PROBLEM STATEMENT   Rivers adjust their channel geometry (width and depth) to carry a given quantity of water and sediment. Such quantities are determined by watershed processes of runoff and erosion, both of which vary in space and in time.  Given the magnitude of these variations, it is somewhat surprising that rivers show such consistency in their geomorphic characteristics. This observation motivates the following questions: What determines the stable width and depth of natural rivers, given the wide range in flow conditions and sediment supply? Why is it that most river channels are adjusted to relatively common floods (say, floods that occur once every other year), when in fact they experience a wide range of flows?  In particular, why aren't rivers adjusted to carry very large flows, since these flows mobilize sediment along the entire channel boundary?

Fig. 1. Colorado River near Cisco, UT.

EXPERIMENTS Experiments are being conducted in a 16-meter flume at the St. Anthony Falls Laboratory, University of Minnesota. The flume is filled with sand and pea-gravel and water is circulated continuously through the flume with a 5-hp centrifugal pump.  Model parameters are scaled approximately to match conditions in the Colorado River.  The top photo on the left shows the initial phase of an experiment in which the channel has adjusted and come to equilibrium with a discharge of about 10 l/s.  Flow in the channel is about 6 cm deep and 40 cm wide; the floodplain along the left side of the flume is 1 m wide.  The bottom photo shows the flume during the initial stages of a flood.  The water flowing over the floodplain is about 1 cm deep. The experiments are designed to test several hypotheses regarding flood flows in self-formed gravel-bed channels: 1. How does the channel evolve in response to unsteady (flood) flows? What processes determine the equilibrium width and depth when water discharge and sediment load vary? 2. How does the deposition of fine sediment along the margin of the channel and in overbank areas affect the hydraulic geometry of a gravel-bed river? 3. How does riparian vegetation affect the hydraulic geometry of a gravel-bed channel?

We have completed numerous experiments simulating overbank floods.  The simulated floods range from 2 to 4 times the bankfull discharge.  In typical experiments, the discharge is held steady for several hours until the bed and banks of the channel come to equilibrium with the flow.  The discharge is then increased to simulate one or more overbank floods.  The figure below shows the sequence of flows produced in Run 6-03.  Discharge was held steady during the first 4 hours of the run while the channel adjusted; the flow was then increased to 13 l/s and held steady for another 8 hours.  Another flood was produced, followed by steady flow, and then another flood.

Detailed measurements of the bed topography are used to track the changes in channel geometry as the experiments proceed.  The figure below plots changes in channel geometry at one cross section during the above experiment.  The curved lines show the position of the channel bed at various times; the dashed lines show the position of the water surface.  The measurements indicate that, with each flood, the channel became successively wider.  Starting from an initial width of about 40 cm, the channel had widened by the end of the experiment to roughly 80 cm.  The channel was stable under both conditions; this observation calls into question the utility of using a single discharge to characterize the flow that forms the channel.

The results of these experiments reinforce the basic need for studying processes of channel evolution under unsteady flows.  In general, we find that it is difficult to sustain overbank floods; in most experiments the channel slowly widens, increasing the bankfull channel capacity until all of the flow is contained within the banks.  The flows generated in our experiments produced stable gravel channels with well-defined equilibrium geometries, but variable widths.  This result is consistent with theory, but inconsistent with what we see in the field.  The contrast in channel response is intriguing, considering that conditions in natural systems are much more variable than those being simulated here.  We are still investigating these processes, however, it appears that bank erosion in natural rivers may be limited by other factors, such as riparian vegetation and effects associated with channel curvature, which are not being simulated here.  Alternatively, it may turn out that bank erosion is not very sensitive to the actual magnitude of the discharge, because shear stress changes at increasingly slower rates as discharge increases.  We hope to investigate these interactions further by modeling the processes of bank erosion in response to a series of simulated floods.  In addition, we are beginning the next phase of the experiments in which we will introduce suspended sediment into the flow.  Sediment that falls out of suspension in low velocity areas can quickly narrow the channel or build-up the height of the floodplain, thus establishing a different channel geometry.

This project is supported by the National Science Foundation under grants to J. Pitlick (BCS-9986338) and J. Pizzuto (BCS-9986238). We thank Gary Parker and Chris Paola for their advice and encouragement, and the staff at SAFL for their assistance in this project.

Parker, G., Self-formed straight rivers with equilibrium banks and mobile bed. Part 2. The gravel river, J. Fluid Mech., 89,127-146, 1978.

Parker, G., Hydraulic geometry of active gravel rivers, J. Hydraul. Div. Am. Soc. Civ. Engr., 105(HY9), 1185-1201, 1979.

Pitlick, J. and R. Cress, 2002, Longitudinal trends in the channel characteristics of a large gravel-bed river, Water Resour. Res., 38, 1216, doi:10.1029/2001WR000898

Pitlick, J. and M.M. Van Steeter, Geomorphology and endangered fish habitats of the upper Colorado River 2. Linking sediment transport to habitat maintenance, Water Resour. Res., 34, 303-316, 1998.

Pizzuto, J.E., Channel adjustments to changing discharges, Powder River, Montana, Geol. Soc. Amer. Bull., 106, 1494-1501, 1994.