Secondary flows induced by spanwise heterogeneous surface roughness play a crucial role in determining engineering-relevant metrics such as surface drag, convective heat transfer, and the transport of airborne scalars. While much of the existing literature has focused on idealized configurations with regularly spaced roughness elements, real-world surfaces often feature irregularities, clustering, and topographic complexity for which the secondary flow response remains poorly understood. To address this gap, we investigate multi-column roughness configurations that serve as a regularized analog of roughness clustering. Using large-eddy simulations, we systematically examine the effects of cluster density and local arrangement on secondary flows, and observe that varying the cluster density gives rise to distinct secondary flow polarities. Through a systematic parameter study, we identify the spanwise gap between the edge-most roughness elements of adjacent columns, normalized by the channel half-height, as a key geometric factor governing this polarity. In addition to analyzing the time-averaged structure, we investigate how variations in polarity affect the instantaneous dynamics of secondary flows. Here, we find that the regions of high- and low-momentum fluid created by the secondary flows alternate in a chaotic, non-periodic manner over time. Further analysis of the vertical velocity signal shows that variability in vertical momentum transport is a persistent and intrinsic feature of secondary flow dynamics. Taken together, these findings provide a comprehensive picture of how the geometric arrangement of roughness elements governs both the mean structure and temporal behavior of secondary flows.
Sathe et al. (Thu,) studied this question.
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