Quantitative Features of Wingtip Vortex Wandering Based on the Linear Stability Analysis

As a result of vortex instability, wingtip vortex exhibits a behavior of wandering. In the paper, a canonical wingtip vortex generated by a NACA001.5 rectangular wing was experimentally investigated using stereoscopic particle image velocimetry and linear stability analysis in times/pace at the azimuthal wavenumber of In =-1 to quantitatively determine its instability features, as well as to analyze the vortex wandering development. Statistical analysis of the vortex core locations indicated that the vortex wandering amplitudes stayed in the range of 0.15-0.40%c within the measured conditions and wake region, where c was the chord length of the rectangular wing. Moreover, the wandering amplitude was amplified along the streamwise location, indicating that the instability of wingtip vortex was gradually enhanced. To quantitatively determine the instability features, the linear stability analysis approach was performed based on the azimuthally averaged fitted profiles in the re-centered flow field. The two continuous branches and a single eigenvalue (corresponding to the primary mode of wingtip vortex) were found in the 'frequency/ spatial spectrum and all distribute in the negative complex plane, demonstrating that wingtip vortex in our experiments is neutrally stable. In addition, the nondirnensional frequency and wavenumbers of the primary mode were nearly identical and stayed within 0.30 +/- 0.04, corresponding to a Strouhal number of St = 0.0496 +/- 0.0019 under different flow configurations. The distributions of vorticity perturbation from the primary mode are identical al difkrent streamwise locations and rotate with the phase of the primary mode periodically, explaining the nearly isotropic features of vortex wandering. The tendencies of temporal/spatial growth rates of the disturbance under different Reynolds numbers and angles of attack, as well as along streamwise locations, share the same trends with that of the wandering amplitude, implying that the vortex wandering development should depend on the instability development.