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![Page 1: Entrainment and non-uniform transport of fine-sediment in coarse-bedded rivers Paul E. Grams & Peter R. Wilcock, Johns Hopkins University Stephen M. Wiele,](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cda5503460f949a3fe5/html5/thumbnails/1.jpg)
Entrainment and non-uniform Entrainment and non-uniform transport of fine-sediment in transport of fine-sediment in
coarse-bedded riverscoarse-bedded rivers
Paul E. Grams & Peter R. Wilcock, Paul E. Grams & Peter R. Wilcock,
Johns Hopkins UniversityJohns Hopkins University
Stephen M. Wiele, US Geological SurveyStephen M. Wiele, US Geological Survey
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AcknowledgementsAcknowledgements
• USGS – Grand Canyon Monitoring and USGS – Grand Canyon Monitoring and Research CenterResearch Center
• National Center for Earth-Surface National Center for Earth-Surface DynamicsDynamics
• University of Minnesota – St Anthony Falls University of Minnesota – St Anthony Falls LaboratoryLaboratory
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Fine sediment transport in Fine sediment transport in rivers with coarse bed materialrivers with coarse bed material
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Sand entrainment from a coarse bed: Two aspects of the problem
1.1. What happens to entrainment as the What happens to entrainment as the sand-bed elevation drops?sand-bed elevation drops?
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Sand entrainment – coarse bed
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Sand entrainment – coarse bed
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Sand entrainment – coarse bed
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Sand entrainment – coarse bed
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Sand entrainment from a coarse bed: Two aspects of the problem
1. What happens to entrainment as the sand-bed elevation drops?
2.2. What is the effect of spatial variability What is the effect of spatial variability in bed condition?in bed condition?
![Page 11: Entrainment and non-uniform transport of fine-sediment in coarse-bedded rivers Paul E. Grams & Peter R. Wilcock, Johns Hopkins University Stephen M. Wiele,](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cda5503460f949a3fe5/html5/thumbnails/11.jpg)
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Outline• Framework of the entrainment formulation
• Describe main channel experiments
• Bed condition and simplified model to represent bed condition
• Non-uniform routing model
• Comparison between predicted and observed bed
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Garcia and Parker (1991) entrainment relation for mixed-size sediment
5,
5,
,
3.01
ˆ
jm
jmjs
ZA
ZAE
m
jjp
jsjm d
duZ
50
6.0,
,, Re
fractionjth for number Reynoldsgrain
0.2 constant
parameter straining
mixturesediment theof sizemedian
fractionjth of size
103.1constant
ion)decomposit(Einstein stressgrain
,
50
7
jp
j
R
m
d
d
A
u
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1 10 100
jmZ ,
jsE ,ˆ
![Page 14: Entrainment and non-uniform transport of fine-sediment in coarse-bedded rivers Paul E. Grams & Peter R. Wilcock, Johns Hopkins University Stephen M. Wiele,](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cda5503460f949a3fe5/html5/thumbnails/14.jpg)
Sand elevation correction function
js
js
E
E
,
,
ˆ
Zzse ˆ1
jsE ,
jsE ,ˆ
= observed dimensionless entrainment rate
= dimensionless entrainment rate for a full sand bed (i.e. Garcia and Parker model)
)ˆ( szf = sand elevation correction function
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.0 0.2 0.4 0.6 0.8 1.0
sz
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Sand elevation correction function
js
js
E
E
,
,
ˆ
Zzse ˆ1
jsE ,
jsE ,ˆ
= observed dimensionless entrainment rate
= dimensionless entrainment rate for a full sand bed (i.e. Garcia and Parker model)
)ˆ( szf = sand elevation correction function
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.0 0.2 0.4 0.6 0.8 1.0
sz
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Non-uniform transport to test Non-uniform transport to test coupled sand entrainment and coupled sand entrainment and sand routing model.sand routing model.
Experiments in main channel at SAFLExperiments in main channel at SAFL
• 2.74 x 84 m flume (40 m test section)2.74 x 84 m flume (40 m test section)
• 60 cm flow depth60 cm flow depth
• Bed roughness: D = 15 cmBed roughness: D = 15 cm
• Feed sediment grain size: ~ 0.13 mmFeed sediment grain size: ~ 0.13 mm
• 5 experimental runs (2-11 hr duration)5 experimental runs (2-11 hr duration)
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Non-uniform transport to test Non-uniform transport to test coupled sand entrainment and coupled sand entrainment and sand routing model.sand routing model.
Experiments in main channel at SAFLExperiments in main channel at SAFL
• Constant Q: 29 l/sConstant Q: 29 l/s• Qs: 2.3 tons/hr for 90 min.Qs: 2.3 tons/hr for 90 min.• Initial bed: bare (no fine sediment)Initial bed: bare (no fine sediment)• Four segmentsFour segments
– 1: 90 min. sediment feed1: 90 min. sediment feed
– 2: 60 min.2: 60 min.
– 3: 145 min.3: 145 min.
– 4: 365 min.4: 365 min.
• 662 min. (11 hr) cumulative run time662 min. (11 hr) cumulative run time
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Non-uniform transport to test Non-uniform transport to test coupled sand entrainment and coupled sand entrainment and sand routing model.sand routing model.
Experiments in main channel at SAFLExperiments in main channel at SAFL
• Bed topography: measured at the end of Bed topography: measured at the end of each run segment, and sampled for grain each run segment, and sampled for grain sizesize
• Suspended sediment concentration: Suspended sediment concentration: Three siphon rakes positioned across Three siphon rakes positioned across channel, analyzed for concentration and channel, analyzed for concentration and grain sizegrain size
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91 min.
152 min.
297 min.
662 min.
Main channel bed
40 m40 m
2.7 m
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Bed of Colorado River in Grand CanyonBed of Colorado River in Grand Canyon
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Bimodal bed – Stripe or Bare
0
40
80
120
160
200
0
2.5
5.0
7.5
10
.0
12
.5
15
.0
0.00
0.00
0.01
0.01
0.02
Sand depth (cm)
1c
Nu
mb
er
of o
bse
rva
tion
sV
olu
me
(m3)
stripebare
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Distribution of sand bed elevations and sand storage
0
40
80
120
160
200
0
2.5
5.0
7.5
10
.0
12
.5
15
.0
0.00
0.00
0.01
0.01
0.02
Sand depth (cm)
1d
0
40
80
120
160
200
0
2.5
5.0
7.5
10
.0
12
.5
15
.0
0.00
0.00
0.01
0.01
0.02
Sand depth (cm)
1c
0
40
80
120
160
200
0.00
0.00
0.01
0.01
0.021b
0
40
80
120
160
200
0.00
0.00
0.01
0.01
0.021a
Vo
lum
e (m
3)N
um
be
r o
f ob
serv
atio
ns
Blue = volume at indicated depthOrange = n for indicated depth
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Sand elevation correction function from bed morphology
stripe sand ain is that bed theoffraction theis
stripe sand ain not is that bed theoffraction theis
(stripes) sand of patchesfor elevation sand modal theis
stripes)-(non bed barefor elevation sand modal theis
elevation bed sand averaged-spatially is
p
b
p
b
s
F
F
z
z
z
bbpps FzFzz ˆˆˆ
pb FF 1
pbpps FzFzz 1ˆˆˆ
bp
bsp zz
zzF
ˆˆ
ˆˆ
b
ss r
zz ˆ
b
pp r
zz ˆ
b
bb r
zz ˆ
0.00
0.20
0.40
0.60
0.80
1.00
0 0.2 0.4 0.6 0.8 1
pF
sz
pz
bz
““linear relation for the linear relation for the fraction of the bed that is fraction of the bed that is covered by sand stripes based covered by sand stripes based on modal stripe and non-on modal stripe and non-stripe elevations”stripe elevations”
![Page 24: Entrainment and non-uniform transport of fine-sediment in coarse-bedded rivers Paul E. Grams & Peter R. Wilcock, Johns Hopkins University Stephen M. Wiele,](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cda5503460f949a3fe5/html5/thumbnails/24.jpg)
Sand elevation correction function from bed morphology
js
jsA
E
E
,
,
ˆ
ZzA
se ˆ1
0.00
0.20
0.40
0.60
0.80
1.00
0 0.2 0.4 0.6 0.8 1
sz
A
jsE ,
jsE ,ˆ
= Spatially-averaged entrainment rate
= Spatially-averaged entrainment rate for a full sand bed
)ˆ( sA zf = Spatially-averaged sand elevation correction
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Non-uniform morphodynamic sediment routing model
• Steady, uniform flow• Mixed-size entrainment (Garcia and
Parker, 1991)• Sand elevation correction function• Non-uniform suspended sediment
concentration profiles– Velocity and eddy viscosity from
measured u profiles• Sediment continuity
– qT = qs (ignoring transport by bedload)– Active layer ~ bed D50 (fully-mixed)
• Boundary conditions– Zero flux at water surface– Flux at bed (entrainment rate)– Sediment feed at upstream end
![Page 26: Entrainment and non-uniform transport of fine-sediment in coarse-bedded rivers Paul E. Grams & Peter R. Wilcock, Johns Hopkins University Stephen M. Wiele,](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cda5503460f949a3fe5/html5/thumbnails/26.jpg)
Non-uniform morphodynamic sediment routing model
• Steady, uniform flow• Mixed-size entrainment (Garcia and
Parker, 1991)• Sand elevation correction function• Non-uniform suspended sediment
concentration profiles– Velocity and eddy viscosity from
measured u profiles• Sediment continuity
– qT = qs (ignoring transport by bedload)– Active layer ~ bed D50 (fully-mixed)
• Boundary conditions– Zero flux at water surface– Flux at bed (entrainment rate)– Sediment feed at upstream end
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1 10 100
jmZ ,
jsE ,ˆ
![Page 27: Entrainment and non-uniform transport of fine-sediment in coarse-bedded rivers Paul E. Grams & Peter R. Wilcock, Johns Hopkins University Stephen M. Wiele,](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cda5503460f949a3fe5/html5/thumbnails/27.jpg)
Non-uniform morphodynamic sediment routing model
• Steady, uniform flow• Mixed-size entrainment (Garcia and
Parker, 1991)• Sand elevation correction function• Non-uniform suspended sediment
concentration profiles– Velocity and eddy viscosity from
measured u profiles• Sediment continuity
– qT = qs (ignoring transport by bedload)– Active layer ~ bed D50 (fully-mixed)
• Boundary conditions– Zero flux at water surface– Flux at bed (entrainment rate)– Sediment feed at upstream end
0.00
0.20
0.40
0.60
0.80
1.00
0 0.2 0.4 0.6 0.8 1
sz
A
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Non-uniform morphodynamic sediment routing model
• Steady, uniform flow• Mixed-size entrainment (Garcia and
Parker, 1991)• Sand elevation correction function• Non-uniform suspended sediment
concentration profiles– Velocity and eddy viscosity from
measured u profiles• Sediment continuity
– qT = qs (ignoring transport by bedload)– Active layer ~ bed D50 (fully-mixed)
• Boundary conditions– Zero flux at water surface– Flux at bed (entrainment rate)– Sediment feed at upstream end
z
CK
zz
Cv
x
Cu
t
Czs
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Non-uniform morphodynamic sediment routing model
• Steady, uniform flow• Mixed-size entrainment (Garcia and
Parker, 1991)• Sand elevation correction function• Non-uniform suspended sediment
concentration profiles– Velocity and eddy viscosity from
measured u profiles• Sediment continuity
– qT = qs (ignoring transport by bedload)– Active layer ~ bed D50 (fully-mixed)
• Boundary conditions– Zero flux at water surface– Flux at bed (entrainment rate)– Sediment feed at upstream end
x
q
t
z Tsp
1
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No SEC
0.00
0.05
0.10Run 1, 90 minmodel, 90 min
0.00
0.05
0.10Run 1, 150 minmodel, 150 min
0.00
0.05
0.10Run 1, 300 minmodel, 300 min
0.00
0.05
0.10Run 1, 660 minmodel, 660 min
Distance from downstream end of test section (m)
Sa
nd
be
d e
leva
tion
(m
)
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
sz
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0.00
0.05
0.10Run 1, 90 minmodel, 90 min
0.00
0.05
0.10Run 1, 150 minmodel, 150 min
0.00
0.05
0.10Run 1, 300 minmodel, 300 min
0.00
0.05
0.10Run 1, 660 minmodel, 660 min
Distance from downstream end of test section (m)
Sa
nd
be
d e
leva
tion
(m
)
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
sz
SEC from 2002 lab
data
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0.00
0.05
0.10Run 1, 90 minmodel, 90 min
0.00
0.05
0.10Run 1, 150 minmodel, 150 min
0.00
0.05
0.10Run 1, 300 minmodel, 300 min
0.00
0.05
0.10Run 1, 660 minmodel, 660 min
Distance from downstream end of test section (m)
Sa
nd
be
d e
leva
tion
(m
)
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
sz
Theoretical SEC
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SEC calibrated to
main channel bed elevations
0.00
0.05
0.10Run 1, 90 minmodel, 90 min
0.00
0.05
0.10Run 1, 150 minmodel, 150 min
0.00
0.05
0.10Run 1, 300 minmodel, 300 min
0.00
0.05
0.10Run 1, 660 minmodel, 660 min
Distance from downstream end of test section (m)
Sa
nd
be
d e
leva
tion
(m
)
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
sz
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Comparison between observed and predicted mean bed elevations
Run Calibrated Theoretical 2002 lab data No SEC
1A Observed 0.037 0.037 0.037 0.037Predicted 0.041 0.045 0.038 0.029RMS 0.009 0.012 0.008 0.014
1B Observed 0.034 0.034 0.034 0.034Predicted 0.035 0.043 0.032 0.022RMS 0.007 0.011 0.008 0.018
1C Observed 0.028 0.028 0.028 0.028Predicted 0.028 0.038 0.025 0.015RMS 0.008 0.010 0.010 0.020
1D Observed 0.025 0.025 0.025 0.025Predicted 0.023 0.032 0.017 0.011RMS 0.012 0.011 0.016 0.022
* all values in meters
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Concentration profiles
Simulated vs. observed
0
10
20
30
40
50
60
0.0E+00 1.0E-04 2.0E-04 3.0E-04 4.0E-04
Left
Center
Right
90 min.
z (c
m)
c
Run 1aSample 2: 82.0 to 71.5 min
0
10
20
30
40
50
60
0.0E+00 1.0E-04 2.0E-04 3.0E-04 4.0E-04
Left
Center
Right
140 min.
z (c
m)
c
Run 1bSample 2: 138.1 to 143.8 min
0
10
20
30
40
50
60
0.0E+00 1.0E-04 2.0E-04 3.0E-04 4.0E-04
Left
Center
Right
290 min.
z (c
m)
c
Run 1cSample 2: 287.0 min
0
10
20
30
40
50
60
0.0E+00 1.0E-04 2.0E-04 3.0E-04 4.0E-04
Left
Center
Right
640 min.
z (c
m)
c
Run 1dSample 3: 634.5 to 643.0 min
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Bed grain size (D50)
Simulated vs. observed
10-5
10-4
10-3
observedmodel
91 min.
D5
0(m
)10 20 30 40
10-5
10-4
10-3
152 min.
10 20 30 4010-5
10-4
10-3
297 min.
Distance from upstream end of test section (m)10 20 30 40
10-5
10-4
10-3
662 min.
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Sand elevation correction functionYes or No? Which to choose?
• Blue – 2002 data– Bed evacuates too
rapidly
• Orange – theoretical– Decent prediction
• Yellow – Calibrated– Best fit to observed
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Sand elevation correction functionYes! Don’t know!
• Blue – 2002 data– Bed evacuates too
rapidly
• Orange – theoretical– Decent prediction
• Yellow – Calibrated– Best fit to observed
0.0
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1.0
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ConclusionsConclusions
• In these conditions of fine sediment transport over a coarse In these conditions of fine sediment transport over a coarse immobile bed, sand stripes developed and persisted as the immobile bed, sand stripes developed and persisted as the fine sediment was evacuated.fine sediment was evacuated.
• This bed condition can serve as the basis for a spatially-This bed condition can serve as the basis for a spatially-averaged sand elevation correction function.averaged sand elevation correction function.
• This function implemented in a non-uniform routing This function implemented in a non-uniform routing model successfully predicts average bed elevation, model successfully predicts average bed elevation, concentration profiles, and bed grain size.concentration profiles, and bed grain size.
• Predicted bed elevations are not very sensitive to the exact Predicted bed elevations are not very sensitive to the exact shape of the correction function. Calibrating the function shape of the correction function. Calibrating the function produces only slightly better results.produces only slightly better results.
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What does the local sand elevation correction function look like?
• Theoretical approach:
dAEA
EA
sLsA 1
• Observations from detailed experiments using PIV
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