STABLE CHANNEL CROSS-SECTIONS OF STRAIGHT SAND RIVERS

A mathematical model is presented for defining the size and cross section of self-formed straight sand rivers in which sediments are actively transported everywhere as bedload and suspended load. A balance of lateral bedload and lateral diffusive transport of suspended sediment is imposed to maintain a stable channel cross section. Singular perturbation technique is employed to solve the sediment balance equation, from which a relation for stable depth is derived. A resistance formula for dune-covered beds is used to obtain stable width. It is revealed theoretically that the channel center depth relative to sediment size is approximately proportional to S-0.8 for natural sand rivers, in which S is longitudinal slope. The analysis is found to agree reasonably well with available laboratory and field data.