MID TERM EXAM 1 WEEK FROM TODAY

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”

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 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.

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 (Leopold and Maddock, 1953)

At-a-Station and Downstream Hydraulic Geometry at-a-station downstream

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

Fonstad and Marcus, 2003 On Soda Butte Creek, measuring bankfull width

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 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 just adequate for the work” “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.” Graphic by Peter Wilcock 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?

Deposition Example of process linkage and complex response 1959 Hebgen Lake earthquake-induced landslide t0, x0 Deposition t2, x3 Incision t2, x2 Incision t3, x3 Locke, 1998 Deposition t3, x4 TIME t1, x1 Incision 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 U 1 A 1 = U 2 A 2

Conservation of Momentum (Force- balance) Newton’s Second Law In steady, uniform flow, Depth-slope product

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 + V 2 /2g + losses –d = depth –Z = elevation above datum, e.g. sea level –V = velocity of flow –g = gravity H1

Energy is neither created nor destroyed Two components –kinetic ( ) –potential (z+h) Energy is also converted to heat, h f H 1 =H 2 + h f Conservation of Energy

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 Using continuity, (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) R 2/3 S 1/2 –Where n = Manning’s roughness coefficient ( ) Flow Resistance Eqns.

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, Manga and Kirchner, 2000, WRR 36,