Semi‐Analytical Models for Predicting the Maximum Longitudinal Flow Velocity in the Confluence Channel

In a channel confluence, different hydrodynamic characteristics can significantly affect the flow structure. As the main and tributary flow converges at the confluence, they are constrained by the recirculation zone, resulting in streamline contraction and an increase in flow velocity, thereby creating a zone of maximum velocity adjacent to the maximum width of the recirculation zone. The maximum flow velocity governs pollutant transport about a confluence and also influences bed erosion; thus, an accurate determination of the maximum flow velocity is crucial. In the present study, a statistical methodology was applied to validate the feasibility of substituting the maximum flow velocity at the widest section of the recirculation zone with the longitudinal maximum flow velocity. Two distinct models were formulated to address the transition between two mixing modes in the shear layer. In the wake mode, the two-control volume approach was applied, using the lowest velocity within the shear layer as a boundary to partition the contracted flow into two control volumes. In the mixing-layer mode, the contracted flow was treated as a single control volume. Those semi-analytical models were validated using 3D numerical results and experimental data collected in laboratory-scale confluence. The validation results demonstrate that both the proposed models could be applied to their respective shear layer modes to accurately predict the maximum longitudinal flow velocity.