Abstract: Compared with isolated wingtip vortices generated by the wings, vortex pairs or even more complex multi-vortices formed after the installation of winglets exhibit more intricate instability characteristics. In this paper, the instability characteristics of wingtip vortices generated by the M6 wings with split winglets under different Reynolds numbers and angles of attack, as well as along the 16 times chord length wake region, are experimentally investigated using the Stereoscopic Particle Image Velocimetry (SPIV) technology and bi-global Linear Stability Analysis (LSA) method. The experimental results show that wingtip vortices contain one upper primary vortex (Vortex-U) and one lower primary vortex (Vortex-L), which are respectively generated by the upper winglet branch and lower winglet branch. These two vortices form an approximately equal strength co-rotating vortex pair, intertwining with each other at the angular velocity of 20 rad/s. The statistical analysis of instantaneous vortex core positions of Vortex-U and Vortex-L show that the wandering amplitudes of the wingtip vortices increase gradually along the streamwise locations and with the increasing Reynolds numbers, while increase first and then decrease with the increasing angles of attack. Moreover, the instability curves of the most unstable modes of Vortex-U/Vortex-L, namely, Model-P/Mode-S, obtained from the temporal bi-global LSA share the same trends with those of wandering amplitudes, indicating that the wandering of wingtip vortices results from their inherent instability characteristics. By increasing the disturbance wavenumber in the flow direction, the tangential wavenumber in Mode-P increases gradually, while in Mode-S, the radial wavenumber increases gradually. Under different flow conditions, the tangential wavenumber of Mode-P is 5-6, the disturbance wavenumber is distributed in [2.75, 5], and the growth rates are always larger than those of Mode-S. Furthermore, the perturbation mode corresponding to the most unstable growth rate covers the whole vortex core region of Vortex-U, suggesting the remarkable prospect of this large tangential wavenumber mode for the wingtip vortex control, as well as indicating that the development of vortex instability can be manipulated by increasing the vortex number.

Key words: SPIV, wingtip vortex, vortex instability, bi-global linear stability analysis, perturbation mode