The symmetry breaking effects of directional roughness in turbulent channel flow*

Directional surfaces form a special class of roughness which breaks the forward/backward or left/right statistical symmetry of rough-wall turbulence, i.e., their fluid dynamic effect depends on the sign of the mean flow direction. In the present study, the directional dependence of the mean flow and turbulence statistics of a surface composed of triangular bars with scalene cross-section is investigated using direct numerical simulations of turbulent channel flow at friction Reynolds number 550. This surface is inspired by ripples and dunes which are typical bedforms found in nature and can experience flows from different directions. When the bars on the surface are normal to the flow direction, the surface corresponds to ratchet-type roughness. In this case, the Hama roughness function significantly differs between the windward and the leeward orientation of the high-slope side of the scalene bars. When the bars are aligned parallel to the flow, the surface corresponds to asymmetric ridge-type roughness. Here, the roughness effect is significantly lower due to the absence of pressure drag. Nevertheless, effects of directionality remain significant, since scalene ridges induce substantial imbalances in secondary currents which can result in net spanwise flow in the channel.