Is the critical Shields stress for incipient sediment motion dependent on channel-bed slope?

Abstract

Data from laboratory flumes and natural streams show that the critical Shields stress for initial sediment motion increases with channel slope, which indicates that particles of the same size are more stable on steeper slopes. This observation is contrary to standard models that predict reduced stability with increasing slope due to the added downstream gravitational force. Processes that might explain this discrepancy are explored using a simple force-balance model, including increased drag from channel walls and bed morphology, variable friction angles, grain emergence, flow aeration, and changes to the local flow velocity and turbulent fluctuations. Surprisingly, increased drag due to changes in bed morphology does not appear to be the cause of the slope dependency because both the magnitude and trend of the critical Shields stress are similar for flume experiments and natural streams, and significant variations in bed morphology in flumes is unlikely. Instead, grain emergence and changes in local flow velocity and turbulent fluctuations seem to be responsible for the slope dependency due to the coincident increase in the ratio of bed-roughness scale to flow depth (i.e., relative roughness). A model for the local velocity within the grain-roughness layer is proposed based on a 1-D eddy viscosity with wake mixing. In addition, the magnitude of near-bed turbulent fluctuations is shown to depend on the depth-averaged flow velocity and the relative roughness. Extension of the model to mixed grain sizes indicates that the coarser fraction becomes increasingly difficult to transport on steeper slopes.