Reynolds Stress Anisotropy in Open-Channel Flow

This paper reports the results of an experimental study characterizing turbulence and turbulence anisotropy in smooth and rough shallow open-channel flows. The rough bed consists of a train of two-dimensional transverse square ribs with a ratio of the roughness height $\left(k\right)$ to the total depth of flow $\left(d\right)$ equal to 0.10. Three rib separations $\left(p/k\right)$ of 4.5, 9, and 18 were examined. Here, $p$ is the pitch between consecutive roughness elements and was varied to reproduce the classical condition of $d$ - and $k$ -type roughness. For each case, two-component velocity measurements were obtained using a laser Doppler velocimetry system at two locations for $p/k=4.5$ and 9: on the top of the rib and above the cavity, and an additional location for $p/k=18$ . The measurements allow examination of the local variations of the higher-order turbulent moments, stress ratios as well as turbulence anisotropy. Large variations of the turbulence intensities, Reynolds shear stress, turbulent kinetic energy and turbulence production are found for $y_1<3k$ . In this region, the flow is more directly influenced by the shear layers from the preceding ribs. The higher-order moments appear to be similar for all rough surfaces beyond $y_1\approx 7k$ . In the outer layer $\left(y_1>3k\right)$ , all higher-order turbulent moments for the $k$ -type roughness show a substantial increase due to the complex interactions between the roughness and the remnants overlying shear layers shed from succeeding ribs. Analysis of the components of the Reynolds stress anisotropy tensor shows that at $p/k=18$ , the flow at $y_1<5k$ tends to be more isotropic which implies that for this particular case, the effect of the roughness density could also be important. On the smooth bed, at the shallower depths, the correlation coefficient near the free surface increases and turbulence tends to become less anisotropic.