On the association of kinematics, spanwise instability and growth of secondary vortex structures in the wake of oscillating foils

Three-dimensional wake of an oscillating foil with combined heaving and pitching motion is numerically evaluated at a range of chord-based Strouhal number (0.32 <= St(c) <= 0.56) and phase offset (90 degrees <= phi <= 270 degrees) at Re= 8000. The changes in phi and St(c) reflect a unique route of transition in mechanisms that govern the origin of spanwise instabilities and growth of secondary wake structures. At lower St(c), heave-dominated kinematics demonstrates a strong secondary leading edge vortex (LEV) as the source of growing spanwise instability on the primary LEV, followed by an outflux of streamwise vorticity filaments from the secondary LEV. With increasing heave domination, the origin of stronger spanwise instability is governed by a counter-rotating trailing edge vortex and LEV that leads to growth of streamwise secondary structures. A decreasing heave domination ultimately coincides with an absence of strong LEV undulations and secondary structures. The consistent transition routes are represented on a phase-space map, where a progression of spanwise instability and growth of secondary structures becomes evident within regimes of decreased heave domination. The increasing strength of circulation for the primary LEV, with increasing St(c), provides a crucial reasoning for this newly identified progression.