Direct numerical simulations of turbulent channel flow over ratchet roughness

The influence of the orientation of ratchet-type rough surfaces on their fluid dynamic roughness effect is investigated using direct numerical simulations of turbulent channel flow at \(Re_{\tau }=395\). The ratchet length-to-height ratio is varied from \(\ell /k=2\) to 16 for a fixed ratchet height of \(k/\delta =0.1\) where \(\delta\) is the mean channel half-height. The results show that both roughness function and mean flow and turbulence statistics strongly depend on the ratchet orientation. Existing empirical formulae, which estimate the roughness function \(\Delta U^+\) or the equivalent sand-grain roughness \(k_s\) based on surface-slope related parameters such as the effective slope or the Sigal-Danberg parameter, fail to accurately predict the differences between ratchet surfaces with high windward slopes and ratchet surfaces with high leeward slopes.