Channelization on plateaus with arbitrary shapes

Abstract

The initiation of channels and the factors that control their spacing is one of the most fundamental problems in geomorphology. Here we present an analysis of channelization that is downstream driven, so called because channelization is initiated at some point away from the divide where the Froude critical flow is achieved. By using two novel techniques, the “frozen time approach” and the “momentary stability concept,” we are able, for the first time, to investigate downstream‐driven channelization that occurs on a plateau with an evolving base profile. The “frozen time approach” assumes that the time evolution of the base state can be ignored in the linearized equations, whereas the “momentary stability concept” assumes that an unsteady base state becomes momentarily unstable to a disturbance when the growth of the disturbance is faster than the evolution of the base state. The analysis shows that an arbitrary slope profile is momentarily unstable and incised by channels before it evolves into a steady base state if the topographic curvature at the location where the Froude critical flow is achieved is sufficiently small. As the curvature decreases further, dominant channel spacing increases slightly in a purely erosional case, while clear dominant channel spacing tends not to appear in an erosional‐depositional case. It is also found from the analysis that in both cases, the channel spacing is on the order of 1000 times the Froude critical depth. The results are compared with field observations and experiments, and they show satisfactory agreement.