MID TERM EXAM 1 WEEK FROM TODAY
http://www.homepage.montana.edu/~kmw/
Today
Fluvial Process
– Geomorphic Work
– Bankfull discharge
– Hydraulic geometry
– Open channel toolbox
Channel Morphology = f(River Work)
 gQS
• Work = Force x distance
• Power = Rate at which work is done
• Stream Power: one way to measure
entrainment and transport of bedload
• The work done by a river is estimated
by
– the amount of sediment it transports during
any given flood
– “the conditions under which rivers adjust or
maintain their morphology”
Geomorphic Work:
Frequency and Magnitude
Transports the most sediment
Elf?
Man?
Giant?
from Wolman and Miller (1960)
ALLUVIAL RIVERS ARE THE AUTHORS OF THEIR OWN
GEOMETRY
• Given enough time, rivers construct their own channels.
• A river channel is characterized in terms of its bankfull geometry.
• Bankfull geometry is defined in terms of river width and
average depth at bankfull discharge.
• Bankfull discharge is the flow discharge when the river is just
about to spill onto its floodplain.
Text by Peter Wilcock/Johns Hopkins Univ.
CAVEAT: NOT ALL RIVERS HAVE A DEFINABLE
BANKFULL GEOMETRY!
Rivers in bedrock often have no
active floodplain, and thus no
definable bankfull geometry.
Highly disturbed alluvial rivers are
often undergoing rapid
downcutting. What used to be the
floodplain becomes a terrace that
is almost never flooded. Time is
required for the river to construct a
new equilibrium channel and
floodplain.
Wilson Creek, Kentucky: a
bedrock stream. Image
courtesy A. Parola.
Reach of the East
Prairie Creek,
Alberta, Canada
undergoing rapid
downcutting due to stream straightening. Image
courtesy D. Andres.
THRESHOLD CHANNELS
Threshold gravel-bed channels
are channels which are barely not
able to move the gravel on their
beds, even during high flows.
These channels form e.g.
immediately downstream of dams,
where their sediment supply is cut
off. They also often form in urban
settings, where paving and
revetment have cut off the supply
of sediment. Threshold
channels are not the authors of
their own geometry.
Trinity Dam on the Trinity River,
California, USA. A threshold
channel forms immediately
downstream.
Adjustments in the Fluvial System
Hydraulic Geometry
• Q = Vel x Cross-sectional flow area
= Vel x width x depth
Which of these 3 variables changes most to
accommodate more Q, either downstream or
at a given location?
• Relationships between width, depth, and
velocity and discharge
• Describes how w, d, v increase with
discharge
Hydraulic Geometry
w  aQ
b
d  cQ
(Leopold and Maddock, 1953)
f
v  kQm
s  gQ
z
Q  w  d  v  aQ  cQ  kQ
ack 1
b  f  m 1
b
f
m
At-a-Station and
Downstream Hydraulic Geometry
at-a-station
w  aQ
.26
downstream
.5
w  aQ
.4
d  cQ
d  cQ
.34
v  kQ
v  kQ
.4
.1
Downstream hydraulic
geometry relations
(Leopold and Maddock,1953)
Used Q = Mean annual flow (MAF)
At-a-station hydraulic
geometry relations
(Leopold and Maddock,1953)
Downstream hydraulic geom. relations
compared for 8 river systems
Rate of increase of w, d and v is similar regardless of river size!
Leopold and Maddock, 1953
On Soda Butte Creek, measuring bankfull width
Fonstad and Marcus, 2003
Adjustments in the Fluvial System
Lane’s balance: Model of the
channel adjustment to water
and sediment loads
• Qs d50 ~ Qw S
– Qs = sediment discharge
(kg/s)
– Qw = water discharge
(cm/s)
– d50 = sediment size (m)
– S = slope (m/m)
Gilbert’s Fluvial Process
• Joined John Wesley Powell survey in Utah, 1874
• First coined the concept of “graded streams”
• A stream’s form is defined by its ability to transport load, and
that a “graded” stream condition will exist when the stream can
just carry the load supplied to it
– “The transportation of debris by running water”, USGS Prof. Paper
86, Gilbert, 1914
• Crux of this hypothesis was that mechanical forces act against
rock to create form
“If a stream which is loaded to its full capacity
reaches a point where the slope is less, it
becomes overloaded and part of the load is dropped,
making a deposit.”
“If a fully loaded stream reaches a point where
the slope is steeper, its enlarged capacity causes
it to take more load, and taking of load erodes
the bed.”
“If the slope of a stream’s bed is not adjusted to the
stream’s discharge and to the load it has to carry,
then the stream continues to erode or deposit, or both
until an adjustment has been effected and the slope is
Graphic by Peter Wilcock
just adequate for the work”
Text by G.K. Gilbert, “Hydraulic
Mining Debris in the Sierra Nevada”
USGS Prof. Paper 105, 1917.
Ex. of Lane’s balance
• Mine discharges large
quantities of fine
grained sediment
(<d50) into river
– River response?
• Madison slide occurs
and deposits large
mass of of
cobble/boulder (>d50)
– River response?
– Complex response?
Example of process linkage and complex response
1959 Hebgen Lake
earthquake-induced
landslide
t0, x0
TIME
SPACE
Incision t1, x1 Deposition t1, x2
Incision t2, x2
Locke, 1998
Deposition t2, x3
Incision t3, x3
Deposition t3, x4
The Open-Channel Toolbox TM Peter Wilcock
• Conservation
Relations
– Conservation of Mass
(Continuity)
– Conservation of
Energy
– Conservation of
Momentum
• Constitutive Relations
– Flow Resistance
– Sediment Transport
Conservation of Mass (Continuity)
• Mass is neither created
nor destroyed
• Inputs = outputs
• Inputs and outputs for
fluid flow are discharge
– Vel x Flow Area
U1A1 = U2A2
Conservation of Momentum (Forcebalance)
• Newton’s Second Law
• In steady, uniform flow,
 F  ma
• Depth-slope product
F  0
g sin AL   o PL
  gRS
Unsteady, nonuniform flow
• Flow accelerates in
space and time
1-d St. Venant eqn.
Rearranged 1-d St. Venant eqn.
Potential Energy and Kinetic
Energy
• Bernoulli energy equation
– H = d + Z + V2/2g + losses
– d = depth
– Z = elevation above datum,
e.g. sea level
– V = velocity of flow
– g = gravity
H1
H1
Conservation of Energy
• Energy is neither created nor destroyed
• Two components
U2
)
2g
– kinetic (
– potential (z+h)
• Energy is also converted to heat, hf
• H1 =H2 + hf
http://ga.water.usgs.gov/edu/hyhowworks.html
Flow Resistance
• Relation between velocity, flow
depth, basal shear stress, and
hydraulic roughness
• A variety of relations exist
including
– Manning’s
– Chezy
• Empirical
• The big unknown: n
(Metric)
Multiply by 1.49 for English units
U
SR
n
2
3
Using continuity,
S 23
Q  UA 
R A
n
Flow Resistance Eqns.
•
•
Chezy
– V= C√RS
– Where
• C=Chezy roughness (22-220)
• V= velocity
• R=hydraulic radius
• S=channel slope
Manning
– V=(1.49/n) R2/3 S1/2
– Where
• n = Manning’s roughness coefficient (0.02-006)
LWD covering less than 2% of
the streambed can provide half
the total roughness or flow
resistance. This results in a finer
streambed substrate.
Buffington and Montgomery 1999, WRR 36, 3507-3521
Manga and Kirchner, 2000, WRR 36, 2373-2379.