Hydrodynamics of steep streams with planar coarse-grained beds: Turbulence, flow resistance, and implications for sediment transport

The hydraulics of steep mountain streams differ from lower gradient rivers due to shallow and rough flows, energetic subsurface flow, and macro-scale form drag from immobile boulders and channel and bed forms. Heightened flow resistance and reduced sediment transport rates in steep streams are commonly attributed to macro-scale form drag; however, little work has explored steep river hydrodynamics in the absence of complex bed geometries. Here we present theory for the vertical structure of flow velocity in steep streams with planar, rough beds that couples surface and subsurface flow. We test it against flume experiments using a bed of fixed cobbles over a wide range of bed slopes (0.4-30%). Experimental flows have a nearly logarithmic velocity profile far above the bed; flow velocity decreases less than logarithmically toward the bed and is nonzero at the bed surface. Velocity profiles match theory derived using a hybrid eddy viscosity model, in which the mixing length is a function of height above the bed and bed roughness. Subsurface flow velocities are large (>1 m/s) and follow a modified Darcy-Brinkman-Forchheimer relation that accounts for channel slope and shear from overlying surface flow. Near-bed turbulent fluctuations decrease for shallow, rough flows and scale with the depth-averaged flow velocity rather than bed shear velocity. Flow resistance for rough, planar beds closely matches observations in natural steep streams despite the lack of bed forms or channel forms in the experiments, suggesting that macro-scale form drag is smaller than commonly assumed in stress-partitioning models for sediment transport.