Analytical Study of the Bed Roughness and Entrainment Ratio of Saline Density Currents on Hydraulic Jump

Density current is produced due to a density contrast with the ambient fluid. This density difference can result from dissolved solids, suspended materials, temperature, etc. Density jumps significantly influence the characteristics of the gravity currents and the ambient fluid (e.g., velocities and concentrations). In this paper, the density jump is studied analytically by considering the bed roughness and entrainment ratio. For both smooth and roughened beds, a generalized relationship was obtained for estimating the conjugate depth ratio as a function of the upstream densimetric Froude number, the entrainment ratio, and the relative roughness. Moreover, various equations for calculating the maximum possible value of the relative roughness, the minimum possible value of the prejump densimetric Froude number, and the maximum possible value of the relative roughness were proposed. The minimum possible value of the conjugate depth ratio was determined. It was found that both the conjugate depth ratio and the length of the roller zone decrease as the bed roughness increases. Moreover, as the entrainment ratio increases, the ratio may also decrease, or may initially increase and then decrease. Finally, a relationship was obtained for estimating the minimum possible value of the obstacle height as a function of the conjugate depth ratio.