A phenomenological model for predicting bedload transport in vegetated channels using near-bed turbulent kinetic energy

Accurate prediction of bedload transport in vegetated riverbeds is critical for wetland protection and ecological restoration. This study develops a novel turbulence-based theoretical model for bedload transport in vegetated flows. The near-bed turbulent kinetic energy (TKE) is derived from the phenomenological theory of turbulence through quantitative analysis of multiscale turbulent eddy structures. For rigid vegetation, the proposed model provides a unified framework for estimating near-bed TKE across diverse configurations, including uniform distribution, patchy clusters, random arrangements with variable diameters, and vertically heterogeneous morphologies, improving upon previous empirical superposition approaches. The predicted near-bed TKE exhibits a robust correlation with measured bedload transport rates compiled from 358 experimental datasets, supporting its validity as a physically meaningful predictor. Following the operators of formulas developed for unvegetated beds, a refined TKE-based bedload transport formulation for vegetated flow is derived using symbolic regression, calibrated on datasets with uniformly distributed cylindrical vegetation. Validation demonstrates that the proposed transport model maintains high accuracy while effectively generalizing to more complex rigid vegetation scenarios. Compared to existing literature models, our formulation shows improved predictive precision and broader applicability.