braided meandering
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The Threshold Between Braided and Meandering Rivers
John Pitlick and Erich MuellerUniversity of Colorado
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(Schumm, 1985)
Channel Patterns
Sunlight Cr., WY
Colorado River, RMNP
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Leopold and Wolman, 1957
Original idea
Distinction based on slope:
For the same discharge, braided
rivers tend to have higher slopes
than meandering rivers
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Lewin and Brewer, 2001
Median Grain size (mm)
U n i t S t r e a m P o w e r ( W / m 2 )
More recent work
ω = ρ g Q S W
Distinction based on unit streampower:
no difference between braided and
meandering channels
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Rubey, 1952
Recall the basic premise:
Given
•
Discharge, Q
•
Sediment load, Qs
• Grain size, D
Find
• Width, B
• Depth, H
• Velocity, U
•
Slope, S
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Given
•
Channel-forming discharge, Q
•
Sediment load, Qs
• Grain size, D
Find
• Width, B
• Depth, H
• Velocity, U
•
Slope, S
Sediment loads are not measuredin many places
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Given
•
Channel-forming discharge, Q
•
Slope, S
• Grain size, D
Find
• Width, B
• Depth, H
• Velocity, U
•
Sediment load, Qs
•
Assume slope is +/- constantover short time scales
• Calculate Qs
Alternative formulation
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To calculate sediment loads we need to know:
1. Width, W
2. Grain size, D
3. Shields stress, *
τ *=
τ o
ρ s − ρ ( )g D
= HS
(s − 1) D
τ c
*= threshold for bed load transport
Are there sign. differences in W, D and t* of braided and meandering rivers?
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Width: Braided rivers are much, much wider than single thread rivers
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width vs. discharge
Ashmore and Sauks, 2006
if width ~ Q1.0
unit discharge (UH) and Shields stress, , would be ~constant
Sunwapta River
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Width adjustment experiments
St. Anthony Falls Lab, U. MN
(with J. Pizzuto and J. Marr)
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Shields stress approaches a constant value at bankfull Q
0.05
0.06
0.07
0.08
1.1
1.2
1.3
1.4
1.5
1.6
1.7
0 60 120 180 240 300 360 420 480 540
S
e
d
N
m
b
T
a
p
S
a
Time min)
Y = 0.086*X-0.066
Very useful result!
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Use that result to predict channel geometry sediment loads
1. Channel-forming Shields stress:
H = τ b* (ρ s ρ −1) D50
S =
(0.048) (1.65) D50
S
U = u* 1
κ ln
11 H
3 D50
⎛
⎝ ⎜
⎞
⎠ ⎟
B = Q 2 HU
2. Mean velocity:
3. Continuity:
where Q2 is the 2-year flood
y = 0.40x0.72
1E-01
1E+00
1E+01
1E+02
1E+03
1E+04
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05
Drainage Area (km2)
2 - y e a r
F l o o d ( m 3 / s )
Colorado
Power (Colorado)
h
W
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0.00
0.05
0.10
0.15
0.20
0.0001 0.001 0.01 0.1
θ
B a n k f u l l
Reach Average Slope
Bankfull :
Based on measurements at > 200 sites in N. America and Britain
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Mt St Helens
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May 18, 1980 eruption • North half of mtn. collapsed largest historic landslide in the world
• Debris avalanche covered an area of ~60 km2
• Buried the NF Toutle River under > 100 m of
sediment
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Toutle River continues to erode
through the debris avalanche…
carries the highest sediment loads of
any river in the US
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Field studies, 2006 & 2007
Measure
• width & depth of active channel
•
average gradient• grain size of the bed material
97.5
98.0
98.5
99.0
99.5
100.0
100.5
0.0 5.0 10.0 15.0 20.0 25.0 30.0
Distance (m)
E l e v
a t i o n ( m )
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NF 125
Field studies, 2007
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Channel-forming flow?
1
10
100
1000
1 10 100 1000 10000
2 - Y e a r F l o o d ( m 3 / s )
Drainage Area (km2)
Q2 = 0.97*A
0.88
SW Washington
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Strategy (recap)
1. Channel-forming Shields stress:
H = τ b* (ρ s ρ −1) D50
S =
(0.048) (1.65) D50
S
U = u* 1κ ln 11 H
3 D50
⎛ ⎝ ⎜
⎞ ⎠ ⎟
B = Q 2 HU
2. Mean velocity:
3. Channel width:
where Q2 is the 2-year flood
h
W
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Finally… estimate bed load
1. Calc. transport rates, q s , for 15 increments of discharge:
2. Weight transport rates byfrequency of discharge, sum
to get annual load:
Segura and Pitlick, 2010, WRR
Qs= Qsii=1
15
∑ f (Qi)
Parker (1979)
qs = k 1−τ c*
τ *
⎛
⎝ ⎜⎜
⎞
⎠ ⎟ ⎟
4.5
= k 1− 1φ ⎛
⎝ ⎜⎜
⎞
⎠ ⎟ ⎟
4.5
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10-2
10-1
100
0 20 40 60 80 100 120
Mount St Helens, WA
B a n k f u l l B e
d L o a d
D i s c h a r g e ( m 3 / s )
Bankfull Discharge (m3 /s)
Qs =3.2e-3*Q1.00
R2 = 0.99
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Sunlight Creek, WY
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EF Big Lost R., ID
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10-4
10-3
10-2
10-1
0 5 10 15 20 25
Big Lost River, ID
B a n k f u l l B e
d L o a d
D i s c h a r g e ( m 3
/ s )
Bankfull Discharge (m3 /s)
Qs =2.6e-4*Q1.20
R2 = 0.91
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Wheres the threshold?
Big Lost River, WY Toutle River, WA
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10-4
10-3
10-2
10-1
100
0 20 40 60 80 100 120
Toutle: Qs = 0.0030Q^1.0
Big Lost: Qs = 0.00026Q^1.2
B a n k f u l l B e d L o a d
D i s c h a r g e ( m
3 / s )
Bankfull Discharge (m3 /s)
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Well-sorted surface layer Poorly sorted surface layer
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Conclusions
1. Effects of sedment supply on channel planform
seem obvious, but we have yet to quantify these effects
2. Average stresses in braided rivers are not any higher
than in single-thread rivers, but…
3. Threshold shear stresses may be lower, hence transportintensities are much higher
4. Linkages between stress and width should be a focus
of future research on braided/meandering transition
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Conditions leading to braiding are partly a function
of the hydrology
Discharges that exceed the threshold for
transport (H = 0.3 m) are quite common
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Grain size:Sunlight Creek, WY
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Shields stress:
0
5
10
15
20
0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40
r
e
q
u
e
n
Ratio of Bankfull to Refernce
Mueller et al. 2005
Single-thread channels
0
2
4
6
8
10
0.00 0.02 0.04 0.06 0.08 0.10 0.12
F r e q u e n c y
ref
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Shields stress:
0
5
10
15
20
0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40
r
e
q
u
e
n
Ratio of Bankfull to Refernce
Mueller et al. 2005
0
2
4
6
8
10
0.00 0.02 0.04 0.06 0.08 0.10 0.12
F r e q u e n c y
ref
LY
FSWR
Braided channels
SW
SU?
TL
SL
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