Exploration of a depth optimization method for the water–sediment flow field around spur dikes in sediment-laden rivers

Spur dikes are crucial hydraulic structures that play a vital role in maintaining riverbank stability and regulating flow patterns. However, in rivers with high sediment concentrations, the complex coupling between water and sediment dynamics around spur dikes often reduces hydraulic efficiency and compromises structural stability. Previous studies on the design optimisation of spur dikes have been constrained by the complexity of hydraulic boundary conditions, subjective parameter selection, and dependence on empirical assumptions, thereby impeding the determination of optimal structural configurations. This study is the first to apply advanced adjoint optimisation algorithms – originally developed in the field of aerodynamics – in combination with two-phase flow theory for the numerical optimisation of hydraulic structures. By computing the sensitivity functions, the proposed method iteratively and simultaneously solves the governing and adjoint equations, thus addressing the aforementioned constraints and enabling refined optimisation of the water – sediment flow structure in spur dike systems. Experimental observations validate both the reliability and accuracy of the numerical simulation results. The results indicate that the application of adjoint optimisation methods to refine the geometric configuration of conventional spur dikes can effectively reconstruct hydrodynamic flow fields and modify the corresponding vortex structures. The optimised spur dikes generate enlarged low-velocity, recirculating, and vortex-dominated regions, which promote sediment deposition, thereby substantially improving sediment deposition efficiency and enhancing overall riverbank stability. Therefore, adjoint optimisation algorithms offer an innovative theoretical foundation for high-level optimisation design and efficient application across a wide range of hydraulic engineering practices.