MID TERM EXAM 1 WEEK FROM TODAY kmw
-
date post
21-Dec-2015 -
Category
Documents
-
view
216 -
download
0
Transcript of MID TERM EXAM 1 WEEK FROM TODAY kmw
Today
Fluvial Process– Geomorphic Work– Bankfull discharge – Hydraulic geometry – Open channel toolbox
Channel Morphology = f(River Work)
• 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”
gQS
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.
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
Trinity Dam on the Trinity River, California, USA. A threshold channel forms
immediately downstream.
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.
Hydraulic Geometry
• Q = Vel x Cross-sectional flow area= Vel x width x depthWhich 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
At-a-Station and Downstream Hydraulic Geometry
34.
4.
26.
kQv
cQd
aQw
1.
4.
5.
kQv
cQd
aQw
at-a-station downstream
Downstream hydraulic geom. relationscompared for 8 river systems
Rate of increase of w, d and v is similar regardless of river size!
Leopold and Maddock, 1953
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 capacityreaches a point where the slope is less, it becomes overloaded and part of the load is dropped,making a deposit.”
“If the slope of a stream’s bed is not adjusted to thestream’s discharge and to the load it has to carry,then the stream continues to erode or deposit, or bothuntil an adjustment has been effected and the slope isjust adequate for the work”
“If a fully loaded stream reaches a point where the slope is steeper, its enlarged capacity causesit to take more load, and taking of load erodes the bed.”
Graphic by Peter WilcockText by G.K. Gilbert, “HydraulicMining 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?
Deposition
Example of process linkage and complex response
1959 Hebgen Lake earthquake-inducedlandslide
t0, x0
Deposition t2, x3Incision t2, x2
Incision t3, x3Locke, 1998
Deposition t3, x4
TIM
E t1, x1Incision t1, x2
SPACE
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 (Force-balance)
• Newton’s Second Law
• In steady, uniform flow,
• Depth-slope product
0F
maF
PLALg o sin
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
• Energy is neither created nor destroyed• Two components
– kinetic ( )– potential (z+h)
• Energy is also converted to heat, hf
• H1 =H2 + hf
Conservation of Energy
g
U
2
2
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
n
RSU
32
Using continuity,
ARn
SUAQ 3
2
(Metric)Multiply by 1.49 for English units
• 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)
Flow Resistance Eqns.