Turbulent flows over canopies of rigid elements with different geometries, spacings and Reynolds numbers are investigated to identify and characterise different canopy density regimes. In the sparse regime, turbulence penetrates relatively unhindered within the canopy, whereas in the dense regime, this penetration is limited. A common measure of canopy density is the ratio of frontal area to bed area, the frontal density λf . While effective for conventional vegetation canopies with no preferential orientation, we observe that λf does not accurately predict the density regime for some less conventional canopy topologies, suggesting that it does not necessarily encapsulate the physics governing the canopy density. To address this, we adopt a direct approach that quantifies the degree of penetration of the overlying turbulence into the canopy. We propose density metrics based on the position and extent of individual flow eddies, in particular those of intense Reynolds shear stress u′v′. We use these metrics to analyse a series of direct numerical simulations for both isotropic- and anisotropic-layout canopies across a range of frontal densities λf ≈ 0.01-2.04, heights h+ ≈ 44-266, element width-to-pitch ratios w/s ≈ 0.06-0.7, and Reynolds numbers Reτ ≈ 180-2000. Our results show that canopies with elements closely packed in the streamwise direction but large spanwise gaps allow for significant turbulence penetration, and thus appear sparser compared to isotropic or spanwise-packed canopies with the same λf . When the spanwise gap is fixed, turbulence penetration remains similar and largely independent of the streamwise pitch and gap between elements. As the spanwise gap increases, eddies penetrate deeper and more vigorously into the canopy. We also show that canopy density and turbulence penetration are Reynolds-number-dependent. A canopy with a fixed geometry can exhibit a dense-like behaviour at low Reτ , but enhanced turbulent penetration as Reτ increases. Our results suggest that the penetration of overlying eddies depends essentially on the spanwise gap between canopy elements and its relative size compared to the typical width of the overlying eddies. Turbulence penetrates easily into the canopy when the spanwise gap is larger than the eddy size, and is essentially precluded from penetrating in the opposite case. A penetration length can then be defined that is of the order of the spanwise gap or the eddy size, whichever is smaller. If the penetration length is small compared to the canopy height, the canopy behaves as dense; if it is comparable, the canopy has an intermediate behaviour; and if it is approximately equal or larger than the canopy height, the eddies penetrate all the way to the canopy bed and the canopy behaves as sparse.
Chen et al. (Wed,) studied this question.