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 open-channel turbulence. Like those in pipes and boundary layers, turbulent velocity profile 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 profile of cross-section of the Mississippi River. In particular, it can well model the velocity dip phenomenon in open-channels where the conventional log-wake law fails.