Drag Coefficient of Emergent Vegetation in a Shallow Nonuniform Flow over a Mobile Sand Bed

Widely distributed in natural rivers and coasts, vegetation interacts with fluid flows and sediments in a variable and complicated manner. Such interactions make it difficult to predict associated drag forces during sediment transport. This paper investigates the drag coefficient for an emergent vegetated patch area under nonuniform flow and mobile bed conditions, based on an analytical model solving the momentum equation following our previous work (Zhang et al., 2020, ). Emergent vegetation was modeled with rigid cylinders arranged in staggered arrays of different vegetation coverage & empty;. Laboratory flume tests were conducted to measure variations in both the water and bed surfaces along a vegetated patch on a sand bed. Based on the experimental and theoretical analyses, a dimensionless drag model integrating both terms of flow properties and bed effects is proposed to predict the drag coefficient Cd over a mobile bed. The calculated values of Cd exhibit two different trends, that is, nonmonotonically or monotonically increasing along the streamwise direction, due to the combined effect of water surface gradient and bed slope. The morphodynamic response of the mobile bed to nonuniform flow manifests as an evolution in the bed slope within the vegetated patch. Ongoing scouring directs the flow's energy toward overcoming the rising Cd and bed slope, leading to a relatively stable stage with a low sediment transport rate. This study advances the existing understanding of the drag coefficient's role over a mobile bed within nonuniform flows. It also enhances the applicability of vegetation drag models in riverine restoration. The drag exerted by vegetation on a riverbed dictates the sediment transport rate with important implications for river morphological evolution. Predicting vegetation drag in nonuniform flow based on the bed characteristics of mobile sand bed conditions poses both theoretical and practical challenges. The implications of this endeavor include the formulation of predictive models for drag and a deeper understanding of the influence of gradually varied flow conditions in rivers. Through both experimental and theoretical investigations, this paper reveals that the drag coefficient exhibits varying patterns along the streamwise direction within the vegetated patch over a mobile sand bed. These patterns manifest in two distinct forms: a steady increase or a parabolic shape, wherein the coefficient initially rises before subsequently decreasing. This contrasts with prior studies on fixed beds, where the drag coefficient consistently follows a parabolic distribution in the streamwise direction. The discrepancy is attributed to the distinct physical contributions of pressure, advection, and bed friction to the drag coefficient. This study provides valuable insights into the importance of flow nonuniformity on vegetation drag, aiding in the prediction of backwater profiles in vegetated flows over a mobile bed. Furthermore, it facilitates modifications to sediment transport within vegetated patches. Vegetation drag in nonuniform flow over a mobile sand bed is explored using the momentum equation Drag coefficient in nonuniform flow over a mobile bed exhibits either a parabolic or a monotonic increase along the streamwise direction Water surface gradient and bed slope contribute to the flow nonuniformity, collectively influencing the variability of the drag coefficient