Abstract
An ordinary differential equation (ODE) for velocity distribution in open channel flows is presented based on an analysis of the Reynolds-averaged Navier–Stokes equations and a log-wake modified eddy viscosity distribution. This proposed equation allows to predict the velocity-dip-phenomenon, i.e. the maximum velocity below the free surface. Two different degrees of approximations are presented, a semi-analytical solution of the proposed ODE, i.e. the full dip-modified-log-wake law (fDMLW-law) and a simple dip-modified-log-wake law (sDMLW-law). Velocity profiles of the two laws and the numerical solution of the ODE are compared with experimental data. This study shows that the dip correction is not efficient for a small Coles' parameter, accurate predictions require larger values. The sDMLW-law shows reasonable agreement and seems to be an interesting tool of intermediate accuracy. The fDMLW-law, with a parameter for dip-correction obtained from an estimation of dip positions, provides accurate velocity profiles.
Acknowledgements
The author would like to thank Dr Junke Guo, University of Nebraska, Lincoln, for having provided the experimental data files.