Modified Second Log-Wake Law for Mean Velocity Distributions Along Vertical and Transverse Directions in Smooth Open-Channel Turbulent Flows With Application to Natural Rivers

This research proposes a generalized model, the modified second log wake law, for the time-averaged primary flow velocity which incorporates the free surface effects (dip and inflection phenomenon) and the secondary current effects. This model is applicable for the cross-sectional velocity distribution in an open channel flows and vertical and transverse velocity distributions in open channels and symmetric channel flows. The study modifies the second log wake law by removing its limitation of the sine integral wake law that requires numerical integration. A modified wake function suggests a major change in the model by making it easily computable. At first the model is proposed for velocity distribution at the channel centerline. Further, it is extended to get the velocity distribution in the whole cross-sectional plane in an artificial open channel and for velocity distribution at different sections of natural rivers. These proposed models are validated with large range of experimental data sets and river data from the Missouri, Mississippi, Rhine, Yangtze, Minjiang and Baitarani Rivers, Conveyance channels and more improved results are achieved. Besides this, these models are also fully compared with previous velocity laws and a reasonably good agreement is obtained. The 2D model is also validated for velocity distribution along the transverse direction in experimental channels and natural rivers and for both the cases results are satisfactory. The model is also validated for velocity distribution from pipe invert to obvert in pipe flows and a good agreement is achieved. Finally, the models for the depth averaged velocity along transverse direction is also proposed and it is found that proposed formulae can reproduce well the depth averaged velocity distributions.