Investigation of unsteady secondary flows and large-scale turbulence in heterogeneous turbulent boundary layers

Following the findings in \cite{wangsawijaya2020}, we re-examine turbulent boundary layers developing over surfaces with spanwise heterogeneous roughness of various wavelengths $0.32 \leq S/\overline{\delta} 3.63$, where $S$ is width strips and $\overline{\delta}$ spanwise-averaged boundary-layer thickness. The cases induce counter-rotating secondary flows, these are compared to large-scale structures that occur naturally smooth wall. Both appear as meandering elongated high- low-momentum streaks instantaneous flow field. Results suggest flows might be spanwise-locked structures, $S/\overline{\delta}$ governing strength possibly efficacy surface locking place (most effective when $S/\overline{\delta} \approx 1$). Conditional averages fluctuating velocity fields both wall result strongly reminiscent streak-vortex instability model. Secondary coexist limits either \gg 1$ or \ll 1$, scale on $\delta$ $S$, respectively. When locked about transition, while relatively unaltered further from transition. In case $S$-scaled confined close surface, coexisting larger penetrate much deeper into layer.