Trajectory of a jet in crossflow in a channel bend

Mixing in rivers is an important issue with many applications in water quality and water resource management. Mixing of effluents with ambient river water is especially important, particularly in river bends, where secondary circulation complicates the mixing process. By comparing measured trajectories from dye tests to velocimetry data measured with an acoustic Doppler velocimeter, this paper models the trajectory of a jet in an open channel bend using a modified formula for a jet trajectory in a straight crossflow. The original formula is shown to be insufficient for modeling the trajectory in the bend. Modifications are proposed using the position of the centre of the main secondary circulation cell to account for the bend effects. In the absence of secondary circulation, the modified formula reduces to the original formula. Once the secondary circulation has developed, the proposed formula is shown to have better residuals, lower root mean squared error, and higher \(R^2\) than the original formula.