Application of the Modified Log-Wake Law in Open-Channels

The modified log-wake law, which was developed for turbulent boundary layers and pipe flows, is extended to turbulent flows in open-channels. 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. A procedure to determine the four model parameters from velocity measurements while keeping κ = 0.41 is presented. 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 fit the velocity dip phenomenon in openchannels where the conventional log-wake law fails.