Predicting the width of the recirculation zone at an ice-covered confluence

In a confluence channel, the recirculation zone, due to its relatively low flow velocity, might be a primary site for pollutant accumulation, sediment deposition, and aquatic organism activity. While the maximum width of the recirculation zone in a confluence can be estimated, models to predict the width of the recirculation zone in an ice-covered confluence are lacking. A one-dimensional semi-analytical model was developed based on the momentum equation, incorporating a ratio function to represent longitudinal acceleration induced by hydrostatic pressure gradients and shear stresses. An empirical expression for this ratio function was obtained via polynomial fitting. Finally, the model was validated using three-dimensional numerical results and laboratory-scale confluence experimental data, demonstrating its ability to accurately quantify variations in the depth-averaged width of the recirculation zone.