A generalized log law formulation for a wide range of boundary roughness typically encountered in natural streams

Applying fluid mechanics principles to mobile bed conditions is simplified by demonstrating that fitting log profiles to streamwise velocity measurements using the plane of zero velocity is applicable to a larger range of roughness conditions than previously expected. Four sets of detailed velocity measurements obtained under the supervision of the authors were analyzed encompassing sediment-scale roughness elements, roughness caused by rigid vegetation, and large-scale roughness elements comprised of mobile bed forms. The analyses resulted in similar normalized zero-plane displacements for all roughness types considered. The zero-plane displacements, d_h, normalized by roughness height, k_s, were 0.20 and 0.26 for the sediment- and vegetation-scale experiments, respectively. The results for two experiments with bed form dominated roughness were 0.41 and 0.34. Estimates of d _h/k_s ranging from 0.2 to 0.4 are therefore recommended for a range of roughness types with the higher end of the range more appropriate for the larger, bed form-scale roughness elements, and the lower end for the sediment-scale roughness elements. In addition, it is demonstrated that the location of the plane of zero velocity is temporally constant even when the bed height is not. The findings can be applied to field velocity measurements under mobile bed conditions facilitating the calculation of turbulence parameters such as shear velocity by using point measurements and providing guidelines for the estimation of an appropriate value for zero-plane displacement.