The mechanism of trailing vortex wandering has long been debated and often attributed to either wind-tunnel effects or a self-induced instability. We remove the effect of wandering from a measured velocity field by averaging and, through a triple decomposition, recover the coherent wandering motion. Based on this wandering motion, the most energetic structures are computed using the proper orthogonal decomposition (POD) and exhibit a helical mode |m| = 1 whose kinetic energy grows with downstream progression. As such, we hypothesize that a vortex instability underlies the wandering motion, and test this hypothesis by performing a spatial stability analysis of a matched Batchelor vortex, which is devoid of wind-tunnel effects. The primary stability mode is marginally stable and is nearly identical, in size and structure, to the principal POD mode. The strikingly similar structure coupled with the measured energy growth supports the proposition that the vortex wandering is the result of an instability. The cause of the wandering is the non-zero radial velocity of the |m| = 1-mode on the vortex centerline, transversely displacing the trailing vortex as observed in experiments. However, the marginal nature of the stability mode prevents any conclusion regarding the specific type of instability.

Designing effective control for complex three-dimensional flow fields proves to be nontrivial. Oftentimes, intuitive control strategies lead to suboptimal control. To navigate the control space, we utilize a linear parabolized stability analysis to guide the design of a control scheme for a trailing vortex flow field aft of a NACA0012 half-wing at an angle of attack α = 5 • and a chord-based Reynolds number Re = 1000. The stability results show that the unstable mode with the smallest growth rate (fifth wake mode) provides a pathway to excite a vortex instability, whereas the principal unstable mode remains in the wake of the wing. Inspired by this finding, we perform direct numerical simulations that excite each mode with body forces matching the shape function from the stability analysis. Relative to the baseline uncontrolled case, the principal wake mode reduces the vortex length, while the fifth wake mode further shortens the tip vortex. Analogously, the streamwise circulation of the trailing vortex is found to be significantly reduced. From these results, we conclude that a rudimentary linear stability analysis can provide key insight into the underlying physics and help engineers design more effective control.

Trailing vortices are generated in aeronautical and maritime applications and produce a variety of adverse effects that remain difficult to control. A stability analysis can direct flow control designers towards pertinent frequencies, wavelengths and locations that may lead to the excitation of instabilities, resulting in the eventual breakup of the vortex. Most models for trailing vortices, however, are far-field models, making implementation of the findings from stability analyses challenging. As such, we perform a stability analysis in the formative region where the numerically computed base flow contains both a two-dimensional wake and a tip vortex generated from a NACA0012 at a $5^{\circ }$ angle of attack and a chord-based Reynolds number of $Re_{c}=1000$. The parallel temporal and spatial analyses show that at three chord lengths downstream of the trailing edge, seven unstable modes are present: three stemming from the temporal analysis and four arising in the spatial analysis. The three temporal instabilities are analogues to three unstable modes in the spatial analysis, with the wake instability dominating in both analyses. The helical mode localized to the vortex co-rotates with the base flow, which is converse with the counter-rotating $m=-1$ instabilities of a Batchelor vortex model, which may be a result of the formative nature of the base-flow vortex. The fourth spatial mode is localized to the tip vortex region. The continuous part of the spectrum contains oscillatory and wavepacket solutions prompting the utilization of a wavepacket analysis to analyse the flow field and group velocity. The structure and details of the full bi-global spectrum will help navigate the design space of effective control strategies to hasten decay of persistent wingtip vortices.