Evaluation of spatial resolution effects in rough wall-bounded turbulence

This study investigates the impact of insufficient spanwise spatial resolution on the measurement accuracy of streamwise velocity fluctuations over rough walls. We use a direct numerical simulation (DNS) database of turbulent open-channel flow over three-dimensional sinusoidal roughness with varied wavelengths and roughness heights. Employing a triple decomposition, we investigate both the attenuation of the turbulent fluctuations (about the local mean), $$u^\prime$$ u ′ and the dispersive stresses (roughness-induced fluctuations of the time-averaged mean about the global mean), $${\tilde{U}}$$ U ~ . A boxcar filter on DNS data is applied to investigate the effects of spanwise spatial filtering on these quantities. Our analysis reveals the significance of two key length-scale ratios for velocity measurements over rough walls: the wire length relative to the spatially and temporally plane-averaged Kolmogorov scale at the roughness crest ( $$l/\langle \eta \rangle _k$$ l / ⟨ η ⟩ k ), and the wire length relative to the roughness spanwise wavelength ( $$l/\Lambda _y$$ l / Λ y ). We observe that maintaining $$l/\langle \eta \rangle _k$$ l / ⟨ η ⟩ k constant while increasing $$l/\Lambda _y$$ l / Λ y attenuates the variance of $${\tilde{U}}$$ U ~ and $$u^\prime$$ u ′ within the roughness sublayer. When fixing $$l/\Lambda _y$$ l / Λ y , an increase in $$l/\langle \eta \rangle _k$$ l / ⟨ η ⟩ k influences the turbulent fluctuations across all wall-normal locations. These findings highlight the necessity of considering both length scales when evaluating spanwise spatial resolution in turbulence measurements over rough walls.