Velocity Distribution and Dip-Phenomenon in Smooth Uniform Open Channel Flows

This paper investigates the mechanism of the dip phenomenon whereby the location of the maximum velocity appears below the free surface vis-à-vis the secondary currents in open-channel flows. It is found that the classical log law gives a good description of the velocity distribution in the inner region if the local shear velocity is introduced into the dimensionless distance, i.e., u*(z)y/ν. In the outer region, where the maximum velocity occurs at some distance below the free surface in a vertical plane, it is found that the velocity deviation from the log law is linearly proportional to the logarithmic distance ln(1-y/h) from the free surface. To this end, the study proposes a dip-modified log law for the velocity distribution in smooth uniform open channel flows. This new law is capable of describing the dip phenomenon, and is applicable to the velocity profile in the region from the near bed to just below the free surface, and transversely, from the center line to the near-wall region of the channel. The dip-modified log law consists of two logarithmic distances, one from the bed ln(u*(z)y/ν), and the other from the free surface ln(1-y/h), respectively, and a dip-correction factor α. The latter is the only parameter that needs to be determined and an empirical equation for α has been proposed in this study. The dip-modified log law has been verified using published experimental data for smooth rectangular open channels and the agreement between the measured and computed velocity profiles is good.