Secondary-current-mediated reorganisation of near-wall VLSMs over spanwise heterogeneous roughness

This study investigates turbulent open-channel flow over spanwise-heterogeneous roughness strips composed of fixed spherical elements, with emphasis on the interaction between roughness-induced secondary currents (SCs) and very-large-scale motions (VLSMs). Direct numerical simulations are performed at friction Reynolds numbers italic Re Subscript tau Baseline almost equals 492 Re τ ≈ 492 Re 492 – 538 538 538, with an additional homogeneous-roughness reference case at italic Re Subscript tau Baseline almost equals 639 Re τ ≈ 639 Re 639. The roughness strips generate persistent, geometry-locked SCs that organise the mean flow into alternating high- and low-momentum pathways, and substantially enhance form-induced stresses relative to both the smooth-wall and homogeneous-roughness references. Rather than uniformly amplifying large-scale motions, the roughness induces a sign-dependent reorganisation of VLSMs: negative-velocity VLSMs are preferentially concentrated above the roughness strips, whereas positive-velocity VLSMs occur more frequently in the inter-strip regions. Conditional correlations further show that, although VLSMs are preferentially identified in the outer region, their strongest statistical footprint remains closely connected to near-wall regions influenced by SC-driven momentum redistribution. Spectral analyses reveal a dynamically connected two-scale pathway, consisting of an outer-scale organisational footprint at lamda Subscript z Baseline divided by h equals upper O left parenthesis 1 right parenthesis λ z / h = O (1) ᵦ/h=O (1) and a smaller near-wall active scale at lamda Subscript z Baseline divided by h almost equals 0. 3 λ z / h ≈ 0. 3 ᵦ/h 0. 3. These results show that roughness-induced SCs govern both the kinematic organisation and the energy-redistribution pathways of VLSMs in spanwise-heterogeneous open-channel flow.