On the structure and dynamics of secondary flows over multicolumn roughness in channel flow

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. Motivated by this gap, we investigate multicolumn roughness configurations that serve as a regularized analogue of roughness clustering. Using large-eddy simulations, we systematically examine secondary flows across a controlled set of configurations in which cluster density and local arrangement are varied in an idealized manner, and observe that these variations give rise to distinct secondary flow polarities. Through a focused parameter study, we identify the spanwise gap between the edge-most roughness elements of adjacent columns, normalized by the channel half-height ( $s_a/H$ ), as a key geometric factor governing this polarity. In addition to analysing 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 behaviour of secondary flows.