Wall turbulence perturbed by a bump with organized small-scale roughness: Coherent structure dynamics

Abstract

Coherent structures over two distinct, organized wall perturbations - a transverse sinusoidal bump with and without small-scale longitudinal grooves - are studied using direct numerical simulations. Large-scale spanwise rollers (SRs) form via shear layer rollup past the bump peak, enveloping a large separation bubble (SB) for both a smooth wall (SW) and a grooved wall (GW). In a GW, small-scale alternatingly spinning jets emanating from the crests' corners merge with the shear layer, altering the SRs compared with SRs in a SW. The underlying coherence of the highly turbulent SRs is educed via phase-locked ensemble averaging. Coherent vorticity contours of SRs are ellipses tilted downward, hence causing co-gradient Reynolds stress. The limited streamwise length of SB precludes SR tumbling, unlike in a free shear layer. The coherent field reveals minibubbles attached to the bump's downstream wall with circulation opposite to that of the SB - they are larger, stronger and more numerous in GW than in SW - reducing skin friction. Compared with SW, the swirling jets in GW increase coherent production while decreasing incoherent production. Additionally, the jets push the SRs to travel faster and farther before reattachment. The SB experiences two different modes of oscillation due to high-frequency advection of the shear layer SR and low-frequency breathing of the SB, where the former dominates in GW and the latter in SW. Negative production is caused by counter-rotating vortex dipoles inducing flow ejections (for both SW and GW) and single vortices penetrating the grooves - both occurring in the region of flow acceleration.