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 \le Stc \le 0.56) and phase offset (90 deg \le \phi \le 70 deg) at Re = 8000. The changes in \phi and Stc reflect a unique route of transition in mechanisms that govern the origin of spanwise instabilities and growth of secondary wake structures. At lower Stc, 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 (TEV ) 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 Stc, provides a crucial reasoning for this newly identified progression.