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

Abstract

Following the findings by Wangsawijaya et al. ( J. Fluid Mech. , vol. 894, 2020, A7), we re-examine the turbulent boundary layers developing over surfaces with spanwise heterogeneous roughness of various roughness half-wavelengths $0.32 \leq S/\bar {\delta } \leq 3.63$ , where $S$ is the width of the roughness strips and $\bar {\delta }$ is the spanwise-averaged boundary-layer thickness. The heterogeneous cases induce counter-rotating secondary flows, and these are compared with the large-scale turbulent structures that occur naturally over the smooth wall. Both appear as meandering elongated high- and low-momentum streaks in the instantaneous flow field. Results based on the triple decomposed velocity fluctuations suggest that the secondary flows are spanwise-locked turbulent structures, with $S/\bar {\delta }$ governing the strength of the turbulent structures and the efficacy of the surface in locking the structures in place (most effective when $S/\bar {\delta } \approx 1$ ). In terms of unsteadiness, we find additional evidence from conditional averages of the fluctuating velocity fields showing that the secondary flows exhibit maximum unsteadiness (or meandering) when $S/\bar {\delta } \approx 1$ . The conditional averages of both spanwise heterogeneous and smooth-wall cases result in structures that are reminiscent of those proposed for the streak-vortex instability model for the inner cycle of wall-bounded turbulence. However, in this case these structures are larger and do not necessarily share the same formation mechanism with the inner cycle. Secondary flows and large-scale structures coexist in the limits where either $S/\bar {\delta } \gg 1$ or $S/\bar {\delta } \ll 1$ , where the secondary flows scale on $\delta$ or $S$ , respectively. When $S/\bar {\delta } \gg 1$ , the secondary flows are locked about the roughness transition, while relatively unaltered large-scale structures occur further from the transition. In the case where $S/\bar {\delta } \ll 1$ , $S$ -scaled secondary flows are confined close to the surface, coexisting with unaltered larger-scale turbulent structures that penetrate much deeper into the layer.