A Generalized Log-Law Formulation For a Wide Range of Boundary Roughness Conditions Encountered in Streams

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Virginia Tech

It is demonstrated that the method for locating a velocity profile origin, or plane of zero velocity, by fitting log profiles to streamwise velocity measurements is applicable to a larger range of roughness scales than previously expected. Five different sets of detailed, experimental velocity measurements were analyzed encompassing sediment-scale roughness elements, roughness caused by rigid vegetation, and large-scale roughness elements comprised of mobile bedforms. The method resulted in similar values of normalized zero-plane displacement for all roughness types considered. The ratios of zero-plane displacement, dh, to roughness height, ks, were 0.20 and 0.26 for the sediment- and vegetation-scale experiments, respectively. The results for the two experiments with bedform dominated roughness were 0.34 and 0.41. An estimate of dh/ks ranging from 0.2 to 0.4 is therefore recommended for a range of roughness types with the higher end of the range being more appropriate for the larger, bedform-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 effects of roughness element packing density were also examined with the identification of a possible threshold at 4%, above which zero-plane displacement is independent of packing density. 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.

sediment transport, zero-plane displacement, log law, bed forms, boundary layers, open channel flow