Application of Modified Log-Wake Law in Open-Channels

We extend the modified log-wake law, which was developed for turbulent pipe and boundary layer flows, to turbulent flows in open-channels. Like those in pipes and boundary layers, turbulent velocity profiles in open-channels can be approximated with three components: (1) the law of the wall that results from the constant bed shear stress; (2) the law of the wake that reflects the effects of gravity, secondary currents and bed roughness; and (3) the cubic correction near the maximum velocity. The modified log-wake law compares very well with experimental data from Coleman, Lyn, Kironoto and Graf and Sarma et al. It also replicates the measured velocity profiles of the Mississippi River. In particular, it can well model the velocity dip phenomenon in open-channels where the conventional log-wake law fails.