Three-dimensional hydrodynamics of a suspended cylindrical canopy patch

Three-dimensional large eddy simulations (LES) are carried out to determine the local hydrodynamics of a suspended canopy patch impinged by a uniform incident flow. The patches are circular (with bulk diameter $\mathrm{D})$ and are made of rigid circular cylinders (height $\mathrm{h}$ and diameter $\mathrm{d})$. Four different patch densities ($\mathrm{\phi =}\mathrm{N}_{\mathrm{c}}\mathrm{d}^{\mathrm{2}}\mathrm{/}\mathrm{D}^{\mathrm{2}})$ and four different patch aspect ratios ($\mathrm{AR=h/D})$ are considered by varying the number of cylinders in the patch ($\mathrm{N}_{\mathrm{c}})$ and the height of the patch ($\mathrm{h})$, respectively. Based on a volumetric-flux budget through the patch surface, the bleeding dynamics inside and in the vicinity of the patch was found to be controlled not only by $\mathrm{\phi }$, but also remarkably by $\mathrm{AR}$. The relative longitudinal bleeding normalized by the total flux entering the patch ($\hat{Q}_{\mathrm{x}}\mathrm{=}\mathrm{Q}_{\mathrm{x}}\mathrm{/}\mathrm{Q}_{\mathrm{influx}})$ was observed to be inhibited by increasing $\mathrm{\phi }$ but insensitive to the variation of $\mathrm{AR}$; the relative lateral bleeding ($\hat{Q}_{\mathrm{y}}\mathrm{=}\mathrm{Q}_{\mathrm{y}}\mathrm{/}\mathrm{Q}_{\mathrm{influx}})$ increases with either increasing $\mathrm{\phi }$ or $\mathrm{AR}$; and the relative vertical bleeding ($\hat{Q}_{\mathrm{z}}\mathrm{=}\mathrm{Q}_{\mathrm{z}}\mathrm{/}\mathrm{Q}_{\mathrm{influx}})$ increases with increasing $\mathrm{\phi }$ while decreases with increasing $\mathrm{AR}$. However, for patches with a constant $\mathrm{\phi }$, an increase in $\mathrm{AR}$ contributes to enhance the absolute strength of vertical bleeding ($\mathrm{Q}_{\mathrm{z}})$ at the patch free end.