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 Formula Presented, where Formula Presented is the width of the roughness strips and Formula Presented 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 Formula Presented governing the strength of the turbulent structures and the efficacy of the surface in locking the structures in place (most effective when Formula Presented). 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 Formula Presented. 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 Formula Presented or Formula Presented, where the secondary flows scale on Formula Presented or Formula Presented, respectively. When Formula Presented, the secondary flows are locked about the roughness transition, while relatively unaltered large-scale structures occur further from the transition. In the case where Formula Presented, Formula Presented-scaled secondary flows are confined close to the surface, coexisting with unaltered larger-scale turbulent structures that penetrate much deeper into the layer.