Hydrodynamic characteristics of undular tidal bores over varying topography based on a non-hydrostatic wave model

Tidal bores are highly unsteady flow phenomena that commonly occur in estuarine and riverine systems with strong tidal forcing and gentle bed slopes, exerting significant impacts on local hydrodynamics and hydraulic structures. Understanding their propagation and transformation mechanisms over complex terrains is essential for both theoretical research and engineering applications. In this study, the non-hydrostatic wave model was employed to investigate the propagation and evolution characteristics of undular tidal bores over varying topography. Through carefully designed numerical experiments, the effects of bore height, pre-bore water depth, and bed slope on the hydrodynamic behavior of undular tidal bores were systematically analyzed. The results indicate that bore height and pre-bore water depth exert a pronounced control on the hydrodynamic characteristics of undular tidal bores, whereas, for the range of conditions considered, variations in bed slope only have a secondary influence on the overall bore propagation. In contrast, introducing a non-uniform bed with a local step or bar over an otherwise flat reach leads to a significant local increase in bore height and in the maximum water level, with the spatial variability of the maximum free surface elevation along the channel reaching up to 37.2% in the most undular case. As the bore height increases from 0.35 to 0.65 m and the pre-bore water depth decreases from 2.5 to 1.8 m, the tidal range across the slope becomes larger, accompanied by noticeable increases in both surface velocity and depth-averaged velocity and by an enhancement of bore celerity before the slope, followed by local deceleration over the incline. Changes in the local bed slope from 1:1 to 1:9 modify the peak bore height by no more than about 2.0%, with an average difference of only 0.4%. The findings of this study enhance the understanding of undular tidal bore dynamics over non-uniform beds and provide a scientific basis for the hydraulic design and safety assessment of in-channel structures in tidal river reaches.