Runoff Routing through Steep Natural Channels

Equations describing steady and unsteady tumbling flow in steep, natural channels are developed and their parameters are evaluated on the basis of field experiments. The hydrologically significant aspects of steady flow can be expressed as a relation between mean storage per unit length (area), A, and discharge, Q. These functions are evaluated experimentally for 13 test reaches using tracer methods. The form A = aQ^b provides consistently good fit to the data. A related study shows that the parameters a and b can be computed from readily available basin data. Nondimensional analysis supports this experimental fact. Unsteady flow data are obtained by observing the passage of small, artificially created surges through the test reaches. Wave propagation appears to be essentially kinematic, but with strong dispersive effects caused by storage in the pool-like channel segments between the frequent critical flow sections. A partial differential equation describing unsteady flow in this type of channel is derived and solved for the initial and boundary conditions of the surge tests. A note on longitudinal dispersion is added as an appendix.