A method for modeling the lateral distributions of depth-averaged velocities behind an emergent vegetation patch

•A method for modeling the lateral distributions of depth-averaged velocity behind an emergent vegetation patch is provided.•The model incorporates bed friction, vegetation-induced resistance, secondary flow effects, and lateral momentum exchange.•The influence of secondary flow term on the lateral distributions of depth-averaged velocity is evaluated.•Some modeling insights for those with limited experience are offered. Aquatic vegetation provides ecological, hydrological, and aesthetic functions for rivers, and measuring velocity in vegetated channels is essential for river management. The paper presents a method for modeling the lateral distributions of depth-averaged velocities behind an emergent vegetation patch. Based on SKM, this approach divides the channel behind an emergent vegetation patch into pseudo-vegetation and free-flow regions, offering analytical solutions for the depth-averaged velocities in these two regions. The model incorporates several critical parameters, including the Darcy–Weisbach coefficient, lateral dimensionless eddy viscosity, drag force coefficient, and secondary flow coefficients. These coefficients are associated with bed friction, vegetation-induced resistance, secondary flow effects, and lateral momentum exchange, respectively, affecting the depth-averaged velocities. A comparison with published experimental data validates that the proposed model can predict the lateral distributions of depth-averaged velocities behind an emergent vegetation patch. A steady wake section exists behind an emergent vegetation patch for low-flow blockage. In the steady wake section, the secondary flow coefficients in pseudo-vegetation and free-flow regions remain relatively constant. Upon exiting the stable wake section, the secondary flow coefficient in the pseudo-vegetation region decreases with increasing distance from an emergent vegetation patch, and it in the free-flow region increases with increasing distance from an emergent vegetation patch. A sensitivity analysis of drag coefficient and secondary flow coefficients suggests that secondary flow coefficient in the free-flow region has a more significant effect on the lateral distributions of depth-averaged velocities compared to drag coefficient and secondary flow coefficient in the pseudo-vegetation region.