  Turbulent flows within and over sparse canopies are investigated using direct
numerical simulations. We focus on the effect of the canopy on the background
turbulence, the part of the flow that remains once the element-induced flow is
filtered out. In channel flows, the distribution of the total stress is linear
with height. Over smooth walls, the total stress is only the `fluid stress'
$\tau_f$, the sum of the viscous and the Reynolds shear stresses. In canopies,
in turn, there is an additional contribution from the canopy drag, which can
dominate within. We find that, for sparse canopies, the ratio of the viscous
and the Reynolds shear stresses in $\tau_f$ at each height is similar to that
over smooth-walls, even within the canopy. From this, a height-dependent
scaling based on $\tau_f$ is proposed. Using this scaling, the background
turbulence within the canopy shows similarities with turbulence over smooth
walls. This suggests that the background turbulence scales with $\tau_f$,
rather than with the conventional scaling based on the total stress. This
effect is essentially captured when the canopy is substituted by a drag force
that acts on the mean velocity profile alone, aiming to produce the correct
$\tau_f$, without the discrete presence of the canopy elements acting directly
on the fluctuations. The proposed mean-only forcing is shown to produce better
estimates for the turbulent fluctuations compared to a conventional,
homogeneous-drag model. The present results thus suggest that a sparse canopy
acts on the background turbulence primarily through the change it induces on
the mean velocity profile, which in turn sets the scale for turbulence, rather
than through a direct interaction of the canopy elements with the fluctuations.
The effect of the element-induced flow, however, requires the representation of
the individual canopy elements.
