Flow resistance and hydraulic geometry in bedrock rivers with multiple roughness length scales.

Abstract

Many models of incision by bedrock rivers predict water depth and shear stress from discharge; conversely, palaeoflood discharge is sometimes reconstructed from flow depth markers in rock gorges. In both cases assumptions are made about flow resistance. The depth‐discharge relation in a bedrock river must depend on at least two roughness length scales (exposed rock and sediment cover) and possibly a third (sidewalls). A conceptually attractive way to model the depth‐discharge relation in such situations is to partition the total shear stress and friction factor, but it is not obvious how to quantify the friction factor for rough walls in a way that can be used in incision process models. We show that a single flow resistance calculation using a spatially‐averaged roughness length scale closely approximates the partitioning of stress between sediment and rock, and between bed and walls, in idealised scenarios. Both approaches give closer fits to the measured depth‐discharge relations in two small bedrock reaches than can be achieved using a fixed value of Manning's n or the Chézy friction factor. Sidewalls that are substantially rougher or smoother than the bed have a significant effect on the partitioning of shear stress between bed and sidewalls. More research is needed on how best to estimate roughness length scales from observable or measurable channel characteristics.