (i.e., A1 and C1, Figs. 5 and 7).

381

This resembles flow separation in the inner bend of rivers as described by Blanckaert 20

Figure 12: From top to bottom, the slope of the sill to LTD transition becomes milder, which causes a change in direction of the inflow angle (black line), while retaining the inner-bend depositional bar. Filled contours indicate sedimentation (orange) and erosion (purple) patterns. The elevation of the scale model is indicated in gray: the darker the higher. Red (blue) arrows indicate depth-averaged velocities over the top (bottom) 1.5 cm of the measured vertical range.

382

et al. (2012), who observed a flow separation cell downstream of the bend apex. To

383

better grasp the flow separation and subsequent inner-bend depositional bar formation,

384

an additional experiment AB1 was performed, designed as a combination of A1 and

385

B1. It consists of a horizontal sill as in experiment A1, but with an increasing sill height

386

from 2.5 to 7.5 cm over the downstream 25 % of the sill. In other words, the slope of

387

the transition from the lowest part of the sill to the LTD crest is 1:2.5, 1:10 and 1:40

388

for A1, AB1 and B1, respectively.

389

Analogous to Fig. 5, the bed level differences of experiments A1, AB1 and B1 are

390

shown in Fig. 12. While the inner-bend depositional bar is present in all cases shown,

391

the inflow angle is different, impacting on the pattern of sedimentation and erosion

392

downstream. This inflow angle, denoted by the black line in Fig. 12, is a measure of

393

flow separation at the bifurcation point. Flow separation intensifies with decreasing

394

steepness of the transition from the sill to the LTD crest (from A, via AB, to B). To

395

limit the amount of sedimentation in the side channel downstream of the bifurcation

396

point, a steep transition is desirable between the sill and the LTD, as in configurations

397

A and C.

21

398

6.2. Divergence bar

399

At the most upstream part of the side channel, a bar is formed caused by the flow

400

diverting into the side channel and over the sill (Fig. 11, location II). One could ar-

401

gue that the formation of this bar is analogous to the formation of an inner-bend bar

402

in case of flow bifurcation, for instance at a side channel take-off. Kleinhans et al.

403

(2013) and van Denderen et al. (2018) describe this phenomenon as development of a

404

bar and scour zone, possibly associated with a flow separation zone as described pre-

405

viously by Neary and Odgaard (1993) for a 90◦ channel offtake. Although no direct

406

velocity measurements are performed in the triangle enclosed by the divergence bar,

407

the flume wall and the rip-rap bank (Fig. 5), the absence of morphological activity in

408

this most upstream part of the side channel reflects the absence of a strong horizontal

409

recirculation. A similar configuration was studied numerically by van Linge (2017)

410

and Jammers (2017). They did observe a horizontal recirculation zone upstream in the

411

side channel, but found no sediment transport over the sill towards this zone (Jammers,

412

2017). Thus, the formation of the divergence bar is dominated by a divergence-induced

413

reduced flow velocity by 1) widening of the flow at the side channel entrance, and 2)

414

increased water depth after the sill.

415

6.3. Sill design and discharge division

416

Simulations by Le et al. (2018a,b) suggest that for a free inflow LTD system, even-

417

tually one of the two channels will close. This is undesirable, because it makes the

418

side channel unsuitable for recreational boating and results in increased discharge and

419

erosion in the main channel. The sill at the entrance of the LTD side channel shows to

420

be an effective regulatory structure to prevent the side channel from closing. A down-

421

stream decreasing sill height (configuration C) minimises the dredging efforts needed

422

to keep the side channel open in the long term, since much of the sediment deposited

423

during low flow is removed during high flow. The discharge division Qside /Qtot , which

424

is an important driving parameter for morphological evolution in both main and side

425

channel, is well below the critical value of 0.27 in experiments B1–D1 (Fig. 9). This

426

critical value has been established as the threshold between effective narrowing and

427

widening of the river after LTD construction. This value is scaled from the field value

428

of 0.12 obtained from Rijkswaterstaat (J. Sieben, pers. comm., 2018), based on 45% of

429

the normal width of the river being modelled (Boersema, 2012). Because the LTD is

22

430

located in the inner bend of the river with the sill approximately at the inflexion point,

431

the actual discharge distribution Qside /Qtot is underestimated in the scale model, which

432

is located in a straight flume. This does not undermine the above conclusions, yet even

433

strengthens the statement that designs B–D are preferred over design A in terms of

434

discharge division. Combining the effects of sill geometry on morphological evolution

435

of the side channel and discharge division over both channels, design C is a promising

436

sill geometry to be considered for field implementation.

437

6.4. Recommendations for future research

438

Although the present study provides clear insights in the morphological effects of

439

horizontal flow separation downstream of the bifurcation at the side channel intake,

440

direct measurements of flow velocities in the flow separation cell could provide com-

441

plementary insights on smaller scale flow patterns and large coherent structures. In

442

retrospect, using an ADV to measure flow velocities did not work out at some loca-

443

tions in the flume due to the limited water depth. The water depth cannot easily be

444

increased, because non-distorted geometric scaling is preferred due to the importance

445

of 3-D flow patterns. This calls for the use of additional measurement methods to mon-

446

itor flow velocities. In the physical scale model, Particle Image Velocimetry could be

447

used to detect coherent structures at the water surface. Alternatively, 3-D numerical

448

modelling and a field campaign in which measurements are taken close to the LTD, us-

449

ing for instance an Acoustic Doppler Current Profiler, could shed light on the detailed

450

flow patterns in this region.

451

7. Conclusions

452

In a physical scale model representing the entrance region of a longitudinal training

453

dam where a sill is constructed, persistent morphological patterns are observed, which

454

resemble field observations. An inner-bend depositional bar develops against the side-

455

channel side of the LTD, analogous to the deposition in the horizontal flow recirculation

456

zone in a sharp river bend. This bar is largely eroded again during high flows. In the

457

upstream part of the side channel, a divergence bar is formed induced by divergence of

458

the flow where the river widens and the depth increases after the sill. Whether or not the

459

divergence bar is eroded during high flows depends on the geometry of the sill. Both

460

bar types are also observed in a field pilot in the Waal River. The degree of erosion or 23

461

sedimentation in the side channel during low and high flow conditions largely depends

462

on the geometry of the sill, which is therefore a suitable instrument for regulating sed-

463

iment transport into the side channel. To limit the amount of sedimentation in the side

464

channel downstream of the bifurcation point, a steep transition is desirable between the

465

sill and the LTD crest. The discharge into the side channel is primarily affected by the

466

cross-sectional area over the sill, and little dependent on other sill characteristics such

467

as the longitudinal slope. Overall, a downstream decreasing sill height (geometry C)

468

is promising because of the balance between minimised net sedimentation effects in

469

the side channel and the required discharge division during low and high water level

470

situations.

471

Acknowledgements

472

This research is part of the research programme RiverCare, supported by the Dutch

473

Technology Foundation STW, which is part of the Netherlands Organization for Sci-

474

entific Research (NWO), and which is partly funded by the Ministry of Economic Af-

475

fairs under grant number P12-14 (Perspective Programme). Additional support was

476

provided by Rijkswaterstaat, part of the Dutch Ministry of Infrastructure and Water

477

Management. We thank Johan R¨omelingh and Pieter Hazenberg (Wageningen Univer-

478

sity & Research) for their technical support. Furthermore, we owe thanks to Judith

479

Poelman, Bas Wullems and especially Daan van Keulen for their practical assistance

480

in the lab. The data and scripts used in this study are publicly available online on

481

https://hdl.handle.net/10411/INMSDG.

482

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63160c45-f3ed-4ad2-84c8-9a1db1e04f0a

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van Vuren, S., Paarlberg, A., Havinga, H., 2015. The aftermath of “Room for the

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River” and restoration works: Coping with excessive maintenance dredging. Journal

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Vermeulen, B., Boersema, M. P., Hoitink, A. J. F., Sieben, J., Sloff, C. J., van der Wal,

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M., 2014. River scale model of a training dam using lightweight granulates. Journal

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of Hydro-environment Research 8 (2), 88–94.

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Wang, Z. B., De Vries, M., Fokkink, R. J., Langerak, A., 1995. Stability of river bi-

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furcations in 1D morphodynamic models. Journal of Hydraulic Research 33 (6),

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739–750.

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Yossef, M. F. M., de Vriend, H. J., 2011. Flow details near river groynes: Experimental investigation. Journal of Hydraulic Engineering 137 (5), 504–516.

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