The concave river long profile: a morphodynamic steady state?

By definition, a morphodynamic steady state is governed by a spatially constant sediment transport rate. As the sediment transport rate is a function of shear stress associated with skin friction, the morphodynamic steady state has been considered to be governed by a spatially constant bed slope. For this reason, the typical concave river long profile has been considered to be a quasi-steady state. The river's steady state has been considered to be one with a spatially constant bed slope, with tributaries inducing a stepwise decrease in bed slope in streamwise direction. Yet, for the sediment transport rate to be spatially constant, it rather is the product of water surface slope and water depth associated with skin friction that needs to be constant. This implies that physical mechanisms that induce streamwise variation in the sediment transport rate can be compensated by a streamwise variation in bed slope so as to guarantee a spatially constant sediment transport rate. Following the river course, such physical mechanisms can be bedrock exposure, partial transport, and a spatially lagging bedform growth. At locations where tributaries increase the water discharge, the above mechanisms cause the river bed profile to be upward concave over a significant reach. At bifucations or at locations where river widening prevails, the river bed profile is upward convex.