SandRiverHydrGeomKarl.ppt
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Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
HYDRAULIC GEOMETRY OF LOWLAND SAND-BED RIVERS
Gary Parker, University of Illinois
Alluvial rivers construct their own channels and floodplains. Channels and
floodplains co-evolve over time.
Fly River,
Papua New Guinea
1
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
LOWLAND SAND-BED RIVERS ARE BEAUTIFUL TO LOOK AT
Beni River, Bolivia
Images courtesy R. Aalto
2
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
LOWLAND SAND-BED RIVERS ARE BEAUTIFUL TO LOOK AT
Mississippi River
and natural levees
downstream of
New Orleans, USA
Paraná River,
Argentina
3
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
LOWLAND SAND-BED RIVERS ARE BEAUTIFUL TO LOOK AT
Fly River, Papua
New Guinea
Okavango River, Botswana
Image courtesy N. Smith
4
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
THE CONCEPT OF BANKFULL DISCHARGE
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
Qbf
5
Q
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
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:
Bbf ~ Qbf0.5
Hbf ~ Qbf0.4
S ~ Qbf0.3
Bbf
Hbf
6
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
BANKFULL PARAMETERS: THE RIVER AND ITS FLOODPLAIN
floodplain
An alluvial river
constructs its own
channel and floodplain.
At bankfull flow the
river is on the verge of
spilling out onto its
floodplain.
channel
Strickland River, Papua New Guinea
Image courtesy W. Dietrich
7
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
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.
Jamuna
(Brahmaputra)
River, Bangladesh.
Image courtesy J.
Imran.
Fly River, Papua New Guinea.
8
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
GRAVEL-BED AND SAND-BED RIVERS
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 cobbleand boulder-bed streams as well. Three such streams are shown below.
Genessee River, New York, USA.
Rakaia River, New Zealand
Raging River, Washington, USA.
9
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
GRAVEL-BED AND SAND-BED RIVERS
A river with a characteristic surface size
between 2 and 16 mm (pea gravel) 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
10
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
GRAVEL-BED AND SAND-BED RIVERS
Sand-bed
Gravel-bed
Transitiona
l
40
Number of reaches
35
30
25
Alberta
Japan
20
15
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
10
5
12
8
-2
56
28
-1
4
-6
64
2
32
-3
6
16
8
-1
-8
4
-4
2
-2
1
-1
0.
5
.5
5
-0
.2
25
-0
0.
12
5
0.
0.
06
25
-0
.1
25
0
(Yamamoto, 1994; Fujita et
al., 1998). Note that most
rivers can be classified as
either gravel-bed or sand-bed.
Grain size range in mm
11
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
SAND-BED STREAMS ARE USUALLY UNARMORED OR POORLY ARMORED
View of the bed of the
unarmored sand-bed North
Loup River, Nebraska. Image
courtesy D. Mohrig
Bed sediment of the
gravel-bed River Wharfe,
U.K., showing a pronounced
surface armor. Photo 12
courtesy D. Powell.
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
CHARACTERIZING BED SEDIMENT IN SAND-BED STREAMS USING
CHARACTERISTIC SIZES D50, D90 AND GEOMETRIC STANDARD DEVIATION g
The grain size distributions to the
left are all from 177 samples from
various river reaches in Alberta,
Canada (Shaw and Kellerhals,
1982).
The samples from sand-bed
reaches typically show unimodal
size distributions, and often have
much less variation in grain size
than the samples from the gravelbed reaches. The sediment of
sand-bed streams can often be
characterized adequately in terms
of a bed median size D50, a size
D90 such that 90 percent of the
sample is finer and a geometric 13
standard deviation g.
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
CHARACTERIZING DOWN-CHANNEL BED 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.
plan view
A
B
A
bed
elevation
S
long profile of centerline bed elevation
down-channel distance
B
14
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
MORE PARAMETERS USED TO CHARACTERIZE BANKFULL
CHANNEL GEOMETRY OF SAND-BED RIVERS
In order to capture as much universality as possible, it is useful to characterize the
bankfull geometry of alluvial sand-bed 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]
D50 = median bed 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]
15
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
DIMENSIONLESS PARAMETERS CHARACTERIZING CHANNEL
BANKFULL GEOMETRY
Qbf
Q̂
2
gD50 D50
= dimensionless bankfull discharge
~ Hbf g1/ 5
H 2/5
Qbf
= dimensionless bankfull depth
~ Bbf g1/ 5
B 2/5
Qbf
= dimensionless bankfull width
Down-channel slope S is already dimensionless.
16
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
MORE DIMENSIONLESS PARAMETERS CHARACTERIZING CHANNEL
BANKFULL GEOMETRY
Frbf
Qbf
BbfHbf gHbf
bf 50
Czbf
Hbf S
RDs50
Qbf
Bbf Hbf gHbf S
Rep50
RgDs50 Ds50
Bbf
Hbf
= bankfull Froude number (dimensionless)
= (estimate of) bankfull Shields number (dimensionless)
= bankfull Chezy resistance coefficient (dimensionless)
= particle Reynolds number (surrogate for grain size:
dimensionless)
= width-depth ratio at bankfull flow (dimensionless)
17
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
INTERPRETATION OF SOME OF THE DIMENSIONLESS PARAMETERS
Bankfull flow velocity Ubf = Qbf/(HbfBbf)
Qbf
Ubf
Frbf
Bbf Hbf gHbf
gHbf
Czbf
Qbf
Ubf
Bbf Hbf gHbf S
gHbf S
Ubf Czbf gHbf S
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-sectionallyFr U/ gH
averaged flow velocity and depth, respectively.
We will find that low-slope sand-bed streams
carry tranquil flow at bankfull conditions.
The relation for Chezy resistance coefficient can be
rewritten so as to make it clear that that a high
value of Czbf implies a low bed resistance.
Specifying Czbf = r(Hbf/kc)1/6, where kc is a composite roughess height and
r is a dimensionless roughness coefficient yields the Manning-Strickler
resistance relation:
g
Ubf r
2 / 3 1/ 2
H
bf S
1/ 6
kc
18
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
INTERPRETATION OF SOME OF THE DIMENSIONLESS PARAMETERS
bf 50
Hbf S
RD50
For the case of steady, uniform (normal) flow with depth H, the
bed shear stress b is given as
b gHS
A dimensionless measure of the ability of the flow to mobilize
sediment is the Shields number,
b
HS
RgD RD
Here bf 50 denotes an estimate of value of * for bankfull flow
based on a surface median size for D. High values of bf 50
denote high mobility of the bed material at bankfull flow.
Rep50
RgD50 D50
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 ~ Ds503/2. 19
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
LOWLAND SAND-BED RIVERS HAVE CONSISTENT BANKFULL
GEOMETRIES
This is illustrated here using data from three sources:
• Set CRST: 7 streams from the compendium of Church and Rood (1983) that
Parker et al. (1998) classified as single-channel sand-bed with D50 < 0.5 mm;
• Set CRMT: 11 streams from the compendium of Church and Rood (1983) that
Parker et al. (1998) classified as multiple-channel (split-channel) sand-bed with
D50 < 0.5 mm;
• Set ST: 29 streams from the compendium of Soar and Thorne (2001) for which
D50 < 0.5 mm.
The limitation of 0.5 mm on D50 was placed because the range 0.1 mm < D50 <
0.5 mm characterizes large, low-slope sand-bed streams. The compendium
does include, however, some smaller sand-bed streams.
The original data for Qbf, Bbf, Hbf, S and Ds50 for each reach can be found in
Excel file SandBankfullData.xls.
20
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
RANGE OF PARAMETERS
Among all four sets of data, the range of parameters is as given below:
Bankfull discharge
Qbf (in meters3/sec)
13 ~ 16,950
Bankfull width
Bbf (in meters)
12 ~ 832
Bankfull depth
Hbf (in meters)
1.2 ~ 13.9
Channel slope
S
4x10-5 ~ 3x10-3
Sediment size
D50 (in mm)
0.14 ~ 0.49
These ranges approximate the range of applicability of the relations in this
presentation.
21
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
WHAT THE DATA SAY
The three data sets tell a consistent story of bankfull channel characteristics.
1.E+02
Dimensionless width
1.E+01
Width CRSC
Width CRMC
Width ST
Depth CRSC
Depth CRMC
Depth ST
Slope CRSC
Slope CRMC
Slope ST
~ ~
B, H, S
Btil, Htil, S
1.E+00
1.E-01
Dimensionless depth
1.E-02
1.E-03
1.E-04
Down-channel bed slope
1.E-05
1.E+08
1.E+09
1.E+10
1.E+11
Qhat
Q̂
1.E+12
1.E+13
22
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
REGRESSION RELATIONS FOR BANKFULL CHANNEL CHARACTERISTICS
~
H 2.52 Q̂0.063
~
, B 0.280Q̂0.153
, S 2.13 Q̂0.357
1.E+02
y = 0.2801x0.1527
1.E+01
~
B
y = 2.5225x-0.0631
Btil, Htil, S
1.E+00
~ ~
B, H, S
1.E-01
Width
Depth
Slope
Power (Width)
Power (Depth)
Power (Slope)
~
H
1.E-02
y = 2.1332x-0.3567
1.E-03
1.E-04
1.E-05
1.E+08
S
1.E+09
1.E+10
1.E+11
Qhat
Q̂
1.E+12
1.E+13
23
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
THE THREE RELATIONS FOR BANKFULL GEOMETRY OF LOWLAND SANDBED STREAMS
2/5
bf
1/ 5
Q
Hbf 2.52
g
Q
bf
gD D2
50
50
2/5
bf
1/ 5
Q
Bbf 0.280
g
0.063
Q
bf
gD D2
50
50
Q
bf
S 2.11
gD D2
50
50
~ Qbf0.337
0.153
~ Qbf0.553
0.357
~ Qbf0.357
24
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
BANKFULL SHIELDS NUMBER
The regression for bankfull Shields number is
bf 3.26 Q̂0.0198
This relation can be reasonably replaced with the approximation
based on the average value:
bf 2.18
1.E+02
1.E+01
~
B
y = 0.2801x0.1527
y = 3.2613x-0.0198
~
B , bf , S
Btil, taus, S
1.E+00
bf
Width
Slope
taustar
av taustar
Power (taustar)
Power (Width)
Power (Slope)
1.E-01
1.E-02
y = 2.1332x-0.3567
1.E-03
S
1.E-04
1.E-05
1.E+08
1.E+09
1.E+10
1.E+11
Qhat
Q̂
1.E+12
1.E+13
25
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
BANKFULL FROUDE NUMBER VERSUS BED SLOPE
All the streams are in the Froude-subcritical range (Fr < 1) at bankfull flow, and all
except two of the streams have bankfull values Frbf < 0.4. The study of low-slope
sand-bed streams is the study of Froude-subcritical flow. This means that
backwater effects cannot be neglected in low-slope sand-bed streams. Note
that the lower the slope, the more tranquil the flow.
1.0
regression: Frbf 1.62 S
0.250
Frbf
y = 1.622x0.2498
0.1
1.E-05
1.E-04
1.E-03
S
1.E-02
26
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
DIMENSIONLESS CHEZY FRICTION COEFFICIENT VERSUS SLOPE
The bankfull Chezy resistance coefficient declines with slope, but is typically in
the range 10 ~ 20, with the larger values applying to lower-slope streams.
Bankfull flow velocity Ubf can be estimated from measured values of Hbf, S and
the diagram below in accordance with the equation Ubf Czbf gH bf S
1.E+02
Czbf
regression: Czbf 1.62 S
0.250
1.E+01
y = 1.622x-0.2502
1.E+00
1.E-05
1.E-04
1.E-03
S
1.E-02
27
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
DIMENSIONLESS CHEZY FRICTION COEFFICIENT VERSUS H/D50
The data can be fitted to a relation of the form
H
Czbf 2.11 bf
D50
0.191
or thus
Ubf 2.11
g
H0.691 S1/ 2
0.191 bf
(D50 )
1.E+02
Czbf
y = 2.1145x0.191
Cz
Power (Cz)
1.E+01
1.E+00
1.E+03
1.E+04
Hbf/D50
1.E+05
28
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
DIMENSIONLESS CHEZY FRICTION COEFFICIENT VERSUS H/D50
But the relation can be almost as accurately fitted to a standard Manning-Strickler
form with r = 8.1:
1/ 6
H
Czbf 8.1 bf
kc
where
k c 750 D50
Ubf 2.69
or thus
g
Hbf2 / 3S1/ 2
1/ 6
(D50 )
1.E+02
Czbf
y = 2.1145x0.191
Cz
Manning-Strickler
Power (Cz)
1.E+01
1.E+00
1.E+03
This will lead to a very
interesting result in a
subsequent lecture!
1.E+04
Hbf/D50
1.E+05
29
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
WIDTH-DEPTH RATIO AT BANKFULL FLOW VERSUS DIMENSIONLESS
DISCHARGE
Lowland sand-bed streams maintain bankfull width-depth ratios that are typically
in the range 10 ~ 100. Larger values favor braiding.
1.0E+03
Bbf/Hbf
1.0E+02
Jamuna
(Brahmaputra)
River,
Bangladesh.
Image courtesy
J. Imran.
1.0E+01
Fly River,
Papua New
Guinea. Image
courtesy Bill
Dietrich.
1.0E+00
1.0E+08
1.0E+09
1.0E+10
1.0E+11
Qhat
Q̂
1.0E+12
1.0E+13
30
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
SHIELDS REGIME DIAGRAM
The regime diagram to
the right shows a plot of
Shields number *
versus particle Reynolds
number Rep.
1.0E+01
1.0E+00
motion threshold
sign. suspension threshold
0.062 mm
2 mm
16 mm
0.5 mm
*
Shown are lines for a)
the onset of motion of
bed material, b) the
onset of significant
suspension of bed
material, and c) lines
corresponding to 0.062
mm, 0.5 mm, 2 mm and
16 m.
onset of significant suspension
of bed sediment
1.0E-01
onset of motion of bed sediment
1.0E-02
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Rep
31
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
OUR SAND-BED STREAMS PLOT IN A RANGE WHERE SUSPENSION
OF BED MATERIAL IS SIGNIFICANT AT BANKFULL FLOW
1.0E+01
onset of significant suspension
of bed sediment
1.0E+00
*
bankfull taus
motion threshold
sign. suspension threshold
0.062 mm
2 mm
16 mm
0.5 mm
1.0E-01
onset of motion of bed sediment
1.0E-02
1.E+00
1.E+01
1.E+02
1.E+03
Rep
1.E+04
1.E+05
32
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
BUT ARE OUR SAND-BED STREAMS REALLY “LOW-SLOPE” STREAMS?
In order to examine this point we expand our data and add three new sets.
• Set ST>0.5: 25 sand-bed streams from the compendium of Soar and Thorne
(2001) that were excluded from the set ST because D50 > 0.5 mm.
• Set Gravel-bed: 72 gravel-bed streams that Parker et al. (submitted) have
used as baseline data for determining dimensionless hydraulic relations of gravel
bed streams, including a) 16 streams from Alberta, Canada selected by Parker
(1979) from the compendium of Kellerhals et al. (1972), b) 23 British streams
from the compendium of Charlton et al. (1978), c) 23 streams from Idaho, USA
from the compendium of Parker et al. (2003) and d) 10 reaches of the Colorado
River, Colorado, USA from Pitlick and Cress (2000). The value D50 for these
streams refers to the surface median size, which is in all cases greater than 25
mm.
• Set Tuscany: 52 Tuscany, Italy from a compendium on which Rinaldi (2003) is
based. These streams are highly modified by human interference; Qbf was not
available, so the two-year flood Q2 has been used in its place. Most of these
streams are gravel-bed, but several are sand-bed and several more have a
surface median size in the range of gravel but less than 16 mm (pea gravel). 33
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
DIMENSIONLESS HYDRAULIC RELATIONS FOR THE EXPANDED DATA SET
Yes! The sand-bed streams do have lower slopes than the gravel-bed streams, and
the sand-bed streams with D50 < 0.5 mm generally have lower slopes than the
sand-bed streams with D50 > 0.5 mm!
100
sand
gravel
10
Width Sand-bed
Width ST>0.5
Width Gravel-bed
Width Tuscany
Depth Sand-bed
Depth ST>0.5
Depth Gravel-bed
Depth Tuscany
Slope Sand-bed
Slope ST>0.5
Slope Gravel-bed
Slope Tuscany
1
Btil, Htil, S
~ ~
B, H, S
0.1
0.01
0.001
0.0001
0.00001
1.E+02
1.E+04
1.E+06
1.E+08
Q̂
Qhat
1.E+10
1.E+12
1.E+14
34
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
DIMENSIONLESS HYDRAULIC RELATIONS FOR EXPANDED DATA SET (contd.)
Note the marked change in bankfull Shields number between sand-bed and gravelbed rivers!
100
sand
gravel
10
Width Sand-bed
Width ST>0.5
Width Gravel-bed
Width Tuscany
Slope Sand-bed
Slope ST>0.5
Slope Gravel-bed
Slope Tuscany
bankfull taus Sand-bed
bankfull taus ST>0.5
bankfull taus Gravel-bed
bankfull taus Tuscany
Btil, Htil, taus
1
~
B , bf , S
0.1
0.01
0.001
0.0001
0.00001
1.E+02
1.E+04
1.E+06
1.E+08
Q̂
Qhat
1.E+10
1.E+12
1.E+14
35
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
SHIELDS REGIME DIAGRAM FOR THE EXPANDED DATA SET
Note how the rivers fall into four characteristic types according to grain size range!
100
sand-bed
gravel-bed
Onset of significant suspension
of bed sediment
10
bankfull taus Sand-bed
bankfull taus ST>0.5
bankfull taus Gravel-bed
bankfull taus Tuscany
motion threshold
suspension threshold
0.0625 mm
2 mm
16 mm
0.5 mm
*
1
0.1
0.01
Yamamoto
(1994)
obtained a very
similar relation
for Japanese
rivers.
Onset of motion of bed sediment
0.001
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06
Rep
36
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
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.
Church, M. and Rood, K., 1983, Catalogue of alluvial river data, Report, Dept, of Geography,
University of British Columbia, Vancouver, B. C., Canada.
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., 1979, Hydraulic geometry of active gravel rivers, Journal of Hydraulic Engineering,
105(9),1185-1201.
Parker, G., Paola, C., Whipple, K. and Mohrig, D., 1998, Alluvial fans formed by channelized
fluvial and sheet flow: theory, J. Hydraul. Engrg., 124(10), 1-11.
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.
Parker, G., Wilcock, P.W., Paola, C., Dietrich, W.E. and Pitlick, J., submitted, Quasi-universal
relations for bankfull hydraulic geometry of single-thread gravel-bed rivers, Journal of
Geophysical Research Earth Surface, submitted April, 2006, downloadable at
http://cee.uiuc.edu/people/parkerg/preprints.htm .
37
Contribution from the National Center for Earth-surface Dynamics
for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006
REFERENCES contd.
Shaw, J. and R. Kellerhals, 1982, The Composition of Recent Alluvial Gravels in Alberta River
Beds, Bulletin 41, Alberta Research Council, Edmonton, Alberta, Canada.
Yamamoto, K., 1994, The Study of Alluvial Rivers, Sankaidou (in Japanese).
Pitlick, J., and Cress, R., 2000, Longitudinal trends in channel characteristics of the Colorado
River and implications for food-web dynamics. Final Report, U.S. Fish and Wildlife Serv.,
Grand Junction, Colo., 45 p. + 21 p. in Appendices.
Rinaldi, M., 2003, Recent channel adjustments in alluvial rivers of Tuscany, central Italy, Earth
Surf. Process. Landforms 28, 587–608.
For more information see Gary Parker’s e-book:
1D Sediment Transport Morphodynamics of Rivers and Turbidity Currents
http://cee.uiuc.edu/people/parkerg/morphodynamics_e-book.htm
38