entrainment and non-uniform transport of fine-sediment in coarse-bedded rivers paul e. grams &...

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

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

Fine sediment transport in Fine sediment transport in rivers with coarse bed materialrivers with coarse bed material

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?

Sand entrainment – coarse bed

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?

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

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

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

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)



• 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



• 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

91 min.

152 min.

297 min.

662 min.

Main channel bed

40 m40 m

2.7 m

Bed of Colorado River in Grand CanyonBed of Colorado River in Grand Canyon

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

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

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”

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

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








0.00

0.20

0.40

0.60

0.80

1.00

0 0.2 0.4 0.6 0.8 1

sz

A








z

CK

zz

Cv

x

Cu

t

Czs








x

q

t

z Tsp

1

No SEC

0.00

0.05

0.10Run 1, 90 minmodel, 90 min

0.00

0.05


0.00

0.05


0.00

0.05


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

0.00

0.05


0.00

0.05


0.00

0.05


0.00

0.05



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

0.00

0.05


0.00

0.05


0.00

0.05


0.00

0.05



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

SEC calibrated to

main channel bed elevations

0.00

0.05


0.00

0.05


0.00

0.05


0.00

0.05



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

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

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

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.

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

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

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

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

sz

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.

What does the local sand elevation correction function look like?

• Theoretical approach:

dAEA

EA

sLsA 1

• Observations from detailed experiments using PIV

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.0 0.5 1.0

sz

entrainment and non-uniform transport of fine-sediment in coarse-bedded rivers paul e. grams &...

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