Evaluation of spatial resolution effects in rough wall-bounded turbulence

Abstract

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′ and the dispersive stresses (roughness-induced fluctuations of the time-averaged mean about the global mean), 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/⟨η⟩k), and the wire length relative to the roughness spanwise wavelength (l/Λy). We observe that maintaining l/⟨η⟩k constant while increasing l/Λy attenuates the variance of U~ and u′ within the roughness sublayer. When fixing l/Λy, an increase in 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.