Hydraulic characteristics and control mechanism of wake-induced free-surface oscillations at inverted-siphon outlets with diversion piers

Wake-induced free-surface oscillations can occur in confined multi-bay outlet flows when coherent vortex shedding from blunt pier tails interacts with the free surface. This study investigates how triangular diversion piers suppress these oscillations at inverted-siphon outlets by integrating prototype observations, generalized physical-model tests, and three-dimensional numerical simulations. The results indicate that, under high-velocity outlet conditions (Reynolds number > 6.1 × 106) in the absence of diversion piers, boundary-layer separation and periodic Kármán wake-vortex shedding occur behind the gate-pier tails. This continuously excites the free surface, producing abnormal oscillations. In contrast, the diversion piers efficiently suppress the wake-induced free-surface response by disrupting the primary vortex-formation region, contracting the recirculation zone, reducing wake coherence, and weakening wake-to-surface forcing. When triangular diversion piers with λ = 3 (λ denotes the ratio of diversion-pier length to gate-pier width) are installed, the oscillation amplitudes in the middle and side bays decrease from 0.537 and 0.482 m to 0.216 and 0.186 m, corresponding to reductions of 59% and 61%, respectively. As λ increases from 0 to 5, both the recirculation zone and the high-vorticity region progressively contract, and the amplitude drops rapidly before approaching convergence. Predictive formulas for water-level oscillation amplitude were developed by incorporating λ, diffusion angle, discharge, and water depth, achieving an average coefficient of determination (R2) of 0.92 and root mean square errors below 0.04 m. These findings elucidate the water-level oscillation mechanism and its control by triangular diversion piers, thereby supporting the engineering design and operation of inverted-siphon outlets.