Velocity and Turbulence Distribution in Unsteady Open-Channel Flows

Abstract

Unsteady flow properties are experimentally studied in an open channel with a rough bed. A recently developed acoustic Doppler velocity profiler (ADVP) is used to obtain instantaneously the flow profiles. From these measurements, using the Fourier components method, the mean velocities, the turbulence intensities and the Reynolds-stress profile, are obtained. Thirty-three different hydrographs are experimentally investigated. The experimental results show several things. First, unsteady flow can be characterized by the overall unsteadiness parameter, Γ\DHG\N, and by the longitudinal pressure-gradient parameter, β\Du\N. Second, the hydrographs investigated are complete dynamic waves, where the time sequence of \IU\N, \IQ\N, and \ID\N is respected, resulting in the looping rating curves. Third, the distribution of the horizontal velocities, \Iū(y)\N is given by the log law with \IB\N\Dr\N ≅ 8.5 ± 15% in the inner region, being almost independent of the unsteadiness, and by the Coles’ law in the entire region where the wake-strength parameter, Π, depends (inconclusively) on the β\Du\N-value. Fourth, the distribution of the vertical velocities, v¯(\Iy\N), being almost always negative, could be explained with a theoretical relation. Fifth, during the passage of a hydrograph, the turbulence intensities (root-mean-square values) and the Reynolds stress in the rising branch are larger than in the falling branch. Finally, using the equation of Reynolds, a theoretical expression for the Reynolds-stress distribution could be obtained, which compares reasonably well with the measured data.