Abstract: Under the influence of vortex instability, wingtip vortex demonstrates a certain motion of wandering in its wake. To understand the mechanism and the evolution of vortex wandering, the instability and its development of the wingtip vortex generated by a NACA0015 rectangular wing are investigated by conducting Stereo Particle Image Velocimetry (SPIV) experiments at different Reynolds numbers and angles of attack. The results show that vortex wandering exists in the wake of 1-6 chordlength and manifests anisotropy that gradually amplifies along its streamwise position. The amplitude of wandering grows faster with streamwise distance at larger angle of attack. Based on the experimental results, the amplification ratio of the spatial/temporal instability of wingtip vortex, frequency of perturbation, and their evolution along the streamwise direction are obtained through linear stability analysis. It is found that the wingtip vortex is marginally stable within Reynolds number=2.1×10⁵-3.5×10⁵ with the perturbation frequency around 3-5 Hz. The fact that wingtip vortex is more unstable at larger angle of attack, shown by larger spatial/temporal growth rate, causes faster development of disturbance, which further leads to a quicker growth of wandering amplitude along the streamwise direction. Meanwhile, the transverse velocity perturbation of the most unstable mode obtained by linear stability analysis reveals strong directionality, which shifts the vortex core and causes the wandering motion of wingtip vortex. Different from the one-dimensional random oscillation, the periodic variance of velocity perturbation forces wingtip vortex to wander in each direction with certain dominate frequency. This velocity perturbation fomented by instability is the mechanism causing vortex wandering. The amplification ratio of instability controls the growth rate of its amplitude, and the directionality and periodicity of velocity perturbation accounts for the feature of this motion.

Key words: SPIV, wingtip vortex wandering, vortex instability, linear stability analysis, perturbation mode