Hydraulic Geometry of Active Gravel Rivers

The hydraulic geometry of straight reaches of wide, active rivers with beds and banks composed of loose gravel is considered. Naive mechanistic formulations lead to the stable channel paradox; stable width is incompatible with an active bed. A resolution of the paradox based on bed stress redistribution due to turbulent lateral transfer of downstream momentum is outlined and is used to obtain three rationally derived regime relations.These dimensionless relations provide channel properties as functions of bed pavement size and two specified variables, e.g., water and sediment discharge, or water discharge and width. Reduction to relations for hydraulic geometry is shown to require information concerning watershed mechanics that is external to the river, and thus fluvially indeterminate. An empirical relation is determined for this purpose, allowing for derivation of dimensionless relations for hydraulic geometry.