  An ordinary differential equation 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 ordinary differential
equation, i.e. the full dip-modified-log-wake law and a simple
dip-modified-log-wake law. Velocity profiles of the two laws and the numerical
solution of the ordinary differential equation 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 simple
dip-modified-log-wake law shows reasonable agreement and seems to be an
interesting tool of intermediate accuracy. The full dip-modified-log-wake law,
with a parameter for dip-correction obtained from an estimation of dip
positions, provides accurate velocity profiles.
