ABSTRACT

River bed-load transport is difficult to measure, and published formulae for approximating the transport rate give dissimilar results. The present paper explores an inferential method which may be useful. The study area is located in Arkansas and eastern Oklahoma, centered on the Arkansas River, from Tulsa to its mouth.

Channel segments are defined as bounded by lakes (either natural or artificial) and by major tributaries. Each segment, within this system, is very close to being in dynamic equilibrium. The water which enters a given segment is the water which leaves it, except for a differential which varies from a maximum of about 0.1%/km, in the drier part of the area, to a minimum of less than 0.001%/km, in the wetter part; this differential may be largely groundwater. Bed load material must show similar behavior, except that, on this hypsometrically stable channel, there is no net source of bed load material in the channel itself. The important changes in Q (water discharge) and q (bed load discharge) occur at the segment boundaries, providing stepped profiles for these two parameters.

The rate of delivery of bed load material (q; in m³/sec) can be estimated from regional erosion rates; the values adopted increase from 0.03 at Tulsa to almost 0.07 at the mouth. The ratio of Q to q therefore falls in the range 6,000 to 18,000. The long-term average velocity of water flow in the main channel is computed to be about 112 cm/sec, which is a reasonable result; and the long-term average velocity of bed load material must be fairly close to 0.17 cm/sec (a velocity ratio of about 650). The long-term average thickness of the moving bed layer is, therefore, calculated to be 17 cm, greater than would be observed at times of low water, and much less than would be obtained in flood times.

In addition to Q and q, other stream measures which must have stepped (e.g., discontinuous) profiles are channel width, channel depth, water velocity, bed load material velocity, bed shear stress, force and work. Local variations in bedrock geology provide complications and exceptions to this general statement. The stepped profiles provide that, for any variable y taken relative to distance x along the channel, dy/dx = constant, within any one segment. This tentative, but encouraging, result suggests that the river system may be, for practical purposes, more simple than has been thought.