Velocity Profile in Steady Flow with Submerged Flexible Vegetation Based on Multi-Factor-dependent Drag Coefficient

Flexible submerged vegetation plays a pivotal role in ecosystem. Understanding the complex impact of flexible vegetation bending on flow drag is crucial. The wide variability in drag coefficients within flexible vegetation poses challenges in accurately predicting flow drag. In this paper, the developed prediction model of velocity profile based on multi-factor-dependent drag coefficient is derived based on Euler-Bernoulli beam assumption, dual-layer averaged velocity model and the relationship between the averaged inclination angle of bent vegetation and Cauchy number. This model makes it possible to calculate the drag coefficients and velocity profiles at the same time, instead of using an assumed constant drag coefficient, and the application of this prediction model is highly favorable with experimental data. Meanwhile, new function of the depth-averaged drag coefficient applicable to submerged and emergent vegetation are presented, describing its relationship with the deformation angle of canopy, Reynolds number, submergence and water depth. The result shows that the drag coefficients for the same vegetation are smaller at higher submergence and Reynolds number. The findings of this study may provide valuable insights into the variability of drag coefficients and the flow structure with submerged flexible vegetation, and being applicable for the restoration and management of freshwater ecosystems.