Bed-load transport in flow with submerged vegetation: From vegetation-mediated energy cascade to its effect on sediment movement

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Abstract
Bed-load transport capacity in vegetated open-channel flow is critical for ecological river management. However, accurate prediction of bed-load transport under submerged vegetation conditions remains challenging due to difficulties in determining bed shear stress. Drawing on the phenomenological theory of turbulence, this study derived an equation for bed shear stress for flows with submerged vegetation and integrated it with the bed-load transport formula originally developed for unvegetated flows to establish a predictive model applicable to both rigid and flexible submerged vegetation. The model involves the deflection height of flexible vegetation, which has conventionally been calculated via iteration and thus impairs model practicality. This study innovatively employs genetic programing to develop an explicit predictor for deflected height, whose integration into the bed-load transport framework markedly enhances the model's applicability. The proposed bed-load transport model elucidates distinct response regimes. Under a constant energy slope, the bed-load transport rate increases with submergence ratio but decreases with vegetation density, whereas these trends are reversed under constant flow velocity. Additionally, under identical hydraulic conditions, bed-load transport rate is lower in flexible vegetation than in rigid vegetation, indicating that flexible vegetation features better performance in controlling bed erosion. The model thus provides a robust tool for sediment management in river restoration projects.
Funding Information
  • National Natural Science Foundation of China (12272281)
  • National Natural Science Foundation of China (U2340216)
  • National Natural Science Foundation of China (52509110)
  • China Postdoctoral Science Foundation (2025M773141)
  • Postdoctor Project of Hubei Province (2025HBBSHCXB019)
  • Postdoctoral Fellowship Program of CPSF (GZB20250724)

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