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), $u^\prime$ and the dispersive stresses (roughness-induced fluctuations of the time-averaged mean about the global mean), $\tilde{U}$. 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 ($l/\langle \eta\rangle_k$), and the wire length relative to the roughness spanwise wavelength ($l/\Lambda$). We observe that maintaining $l/\langle \eta\rangle_k$ constant while increasing $l/\Lambda$ attenuates the variance of $\tilde{U}$ and $u^\prime$ within the roughness sublayer. When fixing $l/\Lambda$, an increase in $l/\langle \eta\rangle_k$ 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.