  We conduct minimal-channel direct numerical simulations of turbulent flow
over two-dimensional rectangular bars aligned in the spanwise direction. This
roughness has been often described as $d$-type, as the roughness function
$\Delta U^+$ is thought to depend only on the outer-layer length scale (pipe
diameter, channel half height or boundary layer thickness). This is in contrast
to conventional engineering rough surfaces, named $k$-type, for which $\Delta
U^+$ depends on the roughness height, $k$. The minimal-span rough-wall channel
is used to circumvent the high cost of simulating high Reynolds number flows,
enabling a range of bars with varying aspect ratios to be investigated. The
present results show that increasing the trough-to-crest height ($k$) of the
roughness while keeping the width between roughness bars, $\mathcal{W}$, fixed
in viscous units, results in non-$k$-type behaviour although this does not
necessarily indicate $d$-type behaviour. Instead, for deep surfaces with
$k/\mathcal{W}\gtrsim 3$, the roughness function appears to depend only on
$\mathcal{W}$ in viscous units. In these situations, the flow no longer has any
information about how deep the roughness is and instead can only `see' the
width of the fluid gap between the bars.
