TY - JOUR
T1 - Outer scaling for open channel flow over a gravel bed
AU - Belcher, Brian J.
AU - Fox, James F.
PY - 2010/6/15
Y1 - 2010/6/15
N2 - 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/aD84 roughness parameter is consistent with the mixed scale used in boundary-layer velocity scaling. This is in agreement with the consistent turbulent structure of the flow for both flat plate boundary-layer and open channel flow scenarios. While R/D84 has been used empirically with depth-averaged velocity and roughness laws for many years, this roughness parameter is shown in a theoretical context due to its influence on the turbulent structure of the flow. The results are applicable to modeling the velocity distribution under fundamental gravel-bed flow cases that span to the bankfull flow regime, which provides a contribution to stream engineering.
AB - 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/aD84 roughness parameter is consistent with the mixed scale used in boundary-layer velocity scaling. This is in agreement with the consistent turbulent structure of the flow for both flat plate boundary-layer and open channel flow scenarios. While R/D84 has been used empirically with depth-averaged velocity and roughness laws for many years, this roughness parameter is shown in a theoretical context due to its influence on the turbulent structure of the flow. The results are applicable to modeling the velocity distribution under fundamental gravel-bed flow cases that span to the bankfull flow regime, which provides a contribution to stream engineering.
KW - Gravel bed
KW - Open channel
KW - Outer scaling
KW - Turbulence
KW - Velocity profile
UR - http://www.scopus.com/inward/record.url?scp=78650252432&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=78650252432&partnerID=8YFLogxK
U2 - 10.1061/(ASCE)EM.1943-7889.0000200
DO - 10.1061/(ASCE)EM.1943-7889.0000200
M3 - Article
AN - SCOPUS:78650252432
SN - 0733-9399
VL - 137
JO - Journal of Engineering Mechanics
JF - Journal of Engineering Mechanics
IS - 1
M1 - 004101QEM
ER -