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