jats:pWe conduct minimal-channel direct numerical simulations of turbulent flow over two-dimensional rectangular bars aligned in the spanwise direction. This roughness has often been described as jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112018001507_inline1" />jats:tex-math$d$</jats:tex-math></jats:alternatives></jats:inline-formula>-type, as the roughness function jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112018001507_inline2" />jats:tex-math$\Delta U+$</jats:tex-math></jats:alternatives></jats:inline-formula> 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 jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112018001507_inline3" />jats:tex-math$k$</jats:tex-math></jats:alternatives></jats:inline-formula>-type, for which jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112018001507_inline4" />jats:tex-math$\Delta U+$</jats:tex-math></jats:alternatives></jats:inline-formula> depends on the roughness height, jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112018001507_inline5" />jats:tex-math$k$</jats:tex-math></jats:alternatives></jats:inline-formula>. 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, jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112018001507_inline6" />jats:tex-math$k$</jats:tex-math></jats:alternatives></jats:inline-formula>, of the roughness while keeping the width between roughness bars, jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112018001507_inline7" />jats:tex-math$W$</jats:tex-math></jats:alternatives></jats:inline-formula>, fixed in viscous units, results in non-jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112018001507_inline8" />jats:tex-math$k$</jats:tex-math></jats:alternatives></jats:inline-formula>-type behaviour although this does not necessarily indicate jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112018001507_inline9" />jats:tex-math$d$</jats:tex-math></jats:alternatives></jats:inline-formula>-type behaviour. Instead, for deep surfaces with jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112018001507_inline10" />jats:tex-math$k/W\gtrsim 3$</jats:tex-math></jats:alternatives></jats:inline-formula>, the roughness function appears to depend only on jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112018001507_inline11" />jats:tex-math$W$</jats:tex-math></jats:alternatives></jats:inline-formula> 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.</jats:p>