the threshold between braided and meandering … · the threshold between braided and meandering...
TRANSCRIPT
The Threshold Between Braided and Meandering Rivers
John Pitlick and Erich Mueller University of Colorado
(Schumm, 1985)
Channel Patterns
Sunlight Cr., WY
Colorado River, RMNP
Leopold and Wolman, 1957
Original idea
Distinction based on slope:
For the same discharge, braided rivers tend to have higher slopes than meandering rivers
Lewin and Brewer, 2001
Median Grain size (mm)
Uni
t Str
eam
Pow
er (W
/m2 )
More recent work
ω = ρ g Q SW
Distinction based on unit stream power:
no difference between braided and meandering channels
Rubey, 1952
Recall the basic premise:
Given
• Discharge, Q
• Sediment load, Qs
• Grain size, D
Find
• Width, B
• Depth, H
• Velocity, U
• Slope, S
Given
• Channel-forming discharge, Q
• Sediment load, Qs
• Grain size, D
Find
• Width, B
• Depth, H
• Velocity, U
• Slope, S
Sediment loads are not measured in many places
Given
• Channel-forming discharge, Q
• Slope, S
• Grain size, D
Find
• Width, B
• Depth, H
• Velocity, U
• Sediment load, Qs
• Assume slope is +/- constant over short time scales
• Calculate Qs
Alternative formulation
To calculate sediment loads we need to know:
1. Width, W
2. Grain size, D
3. Shields stress, *
τ * = τ o
ρs − ρ( )gD = HS
(s − 1)D
τc* = threshold for bed load transport
Are there sign. differences in W, D and t* of braided and meandering rivers?
Width: Braided rivers are much, much wider than single thread rivers
width vs. discharge
Ashmore and Sauks, 2006
if width ~ Q1.0
unit discharge (UH) and Shields stress, , would be ~constant
Sunwapta River
Width adjustment experiments
St. Anthony Falls Lab, U. MN (with J. Pizzuto and J. Marr)
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
Shie
lds
Num
ber, τ*
Tran
spor
t St
age,
φ
Time (min)
Y = 0.086*X-0.066
Very useful result!
Use that result to predict channel geometry sediment loads
1. Channel-forming Shields stress:
H = τb* (ρs ρ−1) D50
S =
(0.048) (1.65) D50S
U = u* 1κ ln 11H
3D50
⎛
⎝⎜
⎞
⎠⎟
B = Q 2HU
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-year F
loo
d (
m3
/s)
Colorado
Power (Colorado)
h
W
0.00
0.05
0.10
0.15
0.20
0.0001 0.001 0.01 0.1
θ
Ban
kfu
ll θ
Reach Average Slope
Bankfull :
Based on measurements at > 200 sites in N. America and Britain
Mt St Helens
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
Toutle River continues to erode through the debris avalanche… carries the highest sediment loads of any river in the US
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)
Ele
vati
on
(m
)
NF 125
Field studies, 2007
Channel-forming flow?
1
10
100
1000
1 10 100 1000 10000
2-Y
ear
Flo
od
(m
3 /s)
Drainage Area (km2)
Q2 = 0.97*A0.88
SW Washington
Strategy (recap)
1. Channel-forming Shields stress:
H = τb* (ρs ρ−1) D50
S =
(0.048) (1.65) D50S
U = u* 1κ ln 11H
3D50
⎛
⎝⎜
⎞
⎠⎟
B = Q 2HU
2. Mean velocity:
3. Channel width:
where Q2 is the 2-year flood
h
W
Finally… estimate bed load
1. Calc. transport rates, qs, for 15 increments of discharge:
2. Weight transport rates by frequency of discharge, sum to get annual load:
Segura and Pitlick, 2010, WRR
Qs= Qsii=1
15
∑ f (Qi)
Parker (1979)qs = k 1−τc*
τ*
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟
4.5
= k 1− 1φ
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟
4.5
10-2
10-1
100
0 20 40 60 80 100 120
Mount St Helens, WA
Ban
kfu
ll B
ed L
oad
Dis
char
ge
(m3 /s
)
Bankfull Discharge (m3/s)
Qs =3.2e-3*Q1.00
R2 = 0.99
Sunlight Creek, WY
EF Big Lost R., ID
10-4
10-3
10-2
10-1
0 5 10 15 20 25
Big Lost River, ID
Ban
kfu
ll B
ed L
oad
Dis
char
ge
(m3 /s
)
Bankfull Discharge (m3/s)
Qs =2.6e-4*Q1.20
R2 = 0.91
Where s the threshold?
Big Lost River, WY Toutle River, WA
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
Ban
kfu
ll B
ed L
oad
Dis
char
ge
(m3 /s
)
Bankfull Discharge (m3/s)
Well-sorted surface layer Poorly sorted surface layer
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 transport intensities are much higher
4. Linkages between stress and width should be a focus of future research on braided/meandering transition
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
Grain size: Sunlight Creek, WY
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
Freq
uenc
yRatio of Bankfull τ* to Refernce τ*
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
Frequency
τ* ref
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
Freq
uenc
yRatio of Bankfull τ* to Refernce τ*
Mueller et al. 2005
0
2
4
6
8
10
0.00 0.02 0.04 0.06 0.08 0.10 0.12
Frequency
τ* ref
LY
FS WR
Braided channels
SW SU
? TL
SL