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. The bank-full depths, widths, depth-averaged watervelocities, and along-channel slopes of alluvial channels are approximatelypower-law functions of bank-full discharge across many orders of magnitude.What mechanisms give rise to these patterns is one of the central questionsof fluvial geomorphology. Here it is proposed that the bank-full depths ofalluvial channels are partially controlled by the maximum heights ofgravitationally stable channel banks, which depend on bank material cohesionand hence on clay content. The bank-full depths predicted by a bank-stabilitymodel correlate with observed bank-full depths estimated from the bends inthe stage–discharge rating curves of 387 U.S. Geological Survey gagingstations in the Mississippi River basin. It is further proposed thatdepth-averaged water velocities scale with bank-full depths as a result of aself-regulatory feedback among water flow, relative roughness, andchannel-bed morphology that limits depth-averaged water velocities towithin a relatively narrow range associated with Froude numbers that have aweak inverse relationship to bank-full discharge. Given these constraints onchannel depths and water velocities, bank-full widths and along-channelslopes consistent with observations follow by conservation of mass andenergy of water flow.

earth surface dynamics

Controls on the hydraulic geometry of alluvial channels: bank stability to gravitational failure, the critical-flow hypothesis, and conservation of mass and energy