Applications of Second Log-Wake Law for Turbulent Velocity Distributions in Laboratory Flumes and Natural Rivers

Natural river velocity distributions are often studied by laboratory flume flows because of similarities of the bed shear stress effects between the two flows. Nevertheless, the velocity distributions in natural rivers are often affected by winds over water surfaces, which are often negligible in laboratory flows. The objective of this research is then to study how water surface shear stress and wind-induced turbulent mixing affect open channel velocity distributions in flume flows and natural river flows. To this end, we first introduce the recent second log-wake law from symmetric and antisymmetric channel flows to open channel flows. We then demonstrate that: (1) a laboratory flume velocity distribution is a superposition of a half symmetric channel flow solution and a half antisymmetric channel flow solution, and (2) a natural river velocity distribution is a superposition of a half symmetric channel flow solution and a complete antisymmetric channel flow solution. These solutions are confirmed by both laboratory and field data including velocity dip and inflection phenomena.