Effects of Secondary Currents on Turbulence Characteristics of Supercritical Open Channel Flows at Low Aspect Ratios

Abstract

In this paper, we present secondary current effects on the turbulence characteristics of supercritical narrow open channel flows over a smooth fixed bed. The main hydraulic parameters are low channel width to flow depth ratios varying between 1 and 2, and Froude numbers (F) ranging from 2 to 4. Detailed profiling of instantaneous streamwise and vertical flow velocities was conducted in a laboratory flume using a 2D laser Doppler anemometry. The cross-sectional distributions of mean flow velocities, turbulence intensities, Reynolds, and bed shear stresses were obtained from the measurements. The mean streamwise and vertical flow velocity distributions reveal that four pairs of secondary current cells are formed: a pair of well-developed free-surface vortices near the water surface, a pair of bottom vortices near the bed, and two pairs of mid-vortices between the free-surface and bottom vortices. These secondary currents cause bulging of the contour lines of the streamwise velocities with respect to the water surface and the bottom corner bisectors resulting in an undulated pattern of the mean velocity distribution across the cross-section. Furthermore, they cause the velocity dip phenomenon, i.e., the maximum flow velocity occurs well below the surface, and redistribute the Reynolds and bed shear stresses in transverse direction. The results demonstrate that decreasing the aspect ratio increases the strength of the secondary currents causing a significant change in flow patterns with larger free-surface vortices compared to the bottom vortices. Compared to the aspect ratio effect, the Froude number only slightly impacts the flow characteristics as a result of flow non-uniformity. For all investigated aspect ratios and Froude numbers, bed shear stresses are concentrated at the flume center, and on average 5 to 10% higher than their mean values. The modified wake-log-law holds both in the inner and outer regions, matching well with the experimental data for all test conditions. The present findings are discussed with literature data, and their impact on engineering applications is demonstrated.