Abstract
In rivers located in mountain areas, a series of steps are often observed to be formed on bedrock. This is called cyclic steps formed by bedrock incision. This study proposes a simplified model for describing the erosion process by abrasion due to bedload, and obtain an equilibrium step shape migrating upstream without changing its shape. It is found that there are three important parameters: the threshold velocity Ut for bedload, the availability function at the Froude critical point pc, and the average slope. Once these three parameters are given, the wavelength L, the erosion rate averaged over one step length En, and the water and bed surface profiles are determined. It is found that qualitative features of steps observed in experiments are well described by the analysis.
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