Laboratory Test of Second Log-Wake Law for Effects of Ice Cover and Wind Shear Stress on River Velocity Distributions

The second log-wake law is a small change of the first log-wake law (or Coles' log-wake law) for turbulent pipe and symmetric channel flows but makes a big difference in modeling wall-bounded turbulent flows. It has been extended to antisymmetric Couette channel flows theoretically and open channel flows empirically. A recent study of natural river flows indicates that a river velocity distribution is a superposition of a complete antisymmetric channel flow solution due to water surface shear stress and a half symmetric channel flow solution due to gravity. The objective of this research then is to test this hypothesis under the effects of ice cover and wind-induced water surface shear stress with laboratory experiments. To this end, a special experimental device was designed to simulate the effects of gravity, ice cover, and wind-induced shear stress. With this device, 236 vertical distributions of streamwise velocity were measured with a particle image velocimetry (PIV) technique under various simulated conditions of ice cover and water surface shear stress, 75 of which are plotted in this paper. All measured velocity distributions are characterized by a bowl-shaped velocity distribution with a dip phenomenon, a typical boundary layer velocity distribution, or an S-shaped velocity distribution with an inflection. All of these three distribution patterns are well described by the second log-wake law, which also agrees with real-world river flow data. Based on the second log-wake law, an innovative three-point method is proposed for river discharge measurements.