Three-dimensional instabilities in the wake of a flapping wing at low Reynolds number

We present a stability analysis of a plunging and pitching wing of infinite aspect ratio at low Reynolds number. Four cases are considered by varying the mean pitch angle and the phase shift between pitching and plunging. Each case is studied by performing two dimensional DNS and Floquet stability analysis. The four cases considered display different wake structures resulting in different mean aerodynamic forces. Two cases produce thrust and lift, one case only thrust (with symmetric plunging and pitching) and the remaining case mainly lift (with the highest mean pitch angle). In addition, the latter case displays a period doubling phenomenon, and it is found to be linearly unstable for long wavelengths, with an instability mode that resembles that of mode A found in the wake of cylinders. Other cases, although being linearly stable, present a convective instability at smaller wavelengths. Finally, the unstable case has been studied with a fully 3D DNS to evaluate the effect of the three-dimensionality on the forces. The resulting flow structure is consistent with the linear stability analysis in the near wake. Further downstream nonlinearities lead to a fully 3D wake. Despite this, the aerodynamic forces on the 3D wing are very similar to those obtained in the 2D simulation.