Active attenuation of a trailing vortex inspired by a parabolized stability analysis*

To design a control strategy for attenuating a trailing vortex, we employ solving the parabolized stability equations (PSE) on a trailing vortex aft of a NACA0012 half-wing at an angle of attack of α=5° and a chord Reynolds number of 1000. For the initial condition of the PSE, we perform a parallel stability analysis at x/c = 0.25, finding numerous unstable modes. As the modes evolve downstream, the principal mode co-rotates with the base flow near the tip vortex region, resulting from the convective nature of the PSE. However, a subdominant mode displays non-monotonic growth rate behavior, becoming unstable as the trailing vortex develops farther downstream, counter-rotating around the tip vortex, which is indicative of a vortex instability. From these results, we hypothesize that the subdominant mode provides a pathway to excite the trailing vortex instability potentially resulting with its attenuation. Hence, we conduct DNS with trailing-edge actuation based on the the principal and subdominant mode shape to attenuate the tip vortex. Although both controlled cases achieve trailing vortex attenuation, the subdominant mode exhibits attenuatation of the trailing vortex more effectively.