Direct numerical simulation of high aspect ratio spanwise-aligned bars

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.