  Turbulent flows over dense canopies of rigid filaments of small size are
investigated for different element heights and spacings using DNS. The flow can
be decomposed into the element-coherent, dispersive flow, the
Kelvin--Helmholtz-like rollers typically reported over dense canopies, and the
background, incoherent turbulence. The canopies studied have spacings $s^+ =
3$--$50$, which essentially preclude the background turbulence from penetrating
within. The dispersive velocity fluctuations are also mainly determined by the
spacing, and are small deep within the canopy, where the footprint of the
Kelvin--Helmholtz-like rollers dominates. Their typical streamwise wavelength
is determined by the mixing length, which is essentially the sum of its height
above and below the canopy tips. For the present dense canopies, the former
remains roughly the same in wall-units, and the latter, which scales with the
drag length, depends linearly on the spacing. This is the result of the drag
being essentially viscous and governed by the planar layout of the canopy. In
shallow canopies, the proximity of the canopy floor inhibits the formation of
Kelvin--Helmholtz-like rollers, with essentially no signature for
height-to-spacing ratios $h/s \approx 1$, and no further inhibition beyond $h/s
\approx 6$. Very small spacings also inhibit the rollers, due to their
obstruction by the canopy elements. The obstruction decreases with increasing
spacing and the signature of the instability intensifies, even if for canopies
sparser than those studied here the instability eventually breaks down. Simple
models based on linear stability can capture some of the above effects.
