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

Abstract

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

Currently under review for publication in J. Fluid Mech

References in corpus (1)

• Streak instability in turbulent channel flow: the seeding mechanism of large-scale motions

Cited by in corpus (1)

• Linear models of strip-type roughness