Abstract. The bank-full depths, widths, depth-averaged water
velocities, and along-channel slopes of alluvial channels are approximately
power-law functions of bank-full discharge across many orders of magnitude.
What mechanisms give rise to these patterns is one of the central questions
of fluvial geomorphology. Here it is proposed that the bank-full depths of
alluvial channels are partially controlled by the maximum heights of
gravitationally stable channel banks, which depend on bank material cohesion
and hence on clay content. The bank-full depths predicted by a bank-stability
model correlate with observed bank-full depths estimated from the bends in
the stage–discharge rating curves of 387 U.S. Geological Survey gaging
stations in the Mississippi River basin. It is further proposed that
depth-averaged water velocities scale with bank-full depths as a result of a
self-regulatory feedback among water flow, relative roughness, and
channel-bed morphology that limits depth-averaged water velocities to
within a relatively narrow range associated with Froude numbers that have a
weak inverse relationship to bank-full discharge. Given these constraints on
channel depths and water velocities, bank-full widths and along-channel
slopes consistent with observations follow by conservation of mass and
energy of water flow.