The flow around submerged canopy patches with finite sizes plays a critical role in the sediment deposition and vegetation evolution. In this study, the submerged canopy patch was modeled as a porous array with a diameter D and a height h consisting of N rigid cylinder elements with a diameter d and exposed to a fully developed turbulent open channel flow with a depth H. High-resolution numerical simulations were conducted to investigate the effects of array density (0.021 ≤ Φ = Nd²/D² ≤ 1) on mean and instantaneous flow fields and three-dimensional coherent structures by fixing the aspect ratio h/D at 1 and the submergence H/h at 2. The results showed that as the array became denser, the streamwise bleeding flow decreased while the lateral and vertical bleeding flow increased. When Φ ≥ 0.098, the group behavior of the array became significant: (1) a vertical shear layer was formed at the top of the array, and the downflow behind the array increased with Φ; (2) horseshoe vortex systems formed around the upstream base of the array; and (3) although no patch-scale vortex shedding was observed in the vorticity field in all simulated cases, there was a dominant dimensionless frequency (St_D) in the power spectrum of the lateral velocity, varying from 0.1614 to 0.1913.

Aquatic plants play a crucial role in the hydrodynamic and material transport processes within the aquatic environments due to the additional flow resistance induced by vegetation stems. In this study, high-resolution numerical experiments were performed to investigate the drag characteristics of circular vegetation patches fully immersed in a turbulent open channel flow. The submerged vegetation patch was modeled as a rigid cylinder array with a diameter D composed of N cylinder elements with a diameter d. The effects of vegetation density Φ (0.023 ≤ Φ ≤ 1) and relative diameter d/D (d/D = 0.051 and 0.072) were tested. The simulation results show that Φ and d/D affect the flow resistance exerted by the vegetation patch by modifying the bleeding flow intensity. With the increase in Φ, the drag forces acting on the individual cylinder elements decrease, whereas the total drag forces of the patch increase. The oscillation strength of the drag force of individual cylinders depends on Φ and the fixed positions within the patch. The presence of the free end of submerged cylinder array leads to enhanced wake entrainment with the increase in Φ. The drag coefficient of the submerged patch is smaller than that of the emergent patch when the dimensionless frontal area aD > 3. However, the two patches exhibit comparable drag coefficients for smaller aD values.

In this study, theoretical and experimental methods are applied to investigate streamwise velocity profiles and transverse momentum exchange in the quasi-equilibrium region in partially vegetated channels. A new eddy viscosity model is proposed to model the transverse momentum exchange in consideration of bottom turbulence, stem-scale turbulence, and turbulence induced by coherent structures. Results show that turbulence induced by coherent structures is the dominant contributor to the momentum exchange. The proposed eddy viscosity model can be well applied for different setups by varying only one proportionality constant $(\xi )$ , which is inversely proportional to the canopy drag ($C_{D}a$ ). The lateral distribution of eddy viscosity is also well predicted and shows a peak just outside the canopy. By assuming the canopy as a rough wall and setting the zero-plane displacement within the canopy to the distance of penetration width, we find that the lateral profiles of the mean streamwise velocity in the outer shear layer follow logarithmic curves. A quantitative relationship between roughness length and canopy drag ($C_{D}a$ ) is, thus, determined similar to that in turbulent rough-wall boundary layers.