Fluvial Processes

This lecture is largely based on Chapter 6 of Ritter along with excerpts from my notes from Prof. Rhodes and Fluvial Forms and Processes by Knighton.

A river has two jobs

1) Transoprt water out of drainage basin.
2) Transport sediment delivered to it (function of climate and drainage and vegetation and topography).

The volume of water that passes by a point in a river over a certain time increment is the discharge (for example, the Tempe Town Lake can apparently withstand about 40,000 cubic feet per second with the dams up). We quantify the water flow in the river as Discharge, Q [L^3/T].
See figure 3.1 from Knighton and Figure 5.3 (Slope Hydrologic Cycle from Ritter et al.) for a description of how water gets from precipitation to the river.

Discharge is related by continuity of water flux at a given channel cross-section as the product of the velocity times the cross-sectional area of the flow:
Q = v * A, where Q is discharge [L^3/T], v is velocity [L/T], and A is area [L^2]
Many channels are effectively rectangular, so we can express the cross-sectional area as the product of width (w) times depth (d):
A = w * d

where Q = discharge,
            A = channel cross-sectional area
            v = channel velocity
            w = channel width
            d = channel depth

For example, the Salt River is about 300 ft wide and about 40 ft deep at the Mill Avenue Bridge and if the velocity is about 30 ft/second for a fast flood, we get
Q = (300 ft * 40 ft)*30ft/sec = 360,000 ft³/sec for a great flood there. Measurements of flow velocity and channel shape can be much more detailed and refine this estimate.

Flow regimes

An important difference in the flow of water in open channels occurs between laminar and turbulent flow.

See the quote from Knighton for succint definitions of the two (page 48) and Figure 3.3 from Knighton.

The other difference in how we can describe flow is with regard to two dimensionless terms:
Reynolds number Re (ratio of driving forces to resisting forces) and is a measure of turbulence (Re<500 for laminar and Re > 2500 for fully turbulent.
and
Froude number F ( ratio of inertial forces to gravity) and is a measure of the relative tranquility or rapidity of the flow (F <1 is subcritical F>1 supercritical flow).

See page 194 from Ritter et al., and Table 3.1 from Knighton for details.

Note the distinctive bedforms that are produced in alluvial channels as depth and F vary (figure 6.3 from Ritter, et al.)

Manning equation for flow velocity

We use a simple formulation called Manning's eequation that relates the flow velocity to the local channel slope (s [dimensionless]), a channel shape parameter called the hydraulic radius [L]--see below, and a
roughness parameter n [L^1/6]. NOTE THAT THIS IS FOR ENGLISH UNITS (feet, seconds). This simple equation derived for non accelerating flows has been useful for estimating flow velocities:

The Manning roughness coefficient (n) is estimated based upon inspection of the channel and its shape: a measure of surface roughness depending on the channel boundary type (see Table 6.1 from Ritter, et al.)
R is the hydraulic radius (see figure 6.2 from Ritter, et al.) The hydraulic radius R is equal to the ratio of the channel area (A) to its wetted perimeter (P):
P = w + 2d
R = A/P
and S is the local channel slope.
Here is a link to another explanation of this problem that I developed for the Computers in Geology course.
Here is a link to a matlab function for calculations of velocity using the manning equation.
Here is how velocity varies with n, with R, and with slope for a given set of parameters.

Sediment transport

Transport modes: Dissolved, suspended, and bedload.
See figure 3.6 from Knighton for a nice summary of sediment moving in and through the fluvial system.
Entrainment is the cellection of processes that initiate the bursts of motion experienced by a particle.

Dissolved load

Material is weathered chemically, and most is delivered to the stream by groundwater.
Data are sparse, but Knighton says that globally about 38 percent of the total load of the world's rivers is dissolved, but this varies greatly. See Table 3.6 from Knighton.

Suspended load

Material supported by flow at least part of the time.

Bedload

Material whose weight is supported by bed of stream during transport.
Major control on channel form.
See figure 3.8 from Knighton for an illustration of the modes of transport.
Sediment transport equations typically rely on excess shear stress at the bed or excess stream power where the excess is the difference between the stress or power and the threshold value necessary for particle motion.
Stream power: omega = gamma*Q*S (often expressed in terms of unit width by dividing by channel width). gamma is the specific weight (gravitational acceleration*density) of water, Q is water discharge, and S is local channel slope.
Bedload transport is difficult to study but laboratory flumes have proven useful and a famous study by Hjulstrom produced the sets of curves for erosion, transported, and deposited shown in Figure 6.8 from Ritter et al.

Rapids along the Colorado River in the Grand Canyon, AZ

An impressive work in geomorphology was performed by Susan W. Kieffer in the 1980s as she studied the geomorphology and hydraulics of the Colorado River in the Grand Canyon. A good reference is Kieffer, S. W., 1990, Hydraulics and geomorphology of the Colorado River in the Grand Canyon, in, Beus S., and Morales, M., Grand Canyon Geology, New York: Oxford University Press, p. 333-383.

The other is Kieffer, S., Graf, J. B., and Schmidt, J. C., 1989, Chapter 3: hydraulics and sediment transport of the Colorado River, in Elston, D. P., Billingsley, G. H., and Young, R. A., Geology of Grand Canyon, northern Arizona (with Colorado River Guides), American Geophysical Union, IGC field trip guide T115/315.

The pool and rapid sequences along many rivers are easily observed and their study can give us insights into the basic concepts of hydraulics and in the development of these impressive river landforms.

See quote from p. 335 (1, Kieffer) and figure 3.1a (Kieffer et al.) on the description of the major features of rapids.

Interpretation of the hydraulics of the rapids is based on the comparison of the rapids with flume studies. See quote on p. 341 (2, Kieffer) about the scale of water flow in the rapids.

Localization of the rapids: "The rapids occur almost exclusively where floods in tributatry canyons, controlled by local or regional faulting or jointing, have delivered large boulders into the river channel" p. 345 (Kieffer).
See figures 4 and 5 (Kieffer) for illustrations of the vertical and horizontal constriction: "...rapids are not formed by sudden drops in channel bed elevation, but rather are a result of vertical and lateral constriction" p. 349 (Kieffer).

Reynolds and Froude numbers as useful descriptions of the flow. Almost all flow in the Grand Canyon is turbulent, but sub and supercritical flows result in major differences in the character of river flow.
See p. 351(3, Kieffer) for a nice description of the water features associated with the transition from supercritical to subcritical flow.

Basic rapid structure: Backwaters (pools)-rapids-runouts
Pools are deep and slow velocity basically ponded behind the constriction.
Converging section of rapids is the portion that has accelerating flow and the transition from sub to supercritical conditions. Flow surface is smooth and depressed.
Diverging section of rapids is the portion in which the flow decelerates in hydraulic jumps. The flow goes from super to subcritical and can be envisioned as a high velocity jet emerginf from a constriction (see figure 8, Kieffer).

Sediment transport: See Hjulstrom criterion in Figure 13 (Kieffer) and the quote from Kieffer et al. (4)

A model for the geomorphic-hydraulic evolution of the river channel at debris fans. See figure 17 and final paragraph (5, Kieffer).

GLG 362/598 Geomorphology

Page last modified October 11, 2000 by Ramón Arrowsmith