Analytical and experimental studies of plant-flow interaction at multiple scales

Abstract

Across scales ranging from individual blades to river reaches, the interaction between water flow and vegetation has important ecological and engineering implications. At the reach-scale, vegetation is often the largest source of hydraulic resistance. Based on a simple momentum balance, we show that the resistance produced by vegetation depends primarily on the fraction of the channel cross-section blocked by vegetation. For the same blockage, the specific distribution of vegetation also plays a role; a large number of small patches generates more resistance than a single large patch. At the patch-scale, velocity and turbulence levels within the canopy set water renewal and sediment resuspension. We consider both steady currents and wave-induced flows. For steady flows, the flow structure is significantly affected by canopy density. We define sparse and dense canopies based on the relative contribution of turbulent stress and canopy drag to the momentum balance. Within sparse canopies, velocity and turbulent stress remain elevated and the rate of sediment suspension is comparable to that in unvegetated regions. Within dense canopies, velocity and turbulent stress are reduced by canopy drag, and the rate of sediment resuspension is lower. Unlike steady flows, wave-induced oscillatory flows are not significantly damped within vegetated canopies. Further, our laboratory and field measurements show that, despite being driven by a purely oscillatory flow, a mean current in the direction of wave propagation is generated within the canopy. This mean current is forced by a wave stress, similar to the streaming observed in wave boundary layers. At the blade-scale, plant-flow interaction sets posture and drag. Through laboratory experiments and numerical simulations, we show that posture is set by a balance between the hydrodynamic forcing and the restoring forces due to blade stiffness and buoyancy. When the hydrodynamic forcing is small compared to the restoring forces, the blades remain upright in flow and a standard quadratic law predicts the relationship between drag and velocity. When the hydrodynamic forcing exceeds the restoring forces, the blades are pushed over in steady flow, and move with oscillatory flow. For this limit, we develop new scaling laws that link drag with velocity.