Mountain Rivers Hydraul Geom.ppt

National Center for Earth-surface Dynamics
Short Course
Morphology,Morphodynamicsand Ecologyof MountainRivers
December 11-12,2005
1
HYDRAULIC GEOMETRY OF MOUNTAIN RIVERS
Gary Parker, University of Illinois
Alluvial rivers construct their own channels and floodplains. Channels and
floodplains co-evolve over time.
Elbow River, Alberta, Canada Browns Gulch, Montana, USA

Short Course
December 11-12,2005
2
Q
Qbf

Let  denote river stage (water surface elevation) [L] and Q
denote volume water discharge [L3/T]. In the case of rivers
with floodplains,  tends to increase rapidly with increasing
Q when all the flow is confined to the channel, but much
less rapidly when the flow spills significantly onto the
floodplain. The rollover in the curve defines bankfull
discharge Qbf.
(The quantities in brackets denote dimensions: here L =
length, T = time and M = mass.)
Minnesota River and
floodplain, USA, during the
record flood of 1965
THE CONCEPT OF BANKFULL DISCHARGE

Short Course
December 11-12,2005
3
PARAMETERS FOR BANKFULL GEOMETRY
This lecture characterizes bankfull geometry in terms of the following parameters:
1. Bankfull discharge Qbf in cubic meters per second [L3/T];
2. Bankfull channel width Bbf is meters [L];
3. Bankfull cross-sectionally averaged channel depth Hbf [L];
4. Down-channel slope S (meters drop per meter distance) [1].
Other parameters are defined in subsequent slides.
Relations for bankfull geometry of the following form are often posited:
3
.
0
bf
4
.
0
bf
bf
5
.
0
bf
bf
Q
~
S
Q
~
H
Q
~
B

Bbf
Hbf

Short Course
December 11-12,2005
4
BANKFULL PARAMETERS: THE RIVER AND ITS FLOODPLAIN
An alluvial river constructs
its own channel and
floodplain. channel
floodplain
At bankfull flow the river is on the verge of spilling out onto its floodplain.

Short Course
December 11-12,2005
5
GRAVEL-BED AND SAND-BED RIVERS
Rivers (or more specifically river reaches) can also be classified according to
the characteristic size of their surface bed sediment, i.e median size Ds50 or
geometric mean size Dsg. A river with a characteristic size between 0.0625 and
2 mm can be termed a sand-bed stream. Two such streams are shown below.
Fly River, Papua New Guinea.
Jamuna
(Brahmaputra)
River, Bangladesh.
Image courtesy J.
Imran.

Short Course
December 11-12,2005
6
A river with a characteristic surface size in excess of 16 mm can be termed a
gravel-bed river. Here the term “gravel” is used loosely to encompass cobble-
and boulder-bed streams as well. Three such streams are shown below.
Genessee River, New York, USA.
Raging River, Washington, USA.
Rakaia River, New Zealand

Short Course
December 11-12,2005
7
A river with a characteristic surface size
between 2 and 16 mm can be termed
transitional in terms of grain size. Such
streams are much less common than
either sand-bed or gravel-bed streams,
but can be found readily enough,
particularly in basins that produce
sediment from weathered granite. An
example is shown to the right.
Hii River, Japan.
Image courtesy H. Takebayashi

Short Course
December 11-12,2005
8
0
5
10
15
20
25
30
35
40
0
.
0
6
2
5
-
0
.
1
2
5
0
.
1
2
5
-
0
.
2
5
0
.
2
5
-
0
.
5
0
.
5
-
1
1
-
2
2
-
4
4
-
8
8
-
1
6
1
6
-
3
2
3
2
-
6
4
6
4
-
1
2
8
1
2
8
-
2
5
6
Grain size range in mm
Number
of
reaches
Alberta
Japan
Sand-bed Gravel-bed
Transitiona
l
The diagram to the left shows
the frequency of river reaches
with various characteristic
grain sizes within two sets,
one from Alberta, Canada
(Kellerhals et al., 1972) and
the other from Japan
(Yamamoto, 1994; Fujita et
al., 1998). Note that most
rivers can be classified as
either gravel-bed or sand-bed.

Short Course
December 11-12,2005
9
MOUNTAIN RIVERS: ALLUVIAL VERSUS BEDROCK
Mountain rivers are generally gravel-bed
rivers.
Not all mountain rivers, however, have a
definable bankfull geometry. For example,
many mountain rivers have little alluvium
and considerable amounts of exposed
bedrock, and are thus not free to construct
their own geometry. In addition, some
gravel-bed rivers have incised in recent
times, and left their floodplains abandoned
as terraces.
Here the following case is considered:
alluvial, gravel-bed mountain streams
with definable floodplains.
Wilson Creek, Kentucky, USA: a
mountain bedrock stream. Image
courtesy A. Parola

Short Course
December 11-12,2005
10
SINGLE-THREAD VERSUS MULTIPLE-THREAD (BRAIDED) MOUNTAIN
RIVERS
Raging River, Washington,
USA: a single-thread gravel-
bed river
Sunwapta River, Canada: a
multiple-thread (braided) gravel-
bed river
The case considered here is that of single-thread streams. A single-thread
stream has a single definable channel, although mid-channel bars may be
present. A multiple-thread, or braided stream has several channels that
intertwine back and forth.

Short Course
December 11-12,2005
11
CHARACTERIZING BED SEDIMENT IN GRAVEL-BED STREAMS: MEDIAN
SURFACE SIZE Ds50
Gravel-bed streams usually show a surface
armor. That is, the surface layer is coarser
than the substrate below.
Bed sediment of the River Wharfe,
U.K., showing a pronounced surface
armor. Photo courtesy D. Powell.
Armored surface
substrate

Short Course
December 11-12,2005
12
CHARACTERIZING DOWN-CHANNEL SLOPE S
Down-channel bed slope is determined from a survey of the long profile of the
channel centerline. The reach chosen to determine bed slope should be long
enough to average over any bars and bends in the channel, which are associated
with local elevation highs and lows.
A
B
bed
elevation
down-channel distance
A
B
S
plan view
long profile of centerline bed elevation

Short Course
December 11-12,2005
13
MORE PARAMETERS USED TO CHARACTERIZE BANKFULL
CHANNEL GEOMETRY OF SINGLE-THREAD GRAVEL-BED RIVERS
In order to capture as much universality as possible, it is useful to characterize the
bankfull geometry of alluvial, gravel-bed mountain streams in dimensionless form.
Thus in addition to the previously-defined parameters:
Qbf = bankfull discharge [L3/T]
Bbf = bankfull width [L]
Hbf = bankfull depth [L]
S = bed slope [1]
Ds50 = median surface grain size [L]
the following parameters are added:
 = density of water [M/L3]
s = material density of sediment [M/L3]
R = (s/ – 1) = sediment submerged specific gravity (~ 1.65 for natural sediment) [1]
g = gravitational acceleration [L/T2]
 = kinematic viscosity of water [L2/T]

Short Course
December 11-12,2005
14
DIMENSIONLESS PARAMETERS CHARACTERIZING CHANNEL
BANKFULL GEOMETRY
5
/
2
bf
5
/
1
bf
Q
g
H
H
~

5
/
2
bf
5
/
1
bf
Q
g
B
B
~

2
50
s
50
s
bf
D
gD
Q
Q̂  = dimensionless bankfull discharge
= dimensionless bankfull depth
= dimensionless bankfull width
Down-channel slope S is already dimensionless.

Short Course
December 11-12,2005
15
MORE DIMENSIONLESS PARAMETERS CHARACTERIZING CHANNEL
BANKFULL GEOMETRY
bf
bf
bf
bf
bf
gH
H
B
Q

Fr
bf
bf
H
B

 50
s
50
s
50
p
D
gD
R
Re
50
s
bf
50
bf
D
R
S
H


S
gH
H
B
Q
Cz
bf
bf
bf
bf
bf 
= width-depth ratio at bankfull flow (dimensionless)
= bankfull Froude number (dimensionless)
= (estimate of) bankfull Shields number (dimensionless)
= bankfull Chezy resistance coefficient (dimensionless)
= particle Reynolds number (surrogate for grain size:
dimensionless)

Short Course
December 11-12,2005
16
INTERPRETATION OF SOME OF THE DIMENSIONLESS PARAMETERS
bf
bf
bf
bf
bf
bf
bf
gH
U
gH
H
B
Q


Fr

 50
s
50
s
50
p
D
gD
R
Re
50
s
bf
50
bf
D
R
S
H


S
gH
U
S
gH
H
B
Q
Cz
bf
bf
bf
bf
bf
bf
bf 

Bankfull flow velocity Ubf = Qbf/(HbfBbf)
Bankfull Froude number characterizes a ratio of
momentum force to gravity force. When Froude
number Fr < 1 the flow is subcritical, or tranquil:
when Fr > 1 the flow is supercritical, or swift. Here
where U and H are cross-sectionally-
averaged flow velocity and depth, respectively.
The relation can be rewritten as
so that a high value of Czbf implies a low
bed resistance.
For the case of steady, uniform (normal) flow, the bed shear stress b is
given as b = gHS where H = depth. A dimensionless measure of the
ability of the flow to mobilize sediment is the Shields number, * =
b/(RgD). Here denotes an estimate of value of * for bankfull
flow based on a surface median size for D.
Since in most cases g = 9.81 m/s2, R  1.65 and   1x10-6 m2/s,
Rep50 is a surrogate for median surface grain size ~ Ds50
3/2.
S
gH
Cz
U bf
bf
bf 

 50
bf
gH
U/

Fr

Short Course
December 11-12,2005
17
SINGLE-THREAD MOUNTAIN GRAVEL-BED RIVERS HAVE CONSISTENT
BANKFULL GEOMETRIES
This is illustrated here using data from four sources:
• 16 streams flowing from the Rocky Mountains in Alberta, Canada
(Kellerhals et al., 1972);
• 23 mountain streams in Idaho (Parker et al., 2003);
• 23 upland streams in Britain (mostly Wales) (Charlton et al. 1978);
• 10 reaches along the upper Colorado River, Colorado (Pitlick and Cress, 2002)
(Each reach represents an average of several subreaches.)
The original data for Qbf, Bbf, Hbf, S and Ds50 for each reach can be found in
Excel file, ToolboxGravelBankfullData.xls.

Short Course
December 11-12,2005
18
RANGE OF PARAMETERS
Among all four sets of data, the range of parameters is as given below:
Bankfull discharge Qbf (in meters3/sec) 2.7 ~ 5440
Bankfull width Bbf (in meters) 5.24 ~ 280
Bankfull depth Hbf (in meters) 0.25 ~ 6.95
Channel slope S 0.00034 ~ 0.031
Surface median size Ds50 (in mm) 27 ~ 167
These ranges approximate the range of applicability of the relations in this
presentation.

Short Course
December 11-12,2005
19
WHAT THE DATA SAY
The four data sets tell a consistent story of bankfull channel characteristics.
0.0001
0.001
0.01
0.1
1
10
100
1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07
Qhat
Btilde,
Htilde,
S
Britain width
Alberta width
Idaho width
Colorado width
Britain depth
Alberta depth
Idaho depth
Colorado depth
Britain slope
Alberta slope
Idaho slope
Colorado slope
H
~
B
~
S
S
,
H
~
,
B
~
Q̂
Dimensionless width
Dimensionless depth
Down-channel bed slope

Short Course
December 11-12,2005
20
y = 0.3785x4E-05
y = 4.6977x0.0661
y = 0.1003x-0.3438
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Qdim
Bdimtilde,
Hdimtilde,
S
Bdimtilde
Hdimtilde
S
Power (Hdimtilde)
Power (Bdimtilde)
Power (S)
3438
.
0
0661
.
0
00004
.
0
Q̂
1003
.
0
S
,
Q̂
698
.
4
B
~
,
Q̂
3785
.
0
H
~ 



To a high degree of approximation, 3785
.
0
H
~
H
~
c 

REGRESSION RELATIONS FOR BANKFULL CHANNEL CHARACTERISTICS
S
,
H
~
,
B
~
Q̂
S
B
~
H
~

Short Course
December 11-12,2005
21
y = 0.3785x4E-05
y = 4.6977x0.0661
y = 0.1003x-0.3438
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Qdim
Bdimtilde,
Hdimtilde,
S
Bdimtilde
Hdimtilde
S
Power (Hdimtilde)
Power (Bdimtilde)
Power (S)
WHY DOES THE RELATION FOR SLOPE SHOW THE MOST SCATTER?
S
,
H
~
,
B
~
Q̂
B
~
H
~
S

Short Course
December 11-12,2005
22
• Rivers can readjust their bankfull depths and widths
over short geomorphic time, e.g. hundreds to thousands
of years.
• Readjusting river valley slope Sv involves moving
large amounts of sediment over long reaches, and
typically requires long geomorphic time (tens of
thousands of years or more).
• As a result, valley slope Sv can often be considered to
be an imposed parameter that the river is not free to
adjust in short geomorphic time.
• The relation between down-channel slope S and
valley slope Sv is S =  Sv, where  denotes channel
sinuosity. Varying the channel sinuosity allows for some
variation in channel slope S at the same valley slope Sv.
WHY DOES THE RELATION FOR SLOPE SHOW THE MOST SCATTER?
A
B
Channel
Valley walls

Short Course
December 11-12,2005
23
THE THREE RELATIONS FOR BANKFULL GEOMETRY OF MOUNTAIN
STREAMS
3438
.
0
2
50
s
50
s
bf
0661
.
0
2
50
s
50
s
bf
5
/
1
5
/
2
bf
bf
5
/
1
5
/
2
bf
bf
D
gD
Q
1003
.
0
S
D
gD
Q
g
Q
698
.
4
B
g
Q
3785
.
0
H





















Short Course
December 11-12,2005
24
BANKFULL FROUDE NUMBER VERSUS BED SLOPE
All but one of the streams are in the Froude-subcritical range (Fr < 1) at bankfull flow.
This does not mean that supercritical flow is dynamically impossible in alluvial
mountain streams. Rather, the sediment transport capacity is typically so high that
alluvium cannot usually be supplied at a fast enough rate. Some braided streams in
glacial outwash have enough sediment supply to maintain supercritical flow.
Bankfull Froude Number versus Down-channel Bed Slope
0.1
1
10
0.0001 0.001 0.01 0.1
S
Fr
bf
Alta
Brit
Ida
Colo
Regression of all four data sets:
205
.
0
bf S
53
.
1
Fr 

Short Course
December 11-12,2005
25
DIMENSIONLESS CHEZY FRICTION COEFFICIENT VERSUS SLOPE
The bankfull Chezy resistance coefficient declines with slope, but is typically in
the range 5 ~ 15. Bankfull flow velocity Ubf can be estimated from measured
values of Hbf, S and the diagram below in accordance with the equation
S
gH
Cz
U bf
bf
bf 
Bankfull Chezy Number versus Down-channel Bed Slope
1
10
100
0.0001 0.001 0.01 0.1
S
Cz
bf
Alta
Brit
Ida
Colo
295
.
0
bf S
53
.
1
Cz 


Short Course
December 11-12,2005
26
DIMENSIONLESS CHEZY FRICTION COEFFICIENT VERSUS H/Ds50
Note that Czbf increases weakly with increasing Hbf/Ds50. A Manning-Strickler
resistance relation implies that Czbf ~ (Hbf/Ds50)1/6, in which case
2
/
1
3
/
2
bf
6
/
1
50
s
bf S
H
)
D
(
g
~
U
Bankfull Chezy Number versus Hbf/Ds50
1
10
100
1 10 100
Hbf/Ds50
Cz
bf
Alta
Brit
Ida
Colo
2
/
1
710
.
0
bf
210
.
0
50
s
bf
210
.
0
50
s
bf
bf
S
H
)
D
(
g
39
.
4
U
D
H
39
.
4
Cz











Short Course
December 11-12,2005
27
Bankfull Shields Number versus Dimensionless Discharge
0.001
0.01
0.1
1
1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07
Qhat

bf
*
Alta
Brit
Ida
Colo
BANKFULL SHIELDS NUMBER VERSUS DIMENSIONLESS DISCHARGE
Gravel-bed streams maintain a bankfull Shields stress that varies little with
dimensionless discharge, and averages to 0.049.
Q̂

Short Course
December 11-12,2005
28
WIDTH-DEPTH RATIO AT BANKFULL FLOW VERSUS DIMENSIONLESS
DISCHARGE
Single-thread mountain gravel-bed streams maintain width-depth ratios that are
typically in the range 10 ~ 60. Note that on the average the Alberta streams are
the widest, and the British streams the narrowest. This is thought to reflect a
more arid versus a more humid environment.
Bankfull Width-Depth Ratio versus Down-channel Bed Slope
1
10
100
0.0001 0.001 0.01 0.1
S
B
bf
/H
bf
Alta
Brit
Ida
Colo

Short Course
December 11-12,2005
29
SHIELDS REGIME DIAGRAM
Mountain gravel-bed streams at bankfull flow are seen to be not far above the
threshold for motion of the surface size Ds50, and well below the threshold for
suspension of the same size.
Shields Diagram with Threshold for Motion, Threshold for Significant
Suspension and Bankfull Shields Number for Gravel-bed Streams
0.001
0.01
0.1
1
10
1 10 100 1000 10000 100000 1000000
Rep

*
suspension
motion
Alta
Brit
Ida
Colo
threshold of motion
(modified Shields curve)
threshold for significant
suspension
50
s
RD
HS


]
10
06
.
0
22
.
0
[
5
.
0
)
7
.
7
(
6
.
0
p
c
6
.
0
p








Re
Re

Short Course
December 11-12,2005
30
REFERENCES
Charlton, F. G., Brown, P. M. and Benson, R. W. , 1978, The hydraulic geometry of some gravel
rivers in Britain, Report INT 180, Hydraulics Research Station, Wallingford, England, 48 p.
Fujita, K., K. Yamamoto and Y. Akabori, 1998, Evolution mechanisms of the longitudinal bed
profiles of major alluvial rivers in Japan and their implications for profile change prediction,
Transactions, Japan Society of Civil Engineering, 600(II-44): 37–50 (in Japanese).
Kellerhals, R., Neill, C. R. and Bray, D. I., 1972, Hydraulic and geomorphic characteristics of
rivers in Alberta, River Engineering and Surface Hydrology Report, Research Council of
Alberta, Canada, No. 72-1.
Parker, G., Toro-Escobar, C. M., Ramey, M. and Beck, S., 2003, Effect Of Floodwater Extraction
On Mountain Stream Morphology, J. Hydraul. Engrg., 129(11), 885-895.
Pitlick, J. and R. Cress 2002 Downstream changes in the channel of a large gravel bed
river. Water Resources Research 38(10), 1216, doi:10.1029/2001WR000898, 2002.
Yamamoto, K., 1994, The Study of Alluvial Rivers, Sankaidou (in Japanese).
For more information see Gary Parker’s e-book:
1D Morphodynamics of Rivers and Turbidity Currents
http://cee.uiuc.edu/people/parkerg/morphodynamics_e-book.htm

Mountain Rivers Hydraul Geom.ppt

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