Influence of Channel Aspect Ratio and Curvature on Flow, Secondary Circulation, and Bed Shear Stress in a Rectangular Channel Bend

Flow within an alluvial channel bend is significantly affected by channel geometry, including curvature ratio (bend radius/channel width, $R/B$) and aspect ratio (channel width/flow depth, $B/H$). High curvature bends ($R/B\le 3$) can experience substantially more erosion than milder curvature bends. This study employs a three-dimensional Reynolds-Averaged Navier-Stokes (RANS) model to investigate the effects of curvature ratio and aspect ratio on bend flow with respect to a high curvature ($R/B=1.5$) base case in a 135° bend. Experimental data are used to validate the RANS model predictions for the high curvature base case with a flat bed (FB) and an equilibrium deformed bed (DB). Five curvature ratios (1.5, 3, 5, 8, and 10) and four aspect ratios (5.00, 6.67, 9.09, and 12.50) are investigated. Results show that a decrease in $R/B$ or $B/H$ for the FB cases results in a strong increase in total circulation of the regions associated with the primary cell of cross-stream circulation (${\mathrm{\Gamma }}_{+}$), an increase in maximum bed shear stress, and an increase in the contribution of the cross-stream component to the total magnitude of bed shear stress. The values of $R/B$ and $B/H$ also affect the structure of the cross-stream flow. The primary cell of cross-stream circulation splits into two clockwise-rotating cells at low $R/B$ values and the cell situated closer to the inner wall induces strong ejections of vorticity. At high $R/B$ values, a secondary counter-clockwise rotating cell forms at the outer bank. At lower $B/H$ values, the primary cell splits into two clockwise-rotating cells. This study shows that the position and size of regions of high bed shear stress, and thus the capacity of the flow to entrain sediment, depend strongly on bend curvature.