chapter 31: erosional narrowing and widening of a channel after dam removal
DESCRIPTION
CHAPTER 31: EROSIONAL NARROWING AND WIDENING OF A CHANNEL AFTER DAM REMOVAL. This chapter was written by Gary Parker, Alessandro Cantelli and Miguel Wong. View of a sediment control dam on the Amahata River, Japan. Image courtesy H. Ikeda. CONSIDER THE CASE OF THE SUDDEN REMOVAL, - PowerPoint PPT PresentationTRANSCRIPT
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
RIVERS AND TURBIDITY CURRENTS© Gary Parker November, 2004
CHAPTER 31:EROSIONAL NARROWING AND WIDENING OF A CHANNEL AFTER DAM
REMOVAL
This chapter was written by Gary Parker, Alessandro Cantelli and Miguel Wong
View of a sediment control dam on the Amahata River, Japan. Image courtesy H. Ikeda.
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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CONSIDER THE CASE OF THE SUDDEN REMOVAL, BY DESIGN OR ACCIDENT, OF A DAM FILLED WITH SEDIMENT
Before removal
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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REMOVAL OF THE DAM CAUSES A CHANNEL TO INCISE INTO THE DEPOSIT
After removal
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
RIVERS AND TURBIDITY CURRENTS© Gary Parker November, 2004
AS THE CHANNEL INCISES, IT ALSO REMOVES SIDEWALL MATERIAL
sidewall sediment eroded as channel incises
top of reservoir deposit
A first treatment of the morphodynamics of this process was given in Chapter 15.
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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EXNER EQUATION OF SEDIMENT CONTINUITY WITH SIDEWALL EROSION
The formulation of Chapter 15 is reviewed here.
Bb = channel bottom width, here assumed constant
b = bed elevationt = elevation of top of bankQb = volume bedload transport rateSs = sidewall slope (constant)p = porosity of the bed deposits = streamwise distancet = timeBs = width of sidewall zone
s = volume rate of input per unit length of sediment from sidewalls
ss
bt SB
sbb
b s
Q
tB
tS2
tB2 b
s
btbss
Ss
Bb
sidewall sediment eroded as channel incises
ttb
Bs
t
b
s > 0 for a degrading channel, i.e. b/t < 0
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
RIVERS AND TURBIDITY CURRENTS© Gary Parker November, 2004
EXNER EQUATION OF SEDIMENT CONTINUITY INCLUDING SIDEWALL EROSION contd.
s
Q
tS2B bb
s
btb
Ss
Bb
sidewall sediment eroded as channel incises
ttb
Bs
t
b
In Chapter 15, the relations of the previous slide were reduced to obtain the relation:
or
s
Q
S2B
1
tb
s
btb
b
That is, when sidewall erosion accompanies degradation, the sidewall erosion suppresses (but does not stop) degradation and augments the downstream rate of increase of bed material load.
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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ADAPTATION TO THE PROBLEM OF CHANNEL INCISION SUBSEQUENT TO DAM REMOVAL: THE DREAM MODELS
1200 ft
Dam
Saeltzer Dam, California before its removal in 2001.
Cui et al. (in press-a, in press-b) have adapted the formulation of the previous two slides to describe the morphodynamics of dam removal. These are embodied in the DREAM numerical models. These models have been used to simulate the morphodynamics subsequent to the removal of Saeltzer Dam, shown below.
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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THE DREAM MODELS
s
Q
S2B
1
tb
s
btbm
b
Specify an initial top width Bbt and a minimum bottom width Bbm.
If Bb > Bbm, the channel degrades and narrows without eroding its banks.
If Bb = Bbm the channel degrades and erodes its sidewalls without further narrowing.
)(S2BB
s
Q
B
1
t
btsbtb
b
b
b
But Bbm must be user-specified.
Ss
Bb > Bbm
Bbt
Ss
Bb = Bbm
sidewall sediment eroded as channel incises
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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SUMMARY OF THE DREAM FORMULATION
Ss
increasing time
no narrowing and sidewall erosion when Bb = Bbm
trajectories of left and right bottom
bank position
top of depositnarrowing without sidewall erosion when Bb > Bbm
But how does the process really work? Some results from the experiments of Cantelli et al. (2004) follow.
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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EROSION PROCESS VIEWED FROM DOWNSTREAM
rte-bookdamremfrontview.mpg: to run without relinking, download to same folder as PowerPoint presentations.
Double-click on the image to see the video clip.
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
RIVERS AND TURBIDITY CURRENTS© Gary Parker November, 2004
NOTE THE TRANSIENT PHENOMENON OFEROSIONAL NARROWING
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
RIVERS AND TURBIDITY CURRENTS© Gary Parker November, 2004
EROSION PROCESS VIEWED FROM ABOVE
Double-click on the image to see the video clip.
rte-bookdamremtopview.mpg: to run without relinking, download to same folder as PowerPoint presentations.
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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EVOLUTION OF CENTERLINE PROFILEUPSTREAM (x < 9 m) AND DOWNSTREAM (x > 9 m) OF THE DAM
Upstream degradation Downstream aggradation
Former dam location
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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CHANNEL WIDTH EVOLUTION UPSTREAM OF THE DAM
The dam is at x = 9 m downstream of sediment feed point.
Note the pattern of rapid channel narrowing and degradation, followed by slow channel widening and degradation. The pattern is strongest near the dam.
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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-6
-5
-4
-3
-2
-1
0
20 21 22 23 24 25
Water Surface Width (cm)
Wat
er S
urf
ace
Ele
vati
on
(cm
)
Progress in time
Subsequent 16.0 minutes of run: period of erosional widening
First 4.3 minutes of run: period of erosional narrowing
REGIMES OF EROSIONAL NARROWING AND EROSIONAL WIDENING
The dam is at x = 9 m downstream of sediment feed point.
The cross-section is at x = 8.2 m downstream of the sediment feed point, or 0.8 m upstream of the dam.
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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SUMMARY OF THE PROCESS OF INCISION INTO A RESERVOIR DEPOSIT
rapid incision with
narrowing
Ss
trajectories of left and right bottom
bank position top of deposit
slow incision with
widening
incisional narrowing suppresses sidewall
erosion
incisional widening enhances sidewall
erosion
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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CAN WE DESCRIBE THE MORPHODYNAMICS OF RAPID EROSIONAL NARROWING, FOLLOWED BY SLOW EROSIONAL WIDENING?
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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The earthflow is caused by the dumping of large amounts of waste rock from the Porgera Gold Mine, Papua New Guinea.
PART OF THE ANSWER COMES FROM ANOTHER SEEMINGLY UNRELATED SOURCE: AN EARTHFLOW IN PAPUA NEW GUINEA
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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THE EARTHFLOW CONSTRICTS THE KAIYA RIVER AGAINST A VALLEY WALL
Kaiya River
earthflow
The Kaiya River must somehow “eat” all the sediment delivered to it by the earthflow.
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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THE DELTA OF THE UPSTREAM KAIYA RIVER IS DAMMED BY THE EARTHFLOW
earthflow
The delta captures all of the load from upstream, so downstream the Kaiya River eats only earthflow sediment
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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THE EARTHFLOW ELONGATES ALONG THE KAIYA RIVER, SO MAXIMIZING “DIGESTION” OF ITS SEDIMENT
A downstream constriction (temporarily?) limits the propagation of the earthflow.
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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THE VIEW FROM THE AIR
Kaiya River
The earthflow encroaches on the river, reducing width, increasing bed shear stress and increasing the ability of the river to eat sediment!
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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THE BASIS FOR THE SEDIMENT DIGESTER MODEL(Parker, 2004)
• The earthflow narrows the channel, so increasing the sidewall shear stress and the ability of the river flow to erode away the delivered material.• The earthflow elongates parallel to the channel until it is of sufficient length to be “digested” completely by the river.
This is a case of depositional narrowing!!!
River
Earthflow Sediment taken sideways into stream
Upstream dam created by earthflow
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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GEOMETRY
H = flow depthn = transverse coordinatenb = Bb = position of bank toeBw = width of wetted banknw = Bb + Bw = position of top
of wetted bankSs = slope of sidewall (const.)b = elevation of bed = volume sediment input per unit streamwise width from earthflow
• The river flow is into the page.• The channel cross-section is assumed to be trapezoidal.• H/Bb << 1.• Streamwise shear stress on the bed region = bsb = constant in n• Streamwise shear stress on the submerged bank region = bss = bsb = constant
in n, < 1.• The flow is approximated using the normal flow assumption.
sw SBH
Ss
inerodible valley wall
b
b+H
Hn
nb
Bb Bw
river
earthflownw
neq̂
neq̂
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
RIVERS AND TURBIDITY CURRENTS© Gary Parker November, 2004
EXNER EQUATION OF SEDIMENT BALANCE ON THE BED REGION
Local form of Exner:
where qbs and qbn are the streamwise and transverse volume bedload transport rates per unit width.
Integrate on bed region with qbs = qbss, qbn = 0;
n
q
s
q
t)1( bnbs
p
bbb n
0
bnn
0
bsn
0p dnn
qdn
s
qdn
t)1(
Ss
inerodible valley wall
b
b+H
Hn
nb
Bb Bw
river
earthflownw
neq̂
bnbnbnsb
bnsbsbbp qq̂,
B
q̂
s
q
t)1(
/t(sediment in bed region)
differential steamwise transport
transverse input from wetted bank region
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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EXNER EQUATION OF SEDIMENT BALANCE ON WETTED BANK REGION
Integrate local form of Exner on wetted bank region with region with:qbs = qbss for nb < n < nb + Bw
qbn = - at n = nt where q denotes the volume rate of supply of sedimentper unit length from the earthflow
Geometric relation:
Result:
w
n
w
b
w
b
n
n
bnn
n
bsn
np dnn
qdn
s
qdn
t)1(
bebnsb
bssbsss
bs
bwp q̂q̂
s
BqHq
sS
1
t
BS
tB)1(
t
BS
tt)Bn(S b
sb
bsb
Ss
inerodible valley wall
b
b+H
Hn
nb
Bb Bw
river
earthflownw
neq̂
neq̂
/t(sediment in wetted bank region)
differential steamwise transport
transverse output to bed region
transverse input from earthflow
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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EQUATION FOR EVOLUTION OF BOTTOM WIDTH
Eliminate b/t between
Note that there are two evolution equations for two quantities, channel bottom elevation b and channel bottom width Bb. To close the relations we need to have forms for qbsb, qbss and . The parameter is specified by the motionof the earthflow.
bnsq̂
b
bnsbsbbp B
q̂
s
q
t)1(
and
to obtain
bewbw
bwbns
b
w
bss
ws
bssbss
ws
bsbbsp q̂
B
1
BB
BBq̂
s
B
B
q
s
H
BS
q
s
q
BS
H
s
q
t
BS)1(
bebnsb
bssbsss
bs
bwp q̂q̂
s
BqHq
sS
1
t
BS
tB)1(
neq̂
Ss
inerodible valley wall
b
b+H
Hn
nb
Bb Bw
river
earthflownw
neq̂
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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FLOW HYDRAULICS
Flow momentum balance: where S = streamwise slope and Bw = H/Ss,
Flow mass balance
Manning-Strickler resistance relation
bsbb
bs
2ss
bbb B
H
S2
1BgHSB
B
H
S
S1S1B
bsbw B
H
S2
11UHBQ
Dnk,k
HC,UC ks
6/1
sr
2/1f
2fb
Here ks = roughness height, D = grain size, nk = o(1) constant. Reduce under the condition H/Bs << 1 to get:
10/3
2b
2r
2w
3/1s
SgB
QkH
Ss
inerodible valley wall
b
b+H
Hn
nb
Bb Bw
river
earthflownw
neq̂
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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BEDLOAD TRANSPORT CLOSURE RELATIONSShields number on bed region:
where R = (s/ - 1) 1.65. Shields number on bank region:
Streamwise volume bedload transport rate per unit width on bed and bank regions is qbsb and qbss, respectively: where s = 11.2 and c* denotes a critical Shields stress,
10/7
10/3
2b
2r
2w
3/1sbb
bb SgB
Qk
D
1
RgD
R
10/7
10/3
2b
2r
2w
3/1s
bbbs
bs SgB
Qk
DRgD
R
5.4
bb
c5.1
bbsbss
5.4
bb
c5.1
bbsbsb 1DRgDq,1DRgDq
(Parker, 1979 fit to relation of Einstein, 1950). Transverse volume bedload transport rate per unit width on the sidewall region is qbns, where n is an order-one constant and from Parker and Andrews (1986),
sbb
cn
5.4
bb
c5.1
bbssbb
cnbssBbnbns S1DRgDSqqq̂
b
Ss
inerodible valley wall
b
b+H
Hn
nb
Bb Bw
river
earthflownw
neq̂
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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SUMMARY OF THE SEDIMENT DIGESTER
10/7
10/3
2b
2r
2w
3/1s
bb SgB
Qk
D
1
R bbbs
5.4
bb
c5.1
bbsbss
5.4
bb
c5.1
bbsbsb
1DRgDq
1DRgDq
sbb
cn
5.4
bb
c5.1
bbsbns S1DRgDq̂
b
bnsbsbbp B
q̂
s
q
t)1(
10/3
2b
2r
2w
3/1s
SgB
QkH
Equation for evolution of bed elevation
Equation for evolution of bottom width
bewbw
bwbns
b
w
bss
ws
bssbss
ws
bsbbsp q̂
B
1
BB
BBq̂
s
B
B
q
s
H
BS
q
s
q
BS
H
s
q
t
BS)1(
Hydraulic relations
Sediment transport relations As the channel narrows the Shields number increases
Higher local streamwise and transverse sediment transport rates counteract channel narrowing
A higher Shields number gives higher local streamwise and transverse sediment transport rates.
The earthflow encroaches on the channel
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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EQUILIBRIUM CHANNEL
Equilibrium channels that transport bedload without eroding their banks can be created in the laboratory (Parker, 1979). The image below shows such a channel (after the water has been turned off). The image is from experiments conducted by J. Pitlick and J. Marr at St. Anthony Falls Laboratoty, University of Minnesota.
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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EQUILIBRIUM CHANNEL SOLUTION
As long as < 1, the formulation allows for an equilibrium channel without widening or narrowing as a special case (without input from an earthflow).
cbbbsbb
c Choose bed shear stress so that bank shear stress = critical value
01DRgDq5.4
bb
c5.1
bbsbss
Streamwise sediment transport on wetted bank
region = 0
0S1DRgDq̂ sbb
cn
5.4
bb
c5.1
bbsbns
Transverse sediment transport on
wetted bank region = 0
b5.4
5.1
csb B1DRgDQ
Total bedload transport rate
10/7
10/3
2b
2r
2w
3/1sbsbc
bb SgB
Qk
D
1
RgD
R
10/3
2b
2r
2w
3/1s
SgB
QkH
Three equations; if any two of Qw, S, H, Qb and Bb are specified, the other three can be computed!!
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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ADAPTATION OF THE SEDIMENT DIGESTER FOR EROSIONAL NARROWING
• As the channel incises, it leaves exposed sidewalls below a top surface t.• Sidewall sediment is eroded freely into the channel, without the
external forcing of the sediment digester.• Bb now denotes channel bottom half-width• Bs denotes the sidewall width of one side from channel bottom to top
surface.• The channel is assumed to be symmetric, as illustrated below.
nt
Bb t
b
Ss
Hn
nb
Bs
river
ss
bt SB
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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INTEGRAL SEDIMENT BALANCE FOR THE BED AND SIDEWALL REGIONS
On the bed region, integrate Exner from n = 0 to n = nb = Bb to get
On the sidewall region, integrate Exner from n = nb to n = nt under the conditions that streamwise sediment transport vanishes over any region not covered with water, and transverse sediment transport vanishes at n = nt
nt
Bb t
b
Ss
Hn
nb
Bs
river
ss
bt SB
b
bnsbsbbp B
q̂
s
q
t)1(
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
RIVERS AND TURBIDITY CURRENTS© Gary Parker November, 2004
INTEGRATION FOR SIDEWALL REGION
Upon integration it is found that
or reducing with sediment balance for the bed region,
nt
Bb t
b
Ss
Hn
nb
Bs
river
ss
bt SB
bnsb
bssbsss
bs
bsp q̂
s
BqHq
sS
1
t
BS
tB)1(
bs
bsbns
b
s
bss
ss
bssbss
ss
bsbbsp BB
BBq̂
s
B
B
q
s
H
BS
q
s
q
BS
H
s
q
t
BS)1(
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
RIVERS AND TURBIDITY CURRENTS© Gary Parker November, 2004
INTEGRAL SEDIMENT BALANCE: SIDEWALL REGION
For the minute neglect the indicated terms:
The equation can then be rewritten in the form:
As the channel degrades i.e. b/t < 0, sidewall material is delivered to the channel.
Erosional narrowing, i.e. Bb/t < 0 suppresses the delivery of sidewallmaterial to the channel.
bnsb
bssbsss
bs
bsp q̂
s
BqHq
sS
1
t
BS
tB)1(
t
BS
tB)1(q̂ b
sb
spbns
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
RIVERS AND TURBIDITY CURRENTS© Gary Parker November, 2004
INTEGRAL SEDIMENT BALANCE: SIDEWALL REGION contd.
rapid incision with
narrowing
Ss
trajectories of left and right bottom
bank position top of deposit
slow incision with
widening
incisional narrowing suppresses sidewall
erosion
incisional widening enhances sidewall
erosion
t
BS
tB)1(q̂ b
sb
spbns
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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INTERPRETATION OF TERMS IN RELATION FOR EVOLUTION OF HALF-WIDTH
bs
bsbns
b
s
bss
ss
bssbss
ss
bsbbsp BB
BBq̂
s
B
B
q
s
H
BS
q
s
q
BS
H
s
q
t
BS)1(
This term always causes widening whenever it is
nonzero.
Auxiliary streamwise termsThis term causes narrowing whenever sediment transport is increasing in the streamwise direction.
But this is exactly what we expect immediately upstream of a dam just after removal: downward concave long profile!
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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REDUCTION FOR CRITICAL CONDITION FOR INCEPTION OF EROSIONAL NARROWING
bs
bsbns
b
b
bsbB
bsbS
bsp BB
BBq̂
s
B
B
qN
s
S
S
qN
t
BS)1(
Narrows if slope increases downstream
WidensEither way
Where NS and NB are order-one parameters,
At point of width minimum Bb/s = 0
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
RIVERS AND TURBIDITY CURRENTS© Gary Parker November, 2004
REDUCTION FOR CRITICAL CONDITION FOR INCEPTION OF EROSIONAL NARROWING contd.
bs
bsbns
b
b
bsbB
bsbS
bsp BB
BBq̂
s
B
B
qN
s
S
S
qN
t
BS)1(
Where Ns and Nb are order-one parameters,
After some reduction,
where M is another order-one parameter.
That is, erosional narrowing can be expected if the long profile of the river is sufficiently downward concave, precisely the condition to be expected immediately after dam removal!
sbb
c
s
sbb SB
BBM
s
S
S
B
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
RIVERS AND TURBIDITY CURRENTS© Gary Parker November, 2004
NUMERICAL MODELING OF THE MORPHODYNAMICS OF EROSIONAL NARROWING AND WIDENING
Wong et al. (2004) used the formulation given in this chapter to numerically model one of the experiments of Cantelli et al. (2004). The code will eventually be made available in this e-book. Meanwhile, some numerical results are given in the next two slides. The reasonable agreement was obtained with a minimum of parameter fitting.
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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0.27
0.29
0.31
0.33
0.35
0.37
0.39
0.41
2.20 3.20 4.20 5.20 6.20 7.20 8.20
Distance in the downstream direction (m)
Wat
er s
urf
ace
elev
atio
n (
m)
initial profilecalc
meas
COMPARISON OF NUMERICAL MODEL WITH EXP. 5 OF CANTELLI et al. (2004): EVOLUTION OF LONG PROFILE
Calculated and measured long profile 1200 seconds after commencement of experiment.
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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0.15
0.17
0.19
0.21
0.23
0.25
0.27
0.29
0 200 400 600 800 1000 1200
Time (seconds)
Ch
ann
el w
idth
at
wat
er s
urf
ace
elev
atio
n (
m)
calc
meas
COMPARISON OF NUMERICAL MODEL WITH EXP. 5 OF CANTELLI et al. (2004): EVOLUTION OF CHANNEL WIDTH
Calculated and measured water surface width 0.9 m upstream of original position of dam.
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1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
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REFERENCES FOR CHAPTER 31Cantelli, C. Paola and G. Parker, 2004, Experiments on upstream-migrating erosional narrowing
and widening of an incisional channel caused by dam removal, Water Resources Research, 40(3), doi:10.1029/2003WR002940.
Cui, ,Y., Parker, G., Braudrick, C., Dietrich, W. E. and Cluer, B., in press-a, Dam Removal Express Assessment Models (DREAM). Part 1: Model development and validation, Journal of Hydraulic Research, preprint downloadable at: http://cee.uiuc.edu/people/parkerg/preprints.htm .
Cui, Y., Braudrick, C., Dietrich, W.E., Cluer, B., and Parker, G, in press-b, Dam Removal Express Assessment Models (DREAM). Part 2: Sample runs/sensitivity tests, Journal of Hydraulic Research, preprint downloadable at: http://cee.uiuc.edu/people/parkerg/preprints.htm .
Einstein, H. A., 1950, The Bed-load Function for Sediment Transportation in Open Channel Flows, Technical Bulletin 1026, U.S. Dept. of the Army, Soil Conservation Service.
Parker, G., 1979, Hydraulic geometry of active gravel rivers, Journal of Hydraulic Engineering, 105(9), 1185‑1201.Parker, G., 2004, The sediment digester, Internal Memorandum 117, St. Anthony Falls
Laboratory, University of Minnesota, 17 p, downloadable at: http://cee.uiuc.edu/people/parkerg/reports.htm .
Wong, M., Cantelli, A., Paola, C. and Parker, G., 2004, Erosional narrowing after dam removal: theory and numerical model, Proceedings, ASCE World Water and Environmental Resources 2004 Congress, Salt Lake City, June 27-July 1, 10 p., reprint available at: http://cee.uiuc.edu/people/parkerg/conference_reprints.htm .
1D SEDIMENT TRANSPORT MORPHODYNAMICSwith applications to
RIVERS AND TURBIDITY CURRENTS