Boundary Shear Stress and Roughness Over Mobile Alluvial Beds

The resistance to flow in the turbulent rough‐flow range depends primarily upon the size, shape, and arrangement of the granular material making up the boundary. We have estimated the hydraulic roughness of mobile alluvial surfaces by inverting sediment‐transport formulas to solve for the local boundary shear stress required to predict the observed sediment flux and size. Inserting this shear stress value and a near‐bed velocity measurement into the law of the wall yields the roughness scale, z0, defined as the height above the bed where velocity goes to zero. If the roughness is related to the coarse fraction of the bedload, such as D84, then z0=0.1D84. This roughness, obtained from mobile, naturally packed, and heterogeneous‐in‐size beds is three times greater than that predicted by the Nikuradse formula developed from nearly uniform and smoothly packed surfaces. We detect no variation in roughness with transport stage, implying that the large static and slowly moving grains determine flow resistance and that momentum extraction by saltating grains is minor. Application of this simple roughness algorithm allows convenient and accurate calculation of the local boundary shear stress.