Velocity distribution and sediment transport in rivers

A theoretical analysis of velocity profiles in sediment-laden flows is presented by means of Prandtl-Karman mixing length theorem. The study shows that the upward velocity of liquid-phase caused by settling sediment leads to the invalidity of log-law and Rouse equation. The theoretical analysis takes into account the upward velocity and shows: (1) the mean velocity in sediment-laden flows follows the log-law, but Karman constant reduces in the main flow region; (2) sediment concentration reduces the mixing length of fluid particles; (3) flow resistance reduces with the presence of sediment concentration; and (4) the sediment concentration profile deviates from the well know Rouse equation. The experimental data agree well with the obtained equations that are derived on the basis of non-zero wall velocity. It is found that the wall-normal velocity should not be neglected in density gradient flows because it induces greater wall-normal velocity than that in pure water flows.