The effect of foil proximity on shear-layer instability around oscillating foils

Three-dimensional vortex dynamics around two pitching foils arranged in side-by-side (parallel) configurations is numerically examined at a range of separation (gap) distances ($0.5c \leqslant y^* \leqslant 1.5c$). In-phase ($\phi =0$) and out-of-phase ($\phi ={\rm \pi}$) motions are considered for Strouhal numbers of $0.3$ and $0.5$ at a Reynolds number of $8000$. In this work, we show that the foil proximity effect, defined as the influence of one foil on the flow characteristics around the other, induces a spanwise instability in the braids of trailing-edge vortices (TEVs) during their roll-up. This is a newly identified instability that manifests itself in the form of secondary vortical structures with opposite circulation compared with the TEVs formed on the foils, which leads to the formation of double necking on the braids of the TEVs. We provide quantitative evidence linking the formation of these secondary structures to the braid instability. The first neck merges with the TEV, while the second neck detaches from the braid region and moves downstream independently. As the foil proximity effect intensifies (spacing between the foils decreases), secondary vortical structures, as well as the necks, become more prominent, leading to the emergence of three-dimensional wake features. Lastly, the influence of kinematics of the foils on three-dimensionality of the wake is investigated. At higher Strouhal numbers, broader regions of high strain are developed near the trailing edge, associated with the detachment of stronger structures from the braids of TEVs. The characterized instability demonstrates consistent properties for in-phase and out-of-phase motions, albeit with specific differences in dynamics of leading-edge vortices.