Experimental and theoretical study of density jumps on smooth and rough beds

摘要

Hydraulic jumps in density currents are technically referred to density jumps. These jumps significantly influence the dynamic and quality characteristics of the gravity currents. The density jump is studied theoretically and experimentally in this study by considering the bed roughness. Experiments were performed in a rectangular laboratory flume (0.4 m width; 0.9 m depth; 8.3 m length). Four rough beds comprised of closely packed gravel particles glued onto the horizontal part of the bed were examined. For both smooth and rough beds, a simple relationship was obtained for estimating the conjugate depth ratio as a function of the relative roughness and the upstream densimetric Froude number. The conjugate depth ratio was found to decrease with increasing relative roughness. The results also indicated that, if the entrainment ratio is specified, the minimum value of the upstream densimetric Froude number increases with increasing relative bed roughness. An equation for calculating the maximum possible value of the relative roughness was also determined. The spatial development of the density current for smooth beds was analysed in both super-critical and sub-critical flow regimes. Good similarity collapses of velocity and concentration profiles were obtained for the super-critical section just upstream of the jump. The concentration distributions located just downstream of the jump, however, exhibited a large scattering of measured data, especially near the bed. It was found that this scattering decreases with the distance from the end of the jump. The results of the experimental runs also indicated that, at a distance about nine times the post-jump current thickness from the end of the jump, the non-dimensional vertical profile of mean velocity has a shape similar to that at the pre-jump section. A new reliable relationship was also proposed for calculating the local velocity inside both the wall and jet regions.