Outer Scaling for Open Channel Flow over a Gravel Bed

Abstract

Similarity analysis is performed for hydraulically rough open channel flow over a gravel bed to provide mixed outer scaling of the mean-velocity profile. The analysis is based on equilibrium turbulent boundary-layer theory derived using the asymptotic invariance principle. Outer scaling based on the similarity theory is validated with velocity measurements from the laboratory and field, having a Reynolds number range that includes 1× 104 , 1× 105 , and 1× 106 and a Froude number range from 0.26 to 0.83. The results show that the free-stream velocity is an appropriate outer scale for gravel-bed river flows at moderate and bankfull stage. The results agree well with the velocity measurements and collapse laboratory and field data, which allow an important connection between open channel research in the laboratory and the applications for which the research is performed in the field. The results show that the R/a D84 roughness parameter is consistent with the mixed scale used in boundary-layer velocity scali...